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EVALUATION OF TIME TO RESPONSE IN SYMPTOM
MANAGEMENT INTERVENTIONS FOR PAIN AND
FATIGUE EXPERIENCED BY CANCER PATIENTS

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EVALUATION OF TIME TO RESPONSE IN SYMPTOM MANAGEMENT
INTERVENTIONS FOR PAIN AND FATIGUE EXPERIENCED BY CANCER
PATIENTS
By

Sangchoon Jeon

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Epidemiology

2009

ABSTRACT
EVALUATION OF TIME TO RESPONSE IN SYMPTOM MANAGEMENT
INTERVENTIONS FOR PAIN AND FATIGUE EXPERIENCED BY CANCER
PATIENTS
By

Sangchoon Jeon

This research was performed to understand how physical and
psychological characteristics of cancer patients impact symptom response to
management interventions for pain and fatigue. In addition, this research used an
approach to define clinically meaningful reductions in pain and fatigue and
identified important predictors of symptom response using. several survival
analysis approaches.

Six hundred and one cancer patients who were undergoing Chemo-
therapy were enrolled in one of two clinical trials (termed A and B) that tested
interventions for managing cancer-related symptoms over an 8 week period. To
define “symptom response” as a clinically meaningful change in symptoms,
severity categories of mild score (31), moderate score (2-4), and severe score (5-
10) were established based on the reported interference with the patient's daily
life. Time to response was measured by counting the number of days from onset
of symptoms to a symptom response, defined as a transition from severe to

moderate, severe to mild, or moderate to mild severity.

Several survival analysis methods were implemented to identify important
predictors of symptom response including age, comorbidity, and depression after
adjusting for gender, site of cancer, physical function, and trial type (A or B). The
survival analyses were performed under different assumptions regarding the
proportional hazards assumption and the type of censoring. First, by assuming
proportional hazards, the log-rank, Wilcoxon, and Cox proportional hazard model
were used. Second, several alternative methods were implemented that do not
require the proportional hazards assumption, including the Lin & Wang’s test,
Cox model with weighted estimations, and Rahbar’s method. The impact of
interval censoring was assessed by generating Accelerated Failure Time (AFT)
models, and finally the effect of the correlation between pain and fatigue were
explored using a marginal Cox regression model.

All final models found a significant comorbidity effect for pain and fatigue.
Low comorbidity was significantly associated with shorter time-to-response for
pain and fatigue in all applied models. There was no significant effect of age after
adjusting for comorbidity in the Cox proportional hazard model or the marginal
Cox regression model. The AFT model found that younger age and less
depressed patients had shorter time-to-response for pain after adjusting for
comorbidity as well as a priori confounders, including gender, site of cancer,
physical function, and trial type (A or B). None of other survival models found
significant association between depression and time-to-response for pain and

fatigue.

ACKNOWLEDGMENTS

I wish to thank members of my guidance committee, Mathew Reeves,
Ph.D., Charles Given, Ph.D., M. Hossein Rahbar, Ph.D., and Hwan Chung, Ph.D.
who provided invaluable direction, intellectual support, and encouragement to
complete this work. My thesis advisor, Dr. Mathew Reeves, has spent
considerable time guiding me in the preparation of this thesis, improving my
epidemiological concepts, and completing this process. I would like to express
my appreciation to Dr. Charles and Barbara Given for sharing their valuable data
and encouragement. I also appreciate to the valuable advices and intellectual
supports from Dr. Alla Sikorskii. I deeply thank my wife, Hyesuk, and two
daughters, Ashley and Claire, for their patience and support during this work.
This research was financially supported by the Family Home Care
Study (principal investigator: Dr. Barbara Given) and the Automated Telephone
Monitoring Symptom Management Study (principal investigator: Dr. Charles
Given). The Family Home Care Study (R01 CA79280) and the Automated
Telephone Monitoring Symptom Management Study (RO1 CA30724) were
funded by the National Cancer Institute. The Institutional Review Board (IRB) of
Michigan State University approved the Family Home Care Study (lRB # 03-247)
and the Automated Telephone Monitoring Symptom Management (lRB # 03-242
for). Yale University (lRB # 0810004338) has approved this secondary analysis

using collected data from these two studies.

TABLE OF CONTENTS

LIST OF FIGURES ............................................................................................ viii
OVERVIEW .......................................................................................................... 1
CHAPTER 1 BACKGROUND OF CANCER-RELATED PAIN AND FATIGUE ...7
1.1 Burden of Pain and Fatigue among Cancer Patients ................................ 7
1.2 Factors Related to Severity of Pain and Fatigue ..................................... 14
CHAPTER 2 BACKGROUNDS FOR MEASURING SYMPTOM RESPONSE...21
2.1 Conventional Measurement: Problems and Suggestions ....................... 22
2. 2 Developing Cut-points and Testing Longitudinal Consistency of Cut-
points ............................................................................................................... 25
2. 3 Defining Response of Pain and Fatigue .................................................. 29

CHAPTER 3 SURVIVAL ANALYSIS FOR TIME TO SYMPTOM RESPONSE .31
3.1 Survival Analysis for Assessing Time to Symptom Response ................ 32
3.2 The log-rank, Wilcoxon Test, and the Cox Proportional Hazard Model...39
3.3 Methods of Survival Analysis without the Proportional Hazard Assumption

48
3.4 Methods of Survival Analysis for Interval Censored Data ....................... 57
3.5 Methods of Survival Analysis When Outcomes Are Not Independent ..... 60
CHAPTER 4 METHODS ..................................................................................... 65
4.1 Clinical Intervention Trials for Symptom Management ............................ 65
4.2 Measures ................................................................................................ 75
4.3 Data Analysis for Identifying Factors Associated Time to Pain and Fatigue
Response ........................................................................................................ 78
CHAPTER 5 RESULTS ...................................................................................... 91
5.1 Demographic and clinical characteristics of the trials .............................. 91
5.2 Meaningful Reductions in Pain and Fatigue among Cancer Patients ..... 93
5.3 Evaluation of Time-to-Response for Pain and Fatigue Symptoms ........ 104
CHAPTER 6 DISCUSSION .............................................................................. 129
6.1 Considering Potential Bias from Combining Data Sets ........................... 129
6.2 Evaluating Clinically Meaningful Change on Symptom Severity .............. 131
6.3 Applying Survival Analysis in the Assessments of Symptom .................. 135
Appendix A The Symptom Assessment at Intervention Contact (Example
for Pain) ........................................................................................................... 142
Appendix B SAS macros ................................................................................ 146

Appendix C The MD Anderson Symptom Inventory (MDASI) .................... 156

Appendix D The Center for Epidemiologic Studies - Depression (CES-D)
scale ................................................................................................................. 159

Appendix E The Short Form - 36 (SF-36) Physical Functioning Sub Scale

.......................................................................................................................... 160
Appendix F The Assessment for Comorbid Conditions .............................. 162
BIBLOGRAPHY ............................................................................................... 164

vi

LIST OF TABLES

Table 1 Factor loadings for the four interference items for each symptom at

contact 1 ............................................................................................................. 80
Table 2 Characteristics of patients in two intervention trials ............................... 92
Table 3 Cut-points with five largest chi-square (Wald test) statistics .................. 94

Table 4 Cut-points for severity categories, number of cases reporting each
symptom, unadjusted mean interference scores, duration before first contact, and
physical function at baseline interview ................................................................ 97

Table 5 Estimated means and standards errors of summed interference score
across 6 intervention contacts by severity level of pain and fatigue* ................ 100

Table 6 Median time to response and unadjusted tests for time-to-response for
pain and fatigue by the log-rank, Wilcoxon, and Cox proportional model ......... 113

Table 7 Final models of time-to-response in pain and fatigue in the Cox
proportional hazard model ................................................................................ 1 15

Table 8 Unadjusted tests for time-to-response in pain and fatigue by the Lin &

Wang's test, the WCM, and the Rahbar's method ............................................ 118
Table 9 Final multivariable models of time-to-response in pain and fatigue in the

AFT model with interval censoring .................................................................... 120
Table 10 Final model of time-to-response in the marginal Cox model .............. 122

Table 11 Recurrence of pain and fatigue after responding to first episode of pain
or fatigue ........................................................................................................... 127

Vii

LIST OF FIGURES

Figure 1 Monitoring symptoms during intervention period .................................. 34
Figure 2 An example of median and mean time-to-symptom response ............. 38
Figure 3 An example of restricted mean time-to-response ................................. 38

Figure 4 Hazard functions and survival functions under the proportional hazard
assumption ......................................................................................................... 43

Figure 5 Example of survival functions when the proportional hazard assumption
is not satisfied ..................................................................................................... 46

Figure 6 Flowchart of patient accrual and retention in the Trial A and B ............ 69

Figure 7 Time line of screening, baseline interview, intervention contacts, and
post interview ...................................................................................................... 71

Figure 8 Distribution of summed interference score (0~40) among mild,
moderate, and severe level of pain and fatigue .................................................. 95

Figure 9 Distributions of individual difference in summed interference scores (0-
40) within the same level of severity for pain and fatigue .................................. 103

Figure 10 Estimated survival function of time to response of pain and fatigue.106
Figure 11 Estimated survival functions of time-to-response in pain by age ...... 110

Figure 12 Estimated survival functions of time-to-response in pain by comorbidity
.......................................................................................................................... 1 10

Figure 13 Estimated survival functions of time-to-response in pain by depression
.......................................................................................................................... 1 1 1

Figure 14 Estimated survival functions of time-to-response in fatigue by age ...... 111

Figure 15 Estimated survival functions of time-to-response in fatigue by
comorbidity ....................................................................................................... 1 12

Figure 16 Estimated survival functions of time-to-response in fatigue by
depression ........................................................................................................ 1 1 2

Figure 17 Cumulative hazard plot of the Cox-Snell residuals for three final
models .............................................................................................................. 124

viii

OVERVIEW

Cancer patients may suffer from multiple symptoms that originate from the
disease itself, the side effects of treatment, or comorbid conditions. Successful
symptom management for cancer patients can help maintain therapeutically
effective chemotherapy, physical and social functioning, and reduce emotional
distress of patients (1-5). To maintain effective management of symptoms, it is
important to understand how physical and emotional conditions of cancer
patients are related to improvement of symptoms in response to interventions.
Pain and fatigue are most prevalent and difficult to resolve among cancer
patients. Severe pain and fatigue cause delay or premature termination of
important therapies or treatments, impair physical function, and cause significant
distress (6, 7). This delay or early termination of treatments may directly affect
survival of cancer patients (8).

This study aims to make two contributions to the research program that
evaluates symptom management for cancer patients. First, understanding the
influence of patient socio-demographic, physical, and emotional conditions on
resolution of symptoms will extend our knowledge of symptom management
interventions by identifying which cancer patients will likely benefit more or less
and sooner or later from symptom management. Second, by defining a clinical
meaningful reduction in each symptom through analysis of time to symptom
response, this study will help define a strategy for evaluating the effectiveness of
interventions for symptom management in cancer patients experiencing pain and

fatigue.

This study will address the following specific research questions:

1)

2)

3)

4)

Can clinically meaningful Changes in pain and fatigue symptoms
be measured using the four dimensions of interference
(emotions, enjoyment of life, relations with others, and general
daily activities) to define clinically meaningful cut-points that
separate levels of symptom severity (mild, moderate, and
severe)?

Using the clinically meaningful severity cut-points, which factors
are predictors of time-to-response in pain and fatigue among
cancer patients when using survival analysis techniques (the log-
rank test, the Wilcoxon test, and the Cox proportional hazard
model) that require the assumption of proportional hazards?

Do the findings based on survival analysis techniques
appropriate for the proportional hazards assumption, hold when
using alternative survival techniques (the Lin & Wang’s test, the
Rahbar’s test, and the Cox model with weighted estimation) that
do not require the proportional hazard assumption?

Do the findings based on survival analysis techniques that are
appropriate for right censoring (the Cox proportional hazard
model and the Cox model with weighted estimation) hold when
using the Accelerated Failure Time model that accounts for

interval censoring?

5) Do the findings from the separate models of pain and fatigue
(the Cox proportional hazard model, the Cox model with
weighted estimation, and the Accelerated Failure Time model)
hold when using the marginal Cox model that accounts for the
correlation between the two symptoms (pain and fatigue)?

Data used in this research are derived from 2 randomized clinical trials of
symptom management. Cancer patients who were undergoing chemotherapy
received symptom management interventions during 6 scheduled intervention
contacts over an 8 week period. Chapter 1 is a comprehensive literature review
that describes what is known about the burden of pain and fatigue among cancer
patients and reviews factors related to severity of these symptoms and their
management. Patient factors include; gender, age, stage of cancer, site of
cancer, the number of comorbid conditions, and depressive symptoms. These
patient factors are important because they may be associated with response of
pain and/or fatigue when interventions are delivered. These factors could
therefore influence the effectiveness of interventions and result in prolonging or
shortening time to response of pain and fatigue.

Chapter 2 describes the methodological issues in assessing symptom
Change and addresses the difficulty of measuring a clinically meaningful
symptom change with conventional methods. Supportive evidence for using
interference based cut-points of symptom severity is described. Previous studies
have suggested methods for developing and testing cut-points to establish

3’ fl

symptom severity categories: such as “mild , moderate”, and “severe”. Symptom

response to interventions for managing pain and fatigue are defined using
transitions among these categories, and used to measure time to symptom
response.

In Chapter 3, several alternative survival analysis methods are introduced
based on their underlying assumptions. The log-rank (Mantel and Haenszel
1959), Wilcoxon (Breslow 1974), and the Cox proportional hazard model (Cox
1972) are commonly used for survival analysis. When survival functions do not
cross one another the hazard functions are proportional, and these methods are
valid. To address how to evaluate time to response of pain and fatigue when the
proportional hazard assumption is not satisfied in survival analysis, we applied 3
different approaches a nonparametric test for equality of survival function (Lin 8
Wang 2004), the Cox model with weighted estimation (Schemper 1992), and a
nonparametric test for equality of survival mean (Rahbar 2007). To answer if the
findings from these survival analysis methods that account for right censoring
can be confirmed using a survival analysis method with interval censoring, the
Accelerated Failure Time (AFT) model is tested. To answer if the identified
factors still have impact on time to response of both pain and fatigue after
accounting for the correlation between two symptoms within a patient, the
marginal Cox model (Wei 1989) was used.

Chapter 4 describes the data and the methods used for the analyses in
this study. Data from 601 cancer patients were collected from the two
intervention trials for symptom management (the Family Home Care for Cancer

project (Trial A) and the Automated Telephone Monitoring for Symptom

Management project (Trail B)). Patients rated their symptoms and multiple
interference items on a 0 to 10 scale at 6 scheduled contacts. They received
symptom management intervention when their symptom severity was rated at a 4
or higher. The optimal cut-points of severity were developed based on the sum of
four interference items1 at the first intervention contact. Severity categories2 from
the identified cut-points were examined to see if they consistently differentiated
across the sum of the four interference items. Once longitudinal differentiation
was confirmed, time to symptom response 3 was used as a measure of
meaningful symptom change in response to interventions. The number of days
from onset contact4 to response contact was recorded as time to response, and
time from onset to last contact without a response was considered the censoring
time. To identify important covariates associated with time to response for pain
and fatigue, several survival analysis methods introduced in Chapter 3 were
employed and their underlying assumptions explicated.

In Chapter 5, results including the development of cut-points and
assessing time to response are described. Based on the identified cut-points,
three severity categories were defined: “mild” (sore of 1), “moderate” (score of 2
through 4), and “severe” (score of 5 or greater). These categories significantly
differentiated the summed interference scores at each of the contacts.

Comorbidity was consistently identified as an important independent covariate

 

1 The 4 interference items include emotions, enjoyment of life, relations with others, and general
daily activities.

2 Severity categories include mild, moderate, and severe level of severity.

3 Symptom response includes transition from severe to moderate, severe to mild, and moderate
to mild categories of symptom severity.

‘ Onset contact is an intervention contact when patient initially reported a severity of 4 or higher
for pain and fatigue.

associated with time to response for pain and fatigue by the different survival
analysis methods used. Patients who had less than 3 comorbid conditions had
shorter time to response for pain and fatigue compared to those who had less
than 3 comorbid conditions. The effects of age and depressive symptom were
not significant in three multivariable models (the Cox proportional hazard model,
the accelerated failure time model, and the marginal Cox model).

In Chapter 6, the following points are summarized: 1) potential biases
associated with combining data sets from two trials 2) evaluation of clinically
meaningful changes in the severity of each symptom, 3) use of survival analysis
to assess time-to-response among symptoms and conclude with an assessment
of the conditions under which each survival technique would be appropriate for
use.

This study demonstrates how to assess symptom changes in response to
intervention in terms of measurement and analysis of symptom data leading to
defining conditions under which time-to-response can be assessed and
alternative approaches for evaluating time-to-response given different
distributional properties of the responses. The developed measure of symptom
response was reviewed as an evaluative measure based on a guideline for
measure in clinical medicine (134). Using different survival analysis methods
provided consistent statistical evidence for the effect of comorbidity on time-to-
response for pain and fatigue. Comorbid conditions are considerable

impediments to reducing pain and fatigue severity through interventions.

CHAPTER 1 BACKGROUND OF CANCER-RELATED PAIN AND FATIGUE

In this chapter, Section 1.1 will describe briefly the experience of pain and
fatigue among cancer patients and its impact on the quality of patient’s daily lives.
The association between cancer-related pain and fatigue during treatments will
also be discussed in this section. In Section 1.2, I will review potential factors
associated with pain and fatigue among cancer patients, in order to evaluate if
these factors are also related to the reduction of pain and fatigue in response to
symptom management.

A literature review was conducted to investigate the burden of pain and
fatigue among cancer patients and the characteristics associated with severity of
pain and fatigue. Relevant literature was found in the MEDLINE database using
the National of Library of Medicine PubMed with the following keywords;
“cancer,” “pain,” “fatigue,” and ”chemotherapy.” Combinations of each keyword
were also used. The review articles were selected by reviewing abstracts; articles

were restricted to the English language and published between 1960 and 2008.

1.1 Burden of Pain and Fatigue among Cancer Patients

This section is an overview of pain and fatigue in terms of the definitions,
prevalence, pathologies, correlation with one another and associations with other
cancer related symptoms. Prevalence describes how commonly cancer patients
suffer from pain and fatigue at any given point in time; and is the preferred term

to describe burden. Incidence measures the burden of symptoms over a specific

time window, however, only prevalence data are presented in the reviewed

studies.

1.1 .1 Cancer-Related Pain

The pain from treatment is greatly short term and its severity varies
relative to the disease itself. According to a practical guideline from the National
Comprehensive Cancer Network (NCCN) (9), pain can be classified into
nociceptive and neuropathic pain according to the predominant mechanisms of
pain pathophysiology. Nociceptive pain, which results from “injury to somatic and
visceral structures and from activating nociceptors,” is described as sharp, well
localized, throbbing, and pressure-like. This type of pain usually occurs after
surgical procedures or from bone metastasis. Neuropathic pain, which results
from “injury to the peripheral or central nervous system,” is described as burning,
sharp, or shooting. It often occurs as an adverse effect of chemotherapy or
radiation therapy (9).

Pain is one of most prevalent symptoms among cancer patients, being
reported between 36% and 75% of patients. Patients with advanced cancer
experience more severe pain (10). In a meta-analysis of fifty-tvvo studies (11),
Everdingen and colleagues estimated the pooled prevalence of pain among
cancer patients for four different subgroups; patients after curative treatment
(33%, 95% confidence interval (CI): 21% to 46%), patients under anticancer
treatment (59%, 95% Cl: 44% to 73%), patients with advanced/metastatic/

terminal disease (64%, 95%Cl: 58% to 69%), and patients at all disease stages

(53%, 95% Cl: 43% to 63%). In a 1991 study of a large population of cancer
patients from seven hospices in Europe, the United States, and Australia, the
prevalence of pain was 60% in breast cancer, 52% in lung cancer, 64% in
colorectal cancer, and approximately 80% in gynecological cancers (12).
According to one cancer pain study (13), 70% of cancer patients with advanced
neoplasm reported pain, while 50% of patients at all stages of cancer reported
pain. Pain is defined as “a sensory and emotional experience associated with
actual or potential tissue damage or described in terms of such damage.” (14)
Cancer-related pain can occur due to the disease or the treatment. When tumor
cells stimulate nerves or cause organ dysfunction patients feel severe pain that
can be relieved by removing the tumor cells. Also, cancer patients often suffer
from pain as a result of surgery, radiation, or chemotherapy.

The National Cancer Institute (NCI) recommends that the management of
pain should be flexible and individualized according to the stage of the disease,
personal preferences, and responses to pain interventions. Patient self-report is
the standard assessment method for pain. Severity of pain is usually rated using
a 0 to 10 point scale; but a categorical or pictorial scale, that uses pictures of
faces for rating pain, is also available (9). Cancer—related pain is managed by
providing psychological supports, specific educational materials, as well as pain-
relieving drugs, such as nonsteroidal anti-inflammatory drugs (NSAIDS), opioids,
and combination of analgesics. The NCCN practice guidelines suggest that
management should be distinguished by three categories (mild, moderate, and

severe) of pain intensity (9). It has been shown that cancer related pain has a

significant association with depression and anxiety. However, the causality
among these symptoms has been debated. Cancer patients with pain reported
severe depression, anxiety, and/or other psychosomatic symptoms in several
studies (15-17). Chronic pain has been considered an important factor leading to
severe depression in cancer patients (18, 19). Depression and/or anxiety from
concern about the disease may worsen pain, and cancer patients with serious

depression and/or anxiety tend to report more pain (15).

1.1 .2 Cancer-Related Fatigue

The National Comprehensive Cancer Network (NCCN) describes cancer-
related fatigue as “a persistent, subjective, sense of tiredness related to cancer
or cancer treatment that interferes with usual functioning.” Although cancer—
related fatigue has been reported as the most important symptom that impairs a
patient’s quality of life and daily activities, it has received less attention in
management compared with other symptoms such as pain, nausea, or vomiting
(20). Fatigue is the most prevalent symptom among cancer patients - a recent
report from the NCCN highlights that 70% to 100% of cancer patients experience
fatigue (21). Most cancer patients suffer from fatigue while receiving cytotoxic
chemotherapy, radiation therapy, bone marrow transplantation, or treatment with
biological response modifiers5 (22). Cancer patients experience fatigue resulting
from the disease itself, cancer treatment, psychosocial burdens, and comorbid

conditions: this fatigue worsens during the course of chemotherapy and persists

 

5 Biological response modifier is a type of cancer treatments that enhances body’s immune
system.

10

for months after completing treatment (23). In a study conducted by Greene et al,
82% of breast cancer patients reported fatigue after the first course of
Chemotherapy (24). Among cancer patients receiving a course of chemotherapy
and radiotherapy, 61% reported clinical fatigue (25). In other studies, 89% and
90% of cancer patients reported some degree of fatigue during their
chemotherapy (26, 27).

Cancer-related fatigue is that most people generally suffer from in normal
life, and it is not relieved by rest or sleep (28). Like pain, fatigue is also subjective
and patient self-reports is the standard method for assessment. Additionally, the
medical history, physical examination, laboratory data, and description of patient
behavior by family members are all important sources of information to gauge the
burden of fatigue, especially for children (22). The NCCN practice guideline
recommends that fatigue be managed by an interdisciplinary institutional
committee, comprised of representatives from medicine, nursing, social work,
physical therapy, and nutrition (22).

Despite the high prevalence of fatigue among cancer patients, the
biochemical, physiological, and behavioral mechanisms of this complex symptom
are poorly understood, making it difficult to identify factors that are associated
with fatigue. However, several risk factors associated with cancer-related fatigue
have been proposed. Hwang and colleagues proposed a multidimensional
conceptual model with Situational, biological, physiological, and psychological
dimensions that predict cancer-related fatigue (29). The situational dimension

represents demographic information including age, gender, stage of cancer,

11

active cancer treatment, and caregiver status. The biological dimension can be
described by serum chemistry profiles. There is evidence that anemia, which is a
common side effect of chemotherapy or radiation therapy in cancer patients, is a
major factor causing fatigue (30, 31). The impact of anemia on fatigue may be
different depending on onset time, patient age, and comorbidity. Psychological
factors, such as depression and anxiety, may contribute to the development of
chronic fatigue before and after chemotherapy among patients with solid tumors
(32). Distress after a diagnosis of cancer can be caused by the initial fatigue,
and other side effects of upset, like insomnia which may also increase in patients
undergoing chemotherapy. In a study of cancer patients with a history of
chemotherapy, fatigue lasted the longest relative to other side effects and had

the greatest impact on activities of daily living (5).

1.1.3 Correlations between Pain and Fatigue

Most cancer patients suffer from a number of symptoms which may impair
function, therefore it is important to evaluate the impact of multiple symptoms on
patient outcomes (33). Pain and fatigue are often observed along with other
common symptoms, such as insomnia and depression in cancer patients (34-40).
It has been observed that pain, fatigue, sleep disturbance, emotional distress,
and poor appetite generally occur together (38). Significant negative effects of
the symptom cluster of pain, fatigue and insomnia on physical function was found
to be independent of the type of cancer, treatment, stage of cancer, or comorbid

conditions (39, 40). Dodd et al. defined a “symptom cluster,” as a group of

12

symptoms that are related to each other. They proposed four groups in cancer
patients based on severity of pain and fatigue (i.e. group 1: high fatigue and low
pain, group 2: low pain and low fatigue, group 3: low fatigue and high pain, group
4: high pain and high fatigue) (33).

Many studies have shown that pain and fatigue are significantly
associated with other common symptoms, treatments, and other factors. For
example, in a study with breast cancer patients, pain and fatigue are related to
one another and their presence is associated with depression, insomnia, and
menopausal symptoms such as hot flashes and night sweats (41). Kaasa et al.
found, based on five studies, that pain and fatigue are more common in the more
severity affected populations (i.e. palliative care and those with bone metastasis)
(42). While chemotherapy alone or in combination with radiation has a significant
impact on the level of fatigue, pain is more closely related to the timing of
treatment or to the advanced nature of the disease (43). However, the
assessment of cancer-related symptoms remains complex due to the multiple
symptoms, the multiple etiologies, varying severity, duration, and, co-occurrence

of symptoms.

1.1.4 Impact of Pain and Fatigue on Function and Quality of Life

Patients who are diagnosed with solid tumors and are undergoing
chemotherapy treatment experience multiple symptoms which are a serious
burden for patients as well as for their oncologists and primary care providers (1).

These symptoms negatively impact dimensions of the quality of life, such as

13

physical functioning and depression, and are related to increased morbidity and
health care costs (5, 44—46). It has been reported that the cancer-related
symptoms have a positive association with negative emotions (47). Gift et al. (48)
and Cooley (49) found that fatigue and pain are the most distressing symptoms
for lung cancer patients. Pain, fatigue, and depression are recognized as
prominent contributors in the suffering experienced by many cancer patients; and
clinical studies have increasingly focused on obtaining a better understanding of

these symptoms, as well as the development of new, more effective treatments.

1.2 Factors Related to Severity of Pain and Fatigue

Effective symptom management is defined as clinical interventions
designed to reduce symptoms through a combination of drugs and other clinical
treatments. Effective symptom management over time is a key to maintaining
therapeutically effective dosing of chemotherapy agents, physical and social
functioning, and to reducing the emotional distress in patients. To increase the
effectiveness of symptom management, it may be important to identify the health
conditions or patient characteristics which impact the management of symptoms.
Identifying factors that predict Change in these symptoms may also contribute to
the design of effective symptom management studies. By evaluating the effects
of interventions designed to manage pain and fatigue, we will be better able to
identify those that actually help to resolve or to relieve these symptoms. Because

pain and fatigue are key symptoms that may indicate the presence of other

14

symptoms (33), the factors associated with the reduction of pain and fatigue may
be important in predicting change in the overall symptom burden during the
period of active symptom management. In this section, potential factors that
influence reduction of pain and fatigue in response to symptom management will

be reviewed.

Gender and Age It is often recommended that the gender and age of
patients should be considered in symptom management (50-53). Since socio-
demographic factors are often associated with disease or other health outcomes,
it may be difficult to interpret their role in symptom response.

It has been argued that female patients report pain and fatigue differently
than male patients. In a recent study, younger patients and female patients had
significantly higher fatigue levels (54). They suspected that higher severity in
younger patients was due to underreporting by patients who were over 80 years
of age. Sechzer and colleagues addressed inappropriate and questionable
generalization of findings in cancer research due to sampling bias toward male
patients. In response, Miaskowski suggested that this bias exists in symptom
management research, and she reviewed articles related to difference in pain
and fatigue according to gender among cancer patients (50). In her review of two
published studies (44, 51) and her own unpublished studies (50), no gender
difference was observed in the prevalence and severity of pain. Research
performed by Cleeland and colleagues (44) found that female patients were more

likely to be untreated for their cancer-related pain compared to male patients. In

15

reviews of gender differences in cancer-related fatigue, three studies that
evaluated outpatients who were undergoing chemotherapy or radiation therapy
(54—56) found that female patients reported higher severity and prevalence of
fatigue. However, these gender differences in severity and prevalence could be
explained by other factors associated with gender, such as site of cancer, and
communication with caregiver. In previous research with 110 cancer patients
receiving a 10 contact cognitive behavioral intervention (57), male patients were
more likely to report necessary more time to resolve their fatigue compared with
female patients in unadjusted analyses. However, resolution for gender was not
significantly associated with time to resolve pain and fatigue after adjusting for
site of cancer. More lung cancer in male patients may be responsible for poor
results concerning fatigue.

Age is another factor potentially associated with pain in terms of its
prevalence, severity, and duration. It has been observed that elderly patients are
more likely to have high risk of comorbid conditions and late stage cancer (53, 58,
59). Elderly patients tend to attribute their pain as a normal part of aging and
avoid reporting pain in order not to disrupt their cancer treatment (60). If elder
patients rate the severity of their pain less than they actually feel, their pain might
not be sufficiently managed by nurses or care providers. Because anxiety is
recognized as a risk factor of fatigue (32), the association between age and
anxiety is an important to account for fact, when evaluating the response of
fatigue in different age groups. In a longitudinal study conducted with hospitalized

cancer patients in Tokyo, younger patients were more distressed and reported

16

more anxiety than elderly patients (61 ). It is possible that relatively severe anxiety
in younger patients decreases the effectiveness of fatigue management among
younger patients. Also based on these findings, elderly patients were probably
less likely to have intervention for pain and fatigue because they under-reported

their symptoms and have higher comorbid conditions.

Cancer Site and Stage Since pain and fatigue can result from treatment
of the disease, site and stage of cancer are important clinical factors likely to be
associated with response to these symptoms. Site and stage of cancer may also
influence the clinical strategy both for treating disease and managing symptoms.
Paters and colleagues observed that patients with ovarian and lung cancer
experience greater fatigue compared to those with breast and other cancers (54).
In a longitudinal study of elderly cancer patients aged 65 or older (43), patients
with lung cancer were significantly more likely to have pain and fatigue compared
with those with breast cancer. Since the site of cancer is usually associated with
several factors, including gender, age, and stage of cancer, it may be difficult to
separate the effect of cancer site on the response time of fatigue from these
other factors.

Significantly longer time in pain resolution was observed in patients with
late stage of cancer compared with those with early stage of cancer (57).
Advanced stages of cancers were more likely to be related to the occurrence of
pain in two studies, but a significant association between the stage of cancer and

the prevalence of fatigue was not observed (43, 62). In a survey of cancer-

17

related pain with the Brief Pain Inventory (BPI), 86% of patients with advanced
cancer believed that their pain was caused by cancer itself (63). When patients
believe their pain is caused by cancer, there is greater interference with their

daily activities (10).

Burden of Comorbidity and Other Symptoms Comorbidity is usually
measured by counting the number of different chronic conditions. Comorbid
conditions are related to older age and chronic fatigue (64). It was found that
both age and comorbidity strongly influence patient clinical decision-making (52,
65, 66); older patients with severe comorbid conditions are less likely to have
intensive cancer treatments (53). According to the NCCN practice guideline;
patient comorbidities are known to be associated with fatigue and they
recommend more attention should be paid to chronic conditions in conjunction
with the treatment of cancer-related fatigue (21 ). In a cohort study among cancer
patients who were older than 64 years of age, high comorbidity, late stage of
cancer, and lung cancer were associated with high risk of pain and fatigue (43).

It is observed consistently that high comorbidity is significantly associated
with high prevalence and longer time to resolve fatigue among cancer patients
undergoing chemotherapy (57). Based on these findings, more comorbid
conditions result in more severe fatigue and may impede treatment of symptoms.
That is, comorbidity is a risk factor for severe fatigue, as well as a modifier of the

effect for symptom management.

18

Since cancer patients usually experience multiple symptoms after
beginning chemotherapy, more symptoms could impede the effect of any single
intervention. Multiple severe symptoms can also produce adverse psychological
outcomes, including anxiety and depression which influence adherence to
treatment (67-69). Co-occurrence of multiple severe symptoms may result in
patients receiving a number of interventions not only for pain and fatigue, but
also for other symptoms. For cancer patients who have poor health-related
outcomes, a large number of interventions may reduce the effect on each of the

symptoms.

Depressive Symptoms A strong interrelationship among pain, fatigue,
and depression has been found (69—73). In a meta-analysis, DiMatteo and
colleagues found that depressive patients are less likely to comply with medical
treatment recommendations (67). They propose several explanations for the
effect of depression on treatment. First, depression often causes a high level of
hopelessness that treatment is not worthwhile. Second, depression may result in
social isolation from individuals who could provide emotional support or
assistance; and third, impairment of' cognitive function could impair memory
which can lead to less compliance among depressed patients.

In general, a measure of fatigue in cancer patients correlates positively
with a measure of depression (74). However, Visser and colleagues suggest that
there is no evidence of a causal relationship between fatigue and depression and

that the same underlying pathology may be responsible for co-occurrence of

19

these two symptom (71). They observed the consistent correlation between
fatigue measured by the Multidimensional Fatigue Inventory (MFl-20) and the
mood component of the Center for Epidemiologic Studies of the Depression
Scale (CES-D) at the start of treatment, 2 weeks after completion of radiotherapy,
and 9 months later. Therefore, depressive symptoms represented by the CES-D

may be a good predictor of change of fatigue during the intervention period.

20

CHAPTER 2 BACKGROUNDS FOR MEASURING SYMPTOM RESPONSE

To examine if the factors described in Chapter 1 have an impact on
symptom response to treatment, it is important to define the change in pain and
fatigue that represents “clinically meaningful change.” The conventional
Conceptualization and operationalization of symptom responses have been
conducted in an unsatisfactory manner. The question is, how can optimal cut-
points for severity be determined based upon different magnitudes of
interference with patient’s daily life. Also, there is the question of whether the
established cut-points can reliably and consistently differentiate interference
scores over time.

Section 2.1 describes the important measurement issues in assessing
pain and fatigue for cancer patients and addresses the difficulty of measuring
clinically meaningful change in symptoms with conventional methods. Section 2.2
describes evidence to support the use of interference based cut-points linking
differences in severity scores to levels of interference. The previously suggested
methods for developing and testing cut-points to establish categories of symptom
severity are also described in Section 2.2. A newly proposed method reduces the
conventional ordinal symptom scale of 0 to 10 into a more clinically practical
classification of three categories: “mild,” moderate,” and “severe." In Section 2.3
Response to interventions will be defined using transitions among these

categories.

21

2.1 Conventional Measurement: Problems and Suggestions

By definition, symptoms are derived from the patient’s perspectives (38).
Patients are often asked to rate the severity of a symptom on a numerical scale.
Since the American Pain Society used the 11-point scale (from 0=not present to
10=worst possible) for measuring pain (75), it has been extended to measure the
severity of other cancer-related symptoms by the NCCN (21). The Brief Pain
Inventory (BPI) (76) and Brief Fatigue Inventory (BFI) (4) are widely used
instruments that assess sensory (severity) and reactive (interference) dimensions
of pain and fatigue, respectively. These instruments define four aspects of
severity (worst, least, average, and pain/fatigue right now) along with how greatly
pain or fatigue interferes with general activities, mood, walking, normal work,
relations with others, enjoyment of life, and Sleep (Appendix A).

Once the numerical scales are established, the next step is taken to
measure the changes in pain and fatigue. The ultimate purpose in measuring the
severity of symptoms is to evaluate the relationship between the reduction of
symptoms and the degree to which that has an impact on the patient’s quality of
life. More specifically, both practitioners and researchers are interested in the
question of how the interventions prescribed by care providers ameliorate
symptoms, and contribute to maintaining and improving patient’s quality of life.
For that purpose, it is necessary to have a valid and reliable method of

measuring and interpreting changes in symptoms.

22

Clinically important changes in the severity of symptoms have been
evaluated in several ways based on either relative difference or absolute
differences (i.e. percent reduction in severity). For instance, Farrar et al. (77)
proposed that an relative improvement of more than 30% on the pain intensity
scale is a clinically important change among cancer patients. They observed pain
intensity for patients who completed clinical trials of pregabalins. The patients
rated their pain on a 0 to 10 point scale at baseline and at the end of the clinical
trial. After completing the clinical trial they also evaluated changes in pain
intensity on a seven-point scale, includes “Very Much Improved”, “Much
Improved”, “Minimally Improved”, “No Change”, “Minimally Worse”, “Much
Worse”, and “Very Much Worse.” Patients who had more than 30% reduction of
pain intensity also evaluated their change in symptoms as “Very Much Improved”
or “Much Improved.” In other studies, a absolute reduction of approximately two
points on a scale of 0 to 10 for pain intensity represented a Clinically important
difference (“Very Much Improved” and “Much Improved” ) (78). Cepeda et al. (79)
performed a study with postsurgical patients to assess meaningful reduction of
pain intensity. Patients rated pain intensity on a 0 to 10 point scale and 4-Likert
scale (None, Mild, Moderate, and Severe) at baseline and every 10 minutes
during administration of analgesic. They also reported the degree improvement in
pain on a 5-point Likert scale. For patients with moderate pain, 35% and 45%
reduction of pain intensity represented “Much Improved” and “Very Much

Improved,” respectively. These ordinal scales are relatively easy to be interpreted

 

6 Pregabalin is an anticonvulsant drug for neuropathic pain

23

by clinicians compared with a 0 to 10 scale. Therefore, in this study, I assessed
cut-points to categorize the severity of symptoms measured on a 0 to 10 scale.

However, the use of the 0 to 10 scale may be not sufficient to evaluate the
impact of pain and fatigue on interferences. For example, Serlin (80) found that ~
the absolute difference in the numerical rating on severity may not always bring
about equal levels of differences in distress or functional impairments. Put
differently, 20% reduction of severity of pain on a scale of 0 to 10 may not always
represent the same percent of improvement in physicalfunction or a reduction of
interference scores. Although the validity and reliability of using a scale of 0 to 10
for measuring symptoms has been confirmed to some degree (81), one serious
problem has yet to be addressed: patients tend to interpret differently the lower,
middle, and higher sections of an 11 point scale (80, 82). For example, from a
clinical perspective, the same thirty percent reduction, for instance, 9 to 6 and 3
to 2, may not be equivalent and thus Should not be interpreted to have the same
meaning.

In response, another approach has been developed to represent a
clinically meaningful reduction by using a 3 level categorization scheme: mild,
moderate, and severe levels of symptoms. Serlin et al. (80) proposed a threefold
classification (mild, moderate, and severe) to describe pain severity, based on a
set of interference items. They identified several advantages of the threefold
categorization. First, patients are likely to use the lower, middle, and higher
sections of the 0 to 10 point scale differently. Second, the threefold classification

would be more useful to both clinicians and investigators than a finer

24

classification with more than three categories. That is, it could facilitate efficient
communication between a patient and clinician. For instance, mild pain would not
seriously distract patients. Moderate pain could be considered the level of pain
that is hard to be ignored by patients. When patients feel their pain needs clinical
attention, pain could be consider being severe. Third, it could reflect the fact that
a non-linear relationship between severity and interference is better captured
with a threefold classification. The non-linear association between severity of
pain and fatigue and interference has been demonstrated (34, 76, 83-85). In
some cancer pain and fatigue studies, the increased rates of interference were
not equal across the 0 to 10 severity scale and relatively small increases were
observed at two points of severity (4, 80). Therefore, the three levels of pain
severity would be more informative than the finer quantitative gradation such as
the 0 to 10 scale. Also the threefold classification has been often used for
assessments of cancer-related pain by the National Comprehensive Cancer
Network (NCCN), and the Agency for Health Care Policy and Research (AHCPR)
(9, 21, 86). These findings are extended to assess the effect of intervention on
fatigue in this study. Significant changes in relationship between interference and
severity of fatigue were observed for the two cut-points that define the threefold

classification (4).

2.2 Developing Cut-points and Testing Longitudinal Consistency of Cut-

points

25

Patients can express the intensity of their pain. The difficulty is that
intensity is an abstract concept that is likely to differ by patient. Cleeland et. al.
found that the variance of patient self-report can be effectively captured by two
dimensions (“sensory” and “reactive”) in pain intensity (76). The sensory
dimension refers to the severity of pain, while the reactive dimension refers to the
interference with the patient’s function and quality of life caused by pain.
Cleeland defines (87) the measure of symptom burden as “a summative indicator
of the severity of the symptoms that are most associated with a disease or
treatment, and a summary of the patient’s perception of the impact of these
symptoms on daily living.” He suggests that both symptom severity (sensory) and
symptom interferences (reactive) constitute symptom burden. A variety of
instruments are designed to assess both the severity of symptoms and their
interference with daily life (4, 74, 88, 89).

Serlin suggests that severity is a primary factor in assessing a symptom,
because it is more crucial to providing successful clinical management (80).
Interference with daily life also is an important factor in understanding how much
patients suffer from a symptom, because serious interference contributes to high
distress in cancer patients (90). Although high correlations between severity and
interference have been observed in several studies (4, 80, 85, 91), severity on 0
to 10 point scale does not always lead to greater interference. For example,
patients who report a severity of 3 may not experience more interference

compared with those who report a severity of 2 or 1. Therefore, categorization of

26

severity based on interference would be a more informative measure since it
describes both symptom severity (sensory) and interference of daily life (reactive).

Anchoring individual patient reports of pain and fatigue severity to
differences in interference using cut-points of mild, moderate, and severe
categories has been shown to be appropriating for both research and clinical
practice (4, 80, 92-94). It is suggested that these established categories, based
on interference scores, provide more stable and more meaningful clinical
interpretation in measuring the impact of behavioral interventions for
management of pain and fatigue than simply calculating the percent of change
using the conventional 0 to 10 scales (77, 78, 95).

There is no agreed-upon definition of the optimal cut-points that separates
mild from moderate and moderate from severe pain or fatigue. Rather, different
researchers define different cut-points. For instance, Serlin et al. (80) performed
an analysis of variance (ANOVA) to find the optimal cut-points of symptom
severity based on interferences in daily life. They defined the following range of
each category using a 1 to 10 scale: 1—4 for mild pain, 5—6 for moderate pain,
and 7—10 for severe pain. The other two studies found the cut-points of severity
based on seven (general activity, mood, walking ability, sleep, enjoyment of life,
normal work, and relations with others) and six interference items (general
activity, mood, walking ability, normal work, relations with others, and enjoyment
of life) using multivariate analysis of variance (MANOVA). In a study with
oncology outpatients (Breast (52%), Prostate (11%), Lung (11%), and Other

(26%)) who experienced pain from bone metastasis, Paul et al. (92) reported that

27

5 and 8 were optimal cut-points for moderate and severe pain, respectively. In
the other study with oncology inpatients (Leukemia (33%), Lymphoma (43%),
Breast (10%), Gastrointestinal (6%), Gynecologic (2%), Genitourinary (1%), and
other (5%)) who experienced fatigue, Mendoza et al. (4) suggested that the cut-
points for severity of fatigue, based on six interference items in the BFI, are 1—3
for mild fatigue, 4—6 for moderate fatigue, and 7-10 for severe fatigue in cancer
patients. These studies had fairly consistent cut-points (4 or 5 for moderate, and
7 or 8 for severe) using the ANOVA or MANOVA. However, it is a question that
the used interference scores had a normal distribution. If they did not have
normal distribution, the result form ANOVA and MANOVA may not be valid.

Our research seeks to determine if, while receiving help with managing
their pain and fatigue over time, patients continue to differentiate among levels of
interference according to whether their symptom is categorized as mild,
moderate, or severe. Patient can report their symptom differently by different
measurements. It is known as shift in response which is a major threat to this
argument. As patients implement strategies that lower the severity of pain or
fatigue, they may “recalibrate” their definitions of severity, interference, or both.
For example, patients may report declines in severity but continue to associate
these new levels of severity with the same or increased interference.
Retrospective assessments are likely to be adjusted by current patient
perceptions. In this research patient responses to interventions are followed,
compared with their reports of interference at each subsequent observation at

which symptoms are rated as severe, moderate or mild. I, then, determine if

28

interference scores consistently differentiate between severe and moderate and
moderate and mild levels of severity of pain and fatigue. If the integrity of the
interference-based severity cut-points are preserved over time, then they can be

used to measure patient’s responses to these intervention strategies (96).

2.3 Defining Response of Pain and Fatigue

This study aims to identify factors, associated with reduction of pain and
fatigue, in response to symptom-management interventions. In order to pursue
this aim, it is important to define “response of symptom” as a meaningful
reduction of symptom, using a reliable measurement of levels of intensity in
symptoms. That is, a symptom response during the intervention would represent
how successfully pain and fatigue were reduced by treatment. The symptom
response can be effectively reflected by a dichotomous variable: “response” or
“non-response”. After the threefold categories of mild, moderate, and severe
were developed to represent levels of severity in symptoms, their longitudinal
consistency in differentiating interference scores were examined. If established
severity categories differentiate the interference consistently over time, then the
meaningful symptom reduction can be captured by transitioning from moderate
or severe to a lower category level.

The underlying hypothesis therefore is that when pain and fatigue move
from a higher category of severity to a lower category (e.g. Severe to moderate

or mild, moderate to mild) they will exhibit substantial reductions in interference

29

scores. I believe that this would represent a clinically important improvement that
oncologists would View as being meaningful. Reduction from moderate to mild
may be less clinically important however. For instance, reduction in fatigue from
3 (moderate) to 1 (mild) may not be considered important by oncologists since
moderate fatigue would not be considered serious enough to alter the treatment
dosing or schedule. However, from a quality of life perspective, a reduction of 3
to 1 in the severity of fatigue corresponds to a decrease in the limitations of daily
activities caused by fatigue and results in substantial improvement in physical
function (21). Therefore, these three shifts (‘severe to moderate’, ‘severe to mild’,
and ‘moderate to mild’) can be interpreted as clinically meaningful reductions in
pain and fatigue, and will be called “symptom response” in this study. Non-
response includes no shift (‘moderate to moderate’ and ‘severe to severe’) and

transition from moderate to severe.

30

CHAPTER 3 SURVIVAL ANALYSIS FOR TIME TO SYMPTOM RESPONSE

Having defined and addressed the relevant measurement issues in
Chapter 2, this chapter discusses statistical and technical issues regarding the
use of survival analyses for analyzing time-to-response for pain and fatigue. To
obtain valid results for testing time-to-response of pain and fatigue, it is important
to understand the basic concepts of time-to-event (response) data and the
underiying assumptions for survival analysis methods. In this chapter, I highlight
the analytical problems associated with assessment of time-to-response of pain
and fatigue. These problems include; 1) the proportional hazard assumption, 2)
interval censoring, and 3) not accounting for the existence of correlations
between two symptom outcomes.

Section 3.1 describes the basic concepts and terminology needed in time-
to-event (response) data including censoring, survival function, and hazard rate.
Commonly used survival analysis methods including the log-rank, Wilcoxon, and
Cox proportional hazard methods are introduced and their underlying
assumptions are discussed in section 3.2. When the underlying assumptions of
these methods are not met, then, section 3.3 introduces three alternative
methods including a nonparametric test for survival functions, a modified Cox
model for a non-proportional hazard model, and a survival analysis method
based on mean time-to-response. Section 3.4 introduces survival models for
using interval censored data. Finally, a marginal Cox model accounting for

correlation between pain and fatigue will be introduced in Section 3.5.

31

3.1 Survival Analysis for Assessing Time to Symptom Response

The concepts of censored data, survival functions, and hazard rates will

be described in this section.

3.1.1 Censoring

The dichotomized outcome “symptom response” can be defined as the
symptom reduction below a pre-specified level over a defined follow-up period,
when exposed to an intervention. Cancer patients who participated in the trials
analyzed in this thesis had their symptoms monitored and received intervention
strategies at 6 contact periods (Case A in Figure 1). However, individual patients
had different time periods over which their pain or fatigue was monitored. These
different monitoring time intervals could have occurred due to the following two
reasons. First, a patient did not complete the scheduled contacts due to lost to
follow-up (for any number of reasons including death, becoming too sick, being
busy, and not being interested) as shown by Case B in Figure 1. Second, the
onset of symptoms was different for each patient. For example, patients could
report their first pain 4 weeks after starting the 8 week study, as shown by Case
C in Figure 1. This patient who reported pain at 4 week could be monitored only
for 4 additional weeks. In contrast, a patient experiencing pain at the first
intervention contact could be monitored for the full 8 weeks.

For these reasons, symptom response is not observed or the exact time-

to-response is not known for some individuals. These types of data, including in-

32

completed observations, are called censored data and there are three possible
censoring schemes; right-censoring, interval-censoring, and left-censoring.

Right-censoring is the most common censoring type. Due to loss to follow-
up or death, monitoring of symptoms is often terminated before patients
experience symptom response. The term of “right-censoring” implies that
symptom response occurs some time after the termination of monitoring patients
or the lost to follow-up. Additionally, even if patients complete the follow-up, there
are some patients who do not experience a response to a symptom until the end
of the study. Any termination of monitoring a symptom before a response occurs
is called right-censoring. Time from onset to termination of monitoring a symptom
or lost to follow-up is becomes the right-censored time for symptom response.
Therefore, right-censored time is always shorter than actual time to response.

Interval-censoring is another form of censoring. This term reflects that
symptom response occurs between two monitoring times but the exact time is
unknown. If a symptom is monitored once every week, actual symptom response
may occur within the interval between the two contacts. Since the exact time to
symptom response is unobservable in this situation, it can be represented by an
interval of time. For Interval-censored time, actual time to response is between
the two interval-censored times.

The third type of censoring is left-censoring, which is encountered when
symptom response already occurred before monitoring symptom starts. If actual

symptom response occurs before the first monitoring contact the time from onset

33

to the first monitoring symptom is left-censored time. The left-censoring was not
observed in the data analyzed in this thesis.

With right-censored data, several survival analysis methods have been
developed to estimate survival curves or assess the importance of covariates.
However, few survival analysis methods and software packages are available for

interval-censored and left-censored data.

Figure 1 Monitoring symptoms during intervention period

 

 

 

 

 

 

 

 

Sympto Symptom
m Onset Response
D M 't ' 'od I I
Case A onI onng pen
' Symptom ' 7
Symptom Lost to follow-up Response I
Case B Onset Monitoring period (Unobserve i
a: I I I J’ . t
I I s t
s t Vmp °m
. ymp om - Response
Onset . . .
I Monitoring period (U serve
Case C I E——>l‘
l l :
1st contact 6th contact

 

 

 

3.1.2 Survival Function and Hazard Rate
The following is a brief overview of the concepts of the survival function
and hazard rate for time to pain and fatigue response. The time to pain and

fatigue response is a primary outcome of this research. It can be interpreted as

34

the duration of pain and fatigue within the intervention period. This time to the
clinical event (e.g. symptom response) can be summarized by the survival

function (S(t)) and hazard rate (h(t) ). The survival function (S(t)) can be defined
as a probability that a patient’s pain or fatigue does not respond during the length
of time (in days), t , from onset, namely S(t) = p[T>t]. We assume that the
distribution of survival time has a density function, f . Then the survival function

can be written as

S(t)=1—Ef(u)du (3.1)

Greater values of survival function reflect longer time to pain and fatigue

response during the follow-up period. In this study, the survival function,S(t), of

time to pain and fatigue response can be estimated by the empirical survival
function given by

Number of patients with response time > t

S t =
( ) Number of patients with symptom at time t

(3.2)

 

Kaplan and Meier (1958) introduced a nonparametric technique for
estimating survival function. The product-limit estimator, which is called the
Kaplan-Meier estimator, uses both censored and non-censored observations

to estimate survival function. Let "t be the number of patients with no

response to pain or fatigue at contact I and dj be the number of patients

having symptom response at contact t, then we can obtain the Kaplan-Meier

estimate of the survival function by

35

k n.-d.

‘ _ J J
SKM (t) _ H n . 9 (3'3)
J=1 J
for t <tSt where t <t <---<t <1 are the

<k)‘ (km (1) (2) (k)<‘(k+1)<”' in)

numbers of days from onset.

The hazard rate (h(t)) represents the risk of event occurring during a

specific time point. According to the Dictionary of Epidemiology published by the
International Epidemiological Association (IEA), the hazard rate is defined as “a
measure of the risk of occurrence of an event at a pOint in time t.” (97) In this
application, the hazard rate is interpreted as a probability that a symptom
responds during time interval t, the conditional on the patient having symptoms
at the start of time interval t. Therefore, it can be expressed by the conditional

probability of response time T divided by time interval 6t as follows;

 

p(tsr<t+azjr>t)}_flt_) (34)
6t _ -

h(t)= 11m { 50),

6t—>0

where f and Sare the probability distribution of symptom response time

and survival function, respectively. Opposite to the survival function, the higher
hazard rate represents a positive outcome for symptom response. That is, a

greater hazard rate can be interpreted as a shorter time to symptom response.
The cumulative hazard, H (t): £h(u)du, which integrates the hazard rate from

onset time to a certain'follow-up time t, is widely used for analyzing time to event
data. It can be obtained from the survival function using the following

equation; H (t) = — Iog(S(t)) .

36

The median and mean of time-to-event are also important statistics to
evaluate time to symptom response. The median time to response is a time point
when the survival function is 0.5. That is, the time point when half of the patients
had responded to their symptoms. For an example, survival function shown in
Figure 2, the median time to response is 14 days. The mean time to response is
the expectation time that individuals experience response in their symptoms, and

is obtained by calculating the area under the survival function, given by

,u = £0 S(u)du. In Figure 2, the mean time to response is 24.6 days. To obtain the

mean time to response, all censoring cases need to occur before the latest
symptom response is observed. However, when there are individuals whose
symptom did not respond throughout the whole duration of the follow-up, the

mean of time-to-response is not available. In this situation, the restricted mean

can be alternatively used, given by p: £S(u)du where r>0 is an observed

maximum time to response (98-101). Figure 3 describes the situation that about
20% of patients did not report symptom response until after 50 days, the reported
maximum time to response. The restricted mean of time to response is an area
under the survival function until 50 days. Therefore, the restricted mean (22.3
days) from Figure 3 is smaller than the mean of time to response (24.6 days)

from Figure 3.

37

Figure 2 An example of median and mean time-to-symptom response

 

_\
O

   

9
01

Median time-to-response:
14 days

  

Survival function of time-to-response

.0
o

 

0 1 0 20 30 40 50 60 70
Time-to-response in days

Figure 3 An example of restricted mean time-to-response

 

_l
0

Survival function of time-to-response
O
01

 

 

 

0 10 20 30 40 50 60 70
Time-to-response in days

38

3.2 The log-rank, Wilcoxon Test, and the Cox Proportional Hazard Model

To assess the association between a covariate and the time to pain and
fatigue response, the probabilities of having pain and fatigue without a response
until a certain time (survival function) are compared across different levels of a
covariate. That is, the null hypothesis of these tests is equality of survival

functions among multiple groups, HO:Sl(t)=S2(t)=---=Sk(t) for all t. This is

also equivalent to testing the equality of the hazard rates. Parametric methods
which assume survival function of a specific form are convenient to estimate the
survival function or mean time to response. However, sometimes it is hard to
know whether a survival time has a specific form such as exponential, lognonnal,
or Weibull. Frequently, nonparametric tests, which compare the empirical survival
functions, are used to examine differences in time to event between covariate

groups.

3.2.1 Nonparametric Tests for Equality of Survival Functions

One nonparametric method was developed by Mantel and Haenszel
(102). They suggested the log-rank test to compare survival functions by deriving
ranks of time to response in two groups. Suppose that there are ranked times to

<t

(2)

<...<tv

(’0

response, t , across two groups and that there are dlj and

(1)
d2]. individual patients who respond to their pain or fatigue in each of the groups

for j: 1,2,...,k. Suppose further that n1]. and n2]. individuals with no responses

39

to pain or fatigue in each of the groups just before time t . . Then there are

(1)

nj=n1j+n2j patients who report their symptom just before time ((1.) and

d j =d j +d2j patients who respond to the symptom at time t . If two groups

I U)
have the same survival function, then the number of patients who are responders

to their symptom in one group, dlj’ have a hypergeometric distribution. Therefore,

the expectation and variance of d1]. is given by e1.=n1jdj/n. and

J J

_ _ 2 _ . _ . .
Vlj “"1j"2jdj(" j d j)/Inj(nj 1)} respectIvely. The log rank test statistIc can

be obtained by summing the differences between the number of observed
symptom responses and the expected number of symptom responses in one

group, given by

°=1
’ ~ 22(1). (3.5)

 

Log-rank Test Statistic =

having a chi-square distribution with one degree of freedom.
Breslow developed the Wilcoxon test for comparing survival functions. In
the Wilcoxon test, the difference between the number of observed responses and

expected number of responses, dlj —e1j, is weighted by the number of patients

with symptoms that do not respond just before time, t . Therefore, this test is

(1‘)

more sensitive to the magnitude of differences in survival functions at earlier

40

times, compared with the log-rank test. That is, the difference in survival function
between groups at one week from onset is more important than that at 4 weeks

from onset. The Wilcoxon test statistic is given by

k
2 ”j‘dlj "“11"

—1
Wilcoxon Test Statistic: J k ~ 12(1), (3.6)
znzvl.
j=1 J J

 

where n j is the total number of individuals with no responses to pain or

fatigue just before time t . . This also has a chi-square distribution with one

(J)
degree of freedom.

Although the log-rank and Wilcoxon tests do not require assumptions
regarding the distribution of the survival function, these tests are appropriate only
when the estimated survival functions in the two groups do not cross. The log-
rank test is more suitable when the proportional hazard assumption is satisfied. I

will discuss in more detail the proportional hazard assumption in the next section.

3.2.2 The Cox Proportional Hazard Model

The nonparametric tests mentioned above are suitable only for univariate
analysis. That is, they are available to compare time-to-response for two or more
groups classified according to a single covariate. However, it is also important to
know the simultaneous impact of patient’s demographic variables or health
related variables on time-to-symptom response. In order to assess associations

between multiple variables and time-to-symptom response, a multivariable

41

statistical model needs to be used. One widely used statistical model for survival
data is the Cox proportional hazard model, developed by Cox (103). This model
does not require any specific distribution of time to response, but it requires an
assumption of proportional hazard between groups over time. Therefore, it is
called a semi-parametric model.

To employ the Cox proportional hazard model, it is important to

understand the “Proportional hazard assumption”. Let hi(t) be the hazard rate of

symptom response at time t for patients in group i for 1': 1,2,.... If the hazard
rate of symptom response for patients in group i is proportional to the hazard for

individuals in a reference group, then it can be expressed by hi(’)=¢ih0(’)
fori=1,2,..., where ¢i is a constant for group i and h0(t) is a hazard rate of

reference group (often called a baseline hazard). Using a lognorrnal distribution

of survival time, two hazard functions, hl(t) and h2(t), are shown in Figure 4,
where ¢1>¢2. In this figure, two hazard and survival functions proportionally

increase over time and therefore their graphs do not cross.
Under the proportional hazard assumption, the ratio of the hazards for

symptom response between group i and reference group, (251., can be set as a

function of covariates x. x. The Cox proportional hazard model with

11’ 12,...,xip .
multiple covariates can be written as
h (t)

i

h0(t)

 

= ¢i = cxp(fl1xi1 + ’62xi2 +W'Bpxip) . (3.7)

42

Figure 4 Hazard functions and survival functions under the proportional

hazard assumption

 

 

0.3"
_ ¢1>¢2
g 0.2_
E kl (t) = ¢1h0(t)
e
g h0(t) fl
I
h2(t) — ¢2h0(t)

 

 

 

 

 

I I l

I I T
0 1 0 20 30 40 50
Time-to-response in days

I

 

 

 

 

1.01““.\
x.
"x
0.8- '_ \x
'5 o 6— \\ S (t)
*6 \
S S '\
“r; 0-4- I")
.2. '\,
\
S x,
“I 0.2- \_
0.0- ......:‘.-N-'IT.T:::: ------------
I I i I l I I i I l I
0 10 2o 30 4o 50

Time-to-response in days

43

Suppose t t

(1) <

<--- < t( k) are kindividual time to response among

(2)
n(2 k) cancer patients. Parameters are estimated from the partial likelihood

function as follows (103);

 

 

 

. «5.-
k eXP( 'fl)
L : n 1 x! ' 1 (3'8)
If E RUG» ,

where R(t(i)) is a set of individuals having no symptom response at time, t, and
5,. is an indicator of censoring (=1 if responded, 0 If lost to follow-up). To account

for tied time to response, the approximate partial likelihood function is suggested

by Breslow (104) as follows;

 

 

 

l ”i
k eXP(S‘fl)
L = l , 3.9
Eli Z eXP(x'J-fl) I I )
l] E R0 (1'))

where di is the number of patients with time to response, t(i) and Si is the sum
of covariates for all. patients. The partial likelihood function is obtained by

counting patient’s symptoms with response and non-response at each ranked
response time (103). Therefore, the partial likelihood function depends only on
the ranked time to symptom response.

The proportional hazard assumption can be tested by adding an

interaction term between a covariate and a function of time, f (t) =Iog(t/ t'), in

the equation 3.7, where t’ is median time to response (105). For instance, if a

44

covariate, xi, does not have a proportional hazard across time t, the ratio of
hazard rates becomes h(t)/ h0(t)=exp(,6xi+yxi f (t)) , where x1. f (t) is the

interaction term between a covariate and a function of time which represents a
change in the ratio of hazard rates over time. When the proportional hazard

assumption is satisfied for covariate, xi, the interaction parameter 7 is zero.
Therefore, testing the null hypothesis (HO : 7:0 vs. 7 i 0), determines whether

the Cox proportional hazard model is appropriate for this covariate. A non-
significant test (p>0.05) indicates that the proportional hazard assumption is
safisfied.

In clinical trials, the output of the Cox proportional model is the hazard
ratio (HR), which indicates a treatment effect on survival or resolution of disease.
For instance, if the outcome is survival time, then a hazard ratio of less than 1 for
the treatment group indicates a longer survival time and therefore a positive
outcome. However in symptom response studies, hazard ratios greater than 1
indicate a positive outcome, in which a patient in the intervention group resolves
symptoms faster than the control group.

The Cox proportional hazard model has a close relationship with the log-
rank test because the Cox proportional hazard model has the same result as that
of the log-rank test when there are no tied observations (105). The log-rank test,
Wilcoxon test, and the Cox proportional hazard model are non-parametric
method and therefore do not require a specific distribution of symptom response

times because they depend on the ranks of response or censored times rather

45

than an actual time interval. However, they still require the strong assumption of
proportionality. Figure 5 part (a) illustrates on example where the actual survival
curves cross one another. In part (b), the Kaplan-Meier estimate shows the same
pattern of survival curves. However, the survival curves estimated from the Cox
proportional hazard model (Part (c)) do not cross each other, because the
survival curves are estimated under the proportional assumption. Therefore,
even if the actual survival curves are different in part (a), the estimated survival
curves from the Cox proportional hazard model are fairly similar in part (c).

These methods are not appropriate, when their underlying assumptions
are not satisfied. Therefore, I will introduce recently proposed methods which are
available for non-proportional survival functions in the next section.

Figure 5 Example of survival functions when the proportional hazard

assumption is not satisfied

 

Survival function

 

 

 

 

l
..4
..4

O 10 20 30 40 50
Time-to-response in days

(a) Actual Survival Curve

46

 

P .O .o 7‘
4:. o: oo o

Kaplan-Meier Estimate

.9
N

 

 

.9
o

 

 

10 26 30 4o 50
Time-to-response in days

0 t

(b) Kaplan Meier Estimates

 

 

 

 

 

 

I

o 10 2b 30 4o 50
Time-to-response in days

L
_.

Estimated survival curve from Cox PH model

(c) Estimated Survival Curves under the proportional hazard assumption

47

3.3 Methods of Survival Analysis without the Proportional Hazard

Assumption

The previously introduced methods are valid when survival functions have
proportional hazards. While the Cox models are popular in health research, they
are valid only under the proportional hazard assumption. Unfortunately, this
assumption is often violated. Schemper (106) lists consequences of
inappropriately using the Cox model when; 1) the power of testing effects of
covariates with non-proportional hazards decreases, and 2) the relative risks for
covariates with increasing or decreasing hazard ratios will be over- or under-
estimated, respectively. The proportionality of hazards should therefore be
checked before a survival analysis is carried out using a Cox model.

In addition, there is the question of how to deal with time-to-response data
when the proportional assumption is not satisfied. In this section, three
alternative methods are introduced.

The first method is a nonparametric test for equality of survival functions
proposed by Lin and Wang (107). When the proportional hazard assumption is
not satisfied, Lin and Wang (107) propose a new nonparametric test that has
greater power to detect overall difference in time to events between groups when

survival curves cross. Let dlj and d2], be the number of responses in Group |
and II at each time tj. The number of patients without any response to pain and

fatigue before time tj is denoted by n1]. and n2], for Group I and II, respectively.

48

When there is no difference between the survival functions of the two groups, the

number of responses, dlj ,has a hypergeometric given by;
_d1j d2) . (3.10)

The expected number of responses in Group I can be obtained from the

 

hypergeometnc distnbutIon gIven by; elj ="1jdj/"j where d}. =de +d2j and

it}. = n + n The new test statistic is obtained by the summation of the squared

Ij 2j'

differences of the number of observed responses in symptom and the expected

k 2
number of responses In symptom at each ranked time, A = Z (de "€le . The

test statistic is obtained from the following equation;

._A—E(A)

_ ,/Var(A) ’

where E(A) and Var(A) are calculated based on the hypergeometric distribution,

T (3.11)

and are given by

k .d ..(n —d.)
1 j 1 (3.12)

 

and

49

k 4 3 2 2
Var(A) = Z {15wlj )—4E(d1j)E(d1j)+6E(d1j )(E(dlj))

j =1
—3(E(d1j»4 —(Var(d1j»2}
(3.13)
According to their simulation study, this test has a higher power of
detection of differences in survival curves between two groups than the log-rank
and Wilcoxon test when the proportional hazard assumption does not hold.
However, this test has less power than the log-rank. and Wilcoxon test when
survival curves do not cross each other. The Lin and Wang test is available for
testing the survival function only between two groups.
The second method is a modified Cox model that weights a coefficient of
a covariate which does not have a proportional hazard relative to the other
covariates (106). This is a modified Cox model for non-proportionality of hazards.
Several survival models have been developed for non-proportional hazards.
Moreau proposed the piecewise proportional hazard model with separated
parameters of a covariate for each interval of survival time (108). The Relative
survival model was proposed by Esteve and colleagues, and to incorporate non-
proportional hazards, it has different baseline hazards for each interval of survival
time (109). Also, Cox suggested an alternative method of including a time by
covariate interaction term in the Cox proportional hazard model (103). Schemper
proposed a Cox Model with weighted estimation (WCM) for non-proportionality of
hazards (106). For parameter estimation for WCM, the partial likelihood function

of the Cox proportional hazard model (Equation 3.9) is modified. In general, the

50

maximum likelihood estimation (MLE) of parameter, ,8, for the Cox proportional

hazard model is obtained by maximizing the partial likelihood function (Equation
3.9). The partial likelihood function for the Cox proportional hazard model has a
maximum value, when the first derivative of log of the partial likelihood function is

zero as follows;

 

k _ 6i. Z . xlrexp(x'j,6)q
——al°gL= Z S. — 16mm» :0. (3.14)
6,6,. i=1 "‘ . Z . exmx'jfl)
JER(I(I))

 

 

For parameter estimation for WCM, the above equation is weighted by a

function of time, f, (ti), for each parameter as follows;

 

 

at L k ' 6i' gin)?” “Wim-

og _ _ JG 1 =

aflr _i§1fr(tz‘) Sir . Z ' exp(x'j,B) 0 (315)
L JERUU» -

 

 

where 4".) is a weighted function for parameter ,Br, and can be

replaced by the number of patients with a non-responded symptom, R(t(i))

(Gehan score) (110), or total sample size times Kaplan Meier Estimator, nF
(Prentice) (111). Schemper demonstrated better power to detect the effect of a
covariate with non-proportional hazard, compared to the Cox proportional hazard
model. Heinze and his colleagues developed a SAS macro for the Cox model
with weighted estimation (WCM) (112).

Rahbar et al. developed new methods to compare mean of survival time
between groups (113-116). With respect to evaluating time-to-response, the

previously discussed methods examine a null hypothesis that there is no

51

difference in survival functions among different levels of covariate across time.
However, Rahbar and his colleagues suggested testing the equality of mean of
time-to-response among different levels of covariate during the follow-up period.
Regardless of difference between tests for survival functions and means of
survival (response) time, the equality test for means in response time is a
feasible way to compare times of response among groups. Also it does not
require the assumption that survival functions do not have proportional hazards.
Rahbar et al. (113) proposed a new nonparametric test for mean survival

time for multiple groups. Let 6’. be a mean time-to-response in groupi. The null

hypothesis of this test is H :61=6 =---=6 . Let it.

0 2 k (1)<ti(2)<m<ti(nl.) be

observed the time in response or censored time in group i, and 61.0.) be an
indicator variable of censoring (1 for response, 0 for censoring). The mean time

to response for group i can be estimated by integrating the estimated survival

function over time, given by;

A n A
6i = kai’iuc +1) ”z°(k)]'SKM(i)(’(/c)) ' (3'16)

The pooled or combined estimator of mean time-to-response among k

groups is given by

A k A A
9‘3 = Z L.6., (3.17)

52

 

where 1:, = 2 2 l 2 . For groupi, Kaplan Meier mean,é,.,
l 6'" n1+6n n2+---+6'n nk
1 2 k

can be obtained from the equation (3.16). The estimator of variance, a; , is

calculated by the following equation;

 

~2 ni A“ i(./))2
art-"i 213(1) K(t .) ’ (3'18)
’ iJ( )
"i n.
where K(t)= 1+ 2:1i11(t( )>t), 201(3)): ZS F(t (19010“) tz(j))'
j:

With the estimated mean and variance, a new test statistic (113), A”, is
proposed to test the difference of survival means among different groups, given
by:

A” =n(é—éC)'F;I(é—éc), (3.19)

where n = n1 +n2 +---+nk is the total number of observations, 67:

( 9 ,-~,ék)' is a vector of Kaplan Meier means, and 6C =(éf,éf,~~,éf)' is a
vector of the combined estimators of means of time-to-response among k
groups, which is defined in equation 3.17, among kgroups. The estimated

variance-covariance matrix of a vector of the estimated mean of time-to-response,

bi =( 1,(92,---,6ik)' , is obtained by the following equation;

53

 

 

""1 ‘3)
1;” = 7,132 7,:2 7an , (3.20)
kinlk f”2k in], )
where y‘nizéizafli,n(1_Li2) +2j¢i 612wj1n£j2’
fin” =—&l?w;}1£i—612,w—lj,nlji42km_15-31w;11n1:m2’and mi,” :ni/"’ i,j=

Rahbar et al. (113) showed that under the null hypothesis of equality of

mean times to response, the sampling distribution of An converges to a Chi-

square distribution with k -1 degrees of freedom.

In the extension of this idea, Rahbar and colleagues have developed a
nonparametric regression model of mean survival time (114-116). The regression
model accounts for effects of two discrete covariates on time-to-response without
the proportional hazard assumption. Rahbar and Gardiner (114, 115) proposed a
linear regression model for the additive effect of discrete covariates on mean of
time-to-event by estimating average increases of mean time-to-event among
different levels of a covariate.

Suppose that there Is a demographic variable such as patient age

--,c and a health related variable

categorized into m1 levels with values, 0 ml

1962,.

,md . Let

such as comorbidity categorized into m2 levels with values, dl’d m2

2

54

Tijk be time-to-response of pain and fatigue for patient i with age of c}. and

comorbidity of dk . Then a linear regression model for time-to-response is

expressed by

Tijk =a+fl1cj +’82dk +8ljk (3.21)

where (1,8 ”62 are unknown parameters and gijk is unobservable error. It

is assumed that al.. is independent and identically distributed with zero mean

jk
and common variance. It is different from a typical linear regression model,

because the distribution of error, al.], , is not assumed to be a normal distribution.

Then the mean time-to-response, 6i]. , is estimated by two covariates, C]. and
d k , given by
Bjk = a + file]. + 'Bzdk (3.22)

Rahbar and Gardiner (115) propose the estimators of coefficients,

a,,61,,62 by a linear combination of Kaplan Meier meansfor each level of the

covariates, éjk (e.g. jth level of age and kth level of comorbidity), given by

A

m2 .k_é.lk
zi,=(szl)‘1 z 2 711—71- (3.23)
k=1j¢jI j J"
m (9 —é
. _ 1 . . ,
fl2=(m1M2) ‘ z z —Jk———J—k—,and (3.24)

j=lk¢k' ck-ck'

55

. _1m1 m2 , , _1m1 .. _1 m2
a=n Z 2 nij. —,61 n X n.d. —,62 n 2 nkck , (3.25)

j=1k=1 J j:] 1'1 k=1-
1 1 m1 m2 m2
where Ml=§m1(m1—I), M2=§m2(m2—1),n= § § njk’ n11: 23 njk’
1-1/(-1 k—l
m1
nk= Z "jk , and "jk is the number of patients at the jth level of age and the
. 1.21

kth level of comorbidity.

An extension of this model, the linear modelwith an interaction effect
between two discrete covariates, was suggested by Rahbar et al. (116). Using
this method, it is possible to identify multiple factors associated with the time of
response in pain and fatigue without a restriction of the proportional hazard
assumption.

In a simulation study, it was shown that this regression model had better
power to detect the interaction effect than the Cox proportional hazard model,
since the rate of censoring before the end of follow-up increases. However, this
method has some drawbacks. First, the largest censoring (lost to follow-up) time
should not be larger than the largest time to response. If this condition is not
satisfied, then the sample mean of time-to-response cannot be estimated.
Second, this method may require a large sample size at each level. Third, this
method does not easily extend to more than two covariates. Fourth, only discrete
covariates are available in this method.

Three methods, Lin 8 Wang’s test, the Cox model with weighted

estimation (WCM), and Rahbar’s method, will be employed in this study to

56

determine if they produce results different from the methods of proportional
hazard based (i.e. the log-rank, Wilcoxon test, and the Cox proportional hazard
model). Since there are no commercial software packages for these methods, a
SAS macro was developed for Lin & Wang’s test and Rahbars methods for this

dissertation (Appendix B).
3.4 Methods of Survival Analysis for Interval Censored Data

All of the previously discussed conventional and alternative survival
methods are developed for “right-censored time data” when exact time-to-event
(response) is known. However, it is often difficult to obtain exact time to response
in clinical trials and observational studies, which are usually designed for
monitoring patients at scheduled times. Therefore, it is important to understand
survival analysis methods for interval censoring when all that is known is that a
symptom response occurred between two scheduled intervals. This next section
reviews the history of developing methods for interval censored data, and
introduces the Accelerated Failure Time (AFT) model for interval censoring that
will be used for this analysis.

In this study, patients were monitored at scheduled contacts for an
observed pain and fatigue response. Because the question was that a patient
has response in the last 7 days, time is observed at intervals so the exact time of
onset or time of response is not known. For example if a patient reported a pain

response at the 4th intervention contact, the actual response time could have

57

occurred any where between the 3rd and 4th contact. This is a type of interval
censoring. Since methods for interval censoring are more complicated and
available software is limited, the typical approach in previous studies is to use
either the lower or upper bound of the interval, or the middle value of the interval
as the exact time of the event. However, these approaches have been criticized
because it may produce biased estimations (117, 118). Therefore, methods for
interval censoring will be examined and their results compared to determine if
they are different from other methods with right censoring.

The Accelerated Failure Time (AFT) model is an available method
incorporating interval censoring to evaluate time-to-response of pain and fatigue,

and it is defined by the transformation:

T = To ex'fl, (3.26)

where T is time to response for a patient with covariates x' = (x ~,xp) and

1”“2"

T0 is time-to-response from baseline distribution corresponding to a covariate

value of zero. The AFT model assumes that the parameters fl’s can accelerate

or decelerate time-to-response for a patient with covariates, x’ = (x1,x2,---,xp).

That is, the effect of covariates in this model is to change the scale but not the
location of a baseline distribution of time to response. From this transformation, a

survival function can be obtained by

5(2 | x) = P[T > z I x] = P[TO > te—xI’B] = 50(te_x'fl), (3.27)

58

where S0 is the survival function for patients with covariate value 0. If logTO

is as, then the ATP model is expressed by logarithm form

log T = x'fl + log T0 = x'fl + 0'8 (3.28)

The error term, 6=(10gT—x'fl)/0, is a random variable that can be

assumed to have one of a variety of distributions including the standard normal,

standard extreme value, and the logistic distribution. If S(t)=P(£i >t) ,
F(t)=P(8i St), and f(t)=dF(t)/dt, parameters B’s and 0' can be estimated

from the log-likelihood function as following (119);

f(u)

log1=zlog[ 0" )+Zlog(S(ui))+Zlog(F(ui))+ZIog(F(ui)—F(vl.)), (3.29)

 

Where ui=(10gti—xl'.fl)/O'. In this equation, the first sum of log-likelihood

includes uncensored observations, the second sum includes right-censored
observations, the third sum includes left-censored observations, and the last sum
includes interval censored observations. Therefore, the AFT model can be
applied to left-, right-, and interval censored data. If an appropriate distribution is
used for time-to-response with interval censoring, it may provide a more accurate
result than that of a Cox proportional hazard model. Advantages of the AFT
model are to incorporate interval censored data and not to be restricted by the
proportional hazard assumption.

Unlike the Cox proportional hazard model, the AFT model does not

provide a hazard ratio. Therefore, there is an alternative interpretation of results

59

from the AFT model. From a AFT model given by Tx =T67 exp(,80+,61X), the

survival time ratio (or the response time ratio), exp(,6) = Tx =1/Tx : 0’ can be used

to measure the effect of a covariate (x) on time-to-response (120). A positive

value of coefficient 8 indicates that a patient who had a higher value of a

covariate (x) took a longer time to response. For example, when a covariate

indicates high comorbidity and ,6 is positive, the response time ratio is
interpreted as a patient with a high comorbidity took a(= cxp(,B))-f0|d longer to

response than one who had a low comorbidity.

3.5 Methods of Survival Analysis When Outcomes Are Not Independent

Unlike the survivorship of patients, in survival analysis of symptom
response in each individual could have multiple events (e.g. response of pain
and fatigue). Since cancer patients usually experience both pain and fatigue (34-
40), time-to-response of pain and fatigue are unlikely to be independent in this
analysis. Single symptom assessment ignores the associations between pain
and fatigue and may underestimate the patient’s total symptom severity burden.
For example, when the effects of symptom management interventions are
evaluated, pain may be more responsive than fatigue and, depending Upon the
association between the two symptoms within individuals, may, indirectly,
decrease in severity more than fatigue. Since pain and fatigue may be

interrelated, as a function of disease, treatment, or patient characteristics, the

60

possible correlation should be taken into account in evaluating times-to-response.
Therefore, the marginal Cox model incorporating correlations between pain and
fatigue will be discussed in this section.

Wei and Lin (121) developed the marginal Cox model for multivariable
failure time observations that accounts for correlation among multiple event times
within any subject. They applied this model to an example where multiple
episodes of viral infections could occur in AIDS patients. To account for the
correlations among multiple infections, a robust sandwich covariance matrix
estimator was used. Suppose that n cancer patients can experience up to 2

x . be covariates

potential events (pain and fatigue responses). Let x kip

kil’xki2""’
for ith cancer patient with symptom k (k =1 for pain, k =2 for fatigue). The

marginal Cox model is given by

hk (t | xkil’xki2"°"xkip) = exp('6k1xkil + ’Bk2xki2 +... +flkpxkip )hk0(t), (3.30)

where h and h2 are baseline hazard functions for pain and fatigue

10 0

response. Parameters, ,6 ,B ,...,,B , are estimated by a method developed
k1 k2 kp

by Wei, Lin, and Weissfeld (WLW method) (121). The robust sandwich
covariance matrix estimator (the empirical covariate matrix estimator), which is
widely used for the generalized estimating equations (GEE) (122), can be used
to account for the correlation between pain and fatigue within an individual.

The marginal Cox proportional hazard model can be used to examine the

different effects of a covariate on each outcome, e.g. pain and fatigue, by

testing ,1?“ = 821. Suppose that ,31 1 and 821 are estimated effect of age on time-

61

to-response in pain and fatigue, respectively. Significant differences between the

two estimates, ,3“ at A indicate that patient age has a different impact on the

21’

response to pain and fatigue. Therefore, the marginal Cox model allows for either

an overall effect of a covariate on both pain and fatigue (if 811:,821), or two

separate effects ( ,6 at ,B ). Most cancer patients undergoing chemotherapy
11 21

experience both pain and fatigue, therefore the marginal Cox model is
appropriate to account for the correlation between the two symptoms.

In summary, time-to-response of pain and fatigue can be evaluated by
using appropriate survival analysis methods; and it is important to understand the
underlying assumptions of each method. In this analysis, I will demonstrate how
to detect meaningful reduction (response) of pain and fatigue, how to define time
in their response, and how to implement survival analysis methods appropriately

according to underlying assumptions.

Specific Aims of the study

The primary question of this study is what factors are associated with
time-to-response of pain and fatigue among cancer patients who are receiving
symptom management interventions in two clinical trials. The interventions are
designed to reduce the severity of symptoms in patients undergoing
chemotherapy by a nurse, coach, or the AVR system during an 8 week interval
penod.

This study will address the following specific research questions:

62

1)

2)

3)

4)

5)

Can clinically meaningful changes in pain and fatigue symptoms be
measured using the four dimensions of interference (emotions,
enjoyment of life, relations with others, and general daily activities) to
define clinically meaningful cut-points that separate levels of symptom
severity (mild, moderate, and severe)?

Using the clinically meaningful severity cut-points, which factors are
predictors of time-to-response in pain and fatigue among cancer
patients when using survival analysis techniques (the log-rank test, the
Wilcoxon test, and the Cox proportional hazard model) that require the
assumption of proportional hazards?

Do the findings based on survival analysis techniques appropriate for
the proportional hazards assumption, hold when using alternative
survival techniques (the Lin 8 Wang’s test, the Rahbar’s test, and the
Cox model with weighted estimation) that do not require the
proportional hazard assumption?

Do the findings based on survival analysis techniques that are
appropriate for right censoring (the Cox proportional hazard model and
the Cox model with weighted estimation) hold when using the
Accelerated Failure Time model that accounts for interval censoring?
Do the findings from the separate models of pain and fatigue (the Cox
proportional hazard model, the Cox model with weighted estimation,

and the Accelerated Failure Time model) hold when using the Cox

63

marginal model that accounts for the correlation between the two

symptoms (pain and fatigue)?

64

CHAPTER 4 METHODS

Section 4.1 describes the two symptom intervention trials and illustrates
the method used to measure the severity of pain and fatigue, and patient
response to interventions designed address to these symptoms. Section 4.2
identifies the independent and dependent collected as part of the two trials.
Finally, the analytical strategy for identifying important factors affecting time to
response among patients with pain and/or fatigue in these trials is presented in

section 4.3.
4.1 Clinical Intervention Trials for Symptom Management

4.1.1 Subjects and Settings

This study utilizes information from two large randomized clinical trials of
symptom management interventions for cancer patients. These trials were
funded by the National Cancer Institute (R01 CA79280, Trial A, Family Home
Care for Cancer: A Community Based Model and R01 CA30724, Trial B,
Automated Telephone Monitoring for Symptom Management) (123, 124). Each
trial compared two symptom management intervention arms. Trial A compared
nurse and non-nurse (Coach) intervention groups, while Trial B compared a
nurse intervention to an Automated Voice Response (AVR) system intervention.
Trial A required that patients should have a caregiver who agreed to participate

in the study. Trial A and B were performed with the same timelines.

65

The same recruitment criteria were used for both trials. Cancer patients
were recruited from one community cancer oncology program, two
comprehensive cancer centers, and six hospital affiliated-community oncology
centers in Michigan, Indiana, Connecticut, and Maryland. From October, 2003
until July, 2006, 1605 eligible patients were approached. The study inclusion
criteria were; 1) 21 years of age or older, 2) have a diagnosis of a solid tumor
cancer or non-Hodgkin’s lymphoma, 3) be undergoing a course of chemotherapy,
4) be ability to speak and read English, 5) possess a touchtone telephone, and 6)
have no cognitive deficits. If a patient had a caregiver, then his/her caregiver
should be able to speak and read English and not have cognitive deficits. Among
the eligible patients, 815 patients consented to participate in either Trial A or B.
The participants were not assigned to any trial particular at the time of initial
recruitment. The trials were approved by the institutional review board (IRB) of
the Michigan State University, as well as lRB’s of the participating sites. The
entry criteria were different between the two trials. The only difference between
the two studies at this stage was that Trial A requires a participation of caregiver
while Trial B does not require.

Second, symptom screening was performed to determine when a patient
would enter into one of the two intervention trials. All enrolled patients undenivent
symptom screening, using the automated telephone response, during the same
time period. Of the 815 recruited, 806 participants were screened to assure that
they met minimum symptom severity criteria. The MD Anderson symptom

inventory (MDASI) was used for this process. This instrument is a widely

66

implemented instrument, designed to assess on a 0-10 scale the severity of
multiple symptoms and the impact of symptoms on daily functioning in cancer
patients (Appendix C). The reliability and validity of this instrument was
demonstrated by Cleeland (34). Based on the MDASI, patients were asked to
rate the severity of 13 cancer-related symptoms (i.e. pain, fatigue, nausea,
disturbed sleep, distressed, shortness of breath, remembering things, lack of
appetite, drowsy, dry mouth, sad, vomiting, and number or tingling), and to
describe the impact on 6 items of symptom-related interference with daily
functioning (i.e. general activity, mood, work around house, relations with other
people, walking, and enjoyment of life) during the last 24 hours. In this screening,
an automated voice response version of MDASI (4) called all patients at home
twice weekly for up to six weeks. Patients with caregivers were entered into Trial
A, when they first scored a 2 or higher on both pain and fatigue or a 3 or higher
on pain or fatigue. Patients, who did not have caregiver or whose caregivers did
not agree to participate, were entered into Trial B, when they first scored a 2 or
higher on at least one symptom. Based on this screening, 257 and 417 patients
were entered into Trial A and B, respectively. During the screening, 76 patients
dropped out and were never entered into the intervention phase. Only 2 patients
never reached the symptom threshold for either of the two trials.

Third, the trial participants completed a baseline interview a week after
they were screened and entered. At the baseline interview, patients reported
their symptoms, but were not given any intervention. Among them, 235 and 437

patients completed their baseline interviews in Trial A and B, respectively. Prior

67

to the baseline interview 23 and 34 patients dropped out from Trial A and B,
respectively. After completing the baseline interview, participants in Trial A were
randomized to a nurse or non-nurse (Coach), and in Trial B they were
randomized to a nurse or automated-voice-response (AVR) system. Following
randomization, intervention groups received 6 intervention contacts during an 8
week intervention period (See section 4.1.2 for further details). At each
intervention contact patients reported symptoms and received interventions, if
symptom severity reached a 4 or higher at the first intervention contact a week
later. Figure 6 summarizes the flow of patients beginning with eligibility and
proceeding through both trials including lost follow-up, as it occurred after the

initial contact point.

68

Figure 6 Flowchart of patient accrual and retention in the Trial A and B

 

 

Eligible and
approached
LConsented (N=815)—I }
Never reached

‘ Screened (N=806) _l
svmntom threshold I

l Tria|A(N=257) 'LTrialB(N=471)—l

 

 

 

Failed to enter
screenino (N=9)

 

Drop-out (N=76)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Drop-out prior Drop-out prior
to baseline to baseline
interview , (, interview
(N 23) Completed Completed IN 34)
baseline baseline
interview interview
(N=235) (N=437)

Followed by Followed by
Drop-out Randomization Randomization Drop-out
before starting before starting
intervention intervention
(N=20) r (N=50)
Started the initial Started the initial
intervention intervention
contact (N=215) contact (N=386)

Drop-out Drop-out
during the during the
intervention intervention
contacts I v contacts
(N 45) Completed Completed (N 42)
interview at 10 interview at 10
week (N=170) week (N=344)

 

69

 

 

 

 

4.1.2 Intervention Trials for Symptom Management

Trial A was designed to compare a nurse-based intervention with an
intervention delivered by a non-nurse coach. In Trial B, the nurse-based arm was
compared with an Automated Voice Response (AVR) system. Each trial was
designed to compare the impact of intervention strategies in reducing the severity
of symptoms for cancer patients undergoing chemotherapy. A nurse, coach, or
the AVR system reached patients by telephone at pre-scheduled time points. The
first four contacts were scheduled weekly, while the 5th and 6th contacts were
every other week (Figure 7). At each intervention contact, the patients were
asked about each of 16 symptoms7, which included 12 symptoms (without
drowsy) from the 13 symptoms at screening, as well as additional 5 symptoms
(i.e. alopecia, constipation, cough, diarrhea, and weakness). In the intervention
contact, nausea and vomiting were measured as one symptom.

In the nurse-based intervention of both Trial A and B, the trained nurse
provided the patients with cognitive behavioral interventions that involved up to
four strategies for dealing with each of their symptoms. The goal of this cognitive
behavioral intervention was to assist patients in acquiring self-management
knowledge, skills, and behaviors to address symptom problems. Cognitive
behavioral strategies were improved to reduce the severity of symptoms, the
impact on emotional distress, and the physical function. In this nurse-based arm,
if a patient reported a symptom severity of 4 or higher, the nurse, with agreement

from the patient, selected one of the 4 cognitive behavioral intervention strategies

 

7 The 16 symptoms include alopecia, anxiety, constipation, cough, depression, diarrhea, difficult
to breath, dry mouth, fatigue, insomnia, nausea/vomiting, pain, peripheral neuropathy, poor
appetite, difficult to remember, and weakness.

70

classified as coping, reframing, education, or eliciting support to overcome the
symptom. Each patient used a Symptom Management Guide (SMG) which
described the cause of each symptom and strategies for managing each
symptom. This manual, written at an 8th grade level, also included information on
when to call the oncologist and how to access other sources of information. The
patients in the non-nurse coach and the AVR arms were referred only to the

SMG, when they reported symptoms at a severity of 4 or higher.

Figure 7 Time line of screening, baseline interview, intervention contacts,

and post interview

 

 

Data collected at baseline:

Age, Gender, CES-D, Physical function (SF-36), Comorbid
conditions, Site of cancer, Stage of cancer,

Date of administration of chemotheraov orotocol

 

 

 

 

 

 

Baseline Post
interview interview
.5. c1 c2 C3 C4 C5 cs 5.
I I
-¢—l—¢-+—¢—¢ I ¢ i H
E \ J
V 10

, 6 Intervention contacts (8weeks)
Screemn

 

Data collected at each contact:
Severity of symptom

Duration of symptom

Date of contact

The number of received interventions

 

 

 

 

 

 

71

4.1.3 Justifications for combining data from Trial A and B

In this study, I combined the data sets from Trial A and B into a single
analytic file in order to achieve a larger sample size. While combining the two
data sets can leads to a selection bias, I believe this possibility is minimal, and
the differences between the two trials are as follows:

First, Trial A required consent from caregivers, whereas Trial B did not
require caregiver participation. Since patients who had impairment in their
physical functioning or who had adverse health conditions might be more likely to
need assistance from caregivers, there is the potential bias that patients in Trial
A might have poorer health compared with those patients in Trial B. Second, Trial
A had somewhat different criteria for the symptom screening than Trial B. When
eligible patients (i.e. those not having a caregiver) reported 2 or higher on
severity of at least one of the 13 symptoms, they were entered into Trial B. In
Trial A, however, patients were screened based on only pain and fatigue. For
Trial A, patients needed to score 2 or higher on severity for both pain and fatigue,
or 3 or higher on either pain or fatigue. Accordingly, patients in Trial A might have
a greater opportunity to report pain and fatigue at early intervention contacts,
compared with those in Trial B. However, despite differences in criteria for the
presence of pain and fatigue, the prevalence of pain and fatigue was not
significantly different between the two trials. Ninety-six and ninety-four percent of
the patients reported a 4 or higher on severity of fatigue in Trial A and B,
respectively. Prevalence of pain in Trial A (54.6%) was a little higher than that in

Trial B (42.8%). This difference no longer existed among the analyzed samples,

72

because the survival analysis of time to response included only patients who had
pain or fatigue during intervention period.

Regardless of the design difference between the two trials, there is
evidence to support combining these data sets in this study.

First, Trial A and B were performed concurrently with the same study
protocol. Patients were screened using the same system. The same nurse
delivered the intervention protocols in nurse-assisted arms of the two trials. In the
education-information arms, Trial A was delivered by a masters prepared social
worker (non-nurse coach arm) and Trial B was delivered by an automated voice
response system (AVR arm). While the mode was different, the protocol for these
arms was identical In terms of the numbers of contacts, amount of time spent
with each patient (approximately 18 minutes per contact), and the use of the
same written materials to deliver symptom management strategies. The time
frame from the recruitment to the end of intervention period was also identical
between the two studies.

Second, the characteristics of the patients were not different between the
two studies. Although more adverse health conditions were expected in patients
with caregivers in Trial A, I did not find differences in comorbid conditions,
depression, or age between the two trials (Table 1 in Chapter 5).

Third, the same instruments were used for assessing symptoms and other
health conditions in both Trial A and B. Therefore, the two trials would be

expected to have similar levels of measurement errors in symptom assessments.

73

Fourth, the different entry criteria for symptom screening did not affect the
demographic difference between the two trials. Although Trial A had different
criteria than Trial B, only two patients were excluded in screening because of the
symptom severity requirements in both Trial A and B. (This in part was due to a
fact that fatigue is the most prevalent symptom experienced by patients
undergoing Chemotherapy (43), affecting close to 80% of patients.)

As to the presence of caregivers in Trial A, there were remaining concerns
about differences in gender and site of cancer between the two trials. More
female and breast cancer patients were likely to be in Trial B compared with Trial
A. It has been observed in a prior research that lung cancer patients experienced
relatively severe pain and fatigue compared with patients with breast or other
cancers (54). There is a question if as to whether differences in cancer type led
to unbalanced patients health conditions at baseline between the two trials. Trial
A has more Lung cancer patients (i.e. Breast (24.7%), Colon (7.4%), Lung
(29.3%), Genitourinary (10.7%), Gastrointestinal (6.5%), Gynecological (6.5%),
Pancreatic (2.3%), Non-Hodgkins lymphoma (7.0%), Myeloma (1.4%), and Other
(4.6%)). Trial B has more breast cancer patients (Breast (41.5%), Colon (13.7%),
Lung (15.0%), Genitourinary (6.9%) Gastrointestinal (3.6%), Gynecological
(8.5%), Pancreatic (3.6%), Non-Hodgkins lymphoma (5.2%), Myeloma (1.0%),
and Other (1.0%)).

At the baseline interview, there were no differences in comorbid conditions,
total number of symptoms or depression. However, patients in Trial A had lower

levels of physical functioning (SF-36) at baseline compared with those patients in

74

Trial B. To control for the baseline differences, the final models were adjusted for
cancer site, sex, and physical functioning at baseline. If the effects of cancer Site
are different between the two trials, then the effect of cancer site could influence
by the effects of intervention. For-example, if the non-nurse coach intervention in
Trial A is more effective for lung cancer patients, than the AVR intervention in
Trial B, the cancer site effect can be overestimated, because there were more
lung cancer patients in Trial A. To correct on this concern, the interaction
between trial arm and selected covariates (cancer site, gender, and physical
function) that differ by trial will be explored in multivariable analysis. Finally, by
comparing final models for combined data with separate models for each trial, it
will be shown that the identified factors associated with pain and fatigue

response are not due to the differences between the two trials.

4.2 Measures

Symptoms were monitored at the baseline interview, at the each of the 6
intervention contacts (covering 8 weeks), and at the ten week (post-intervention)
interview (Figure 7). At each contact, symptom management Interventions were
given to patients if they reported severity of 4 or higher among the 16 symptoms.
The dates of the two interviews and 6 intervention contacts were recorded.
Demographic data, depressive symptom, physical function, comorbidity were
collected at the baseline interview. Site and stage of cancer were obtained from

medical records.

75

Outcome Variable At each of 6 intervention contacts, severity of 16
symptoms 8 and 5 interference 9 items were recorded using a developed
instrument based on Brief Pain Inventory (76) and Brief Fatigue Inventory (4)
(Appendix A). Patients were asked to rate the average severity of pain and
fatigue in the past 7 days on a scale of 0 (not present) to 10 (worst). When pain
or fatigue was present (i.e. severity > 0), patients rated on a scale of 0 to 10 the
extent to which that symptom interfered with their enjoyment of life, relations with
others, general daily activities, emotions, and sleep.

The primary outcome variable for these trials is time-to-response in days
for pain and fatigue. In order to evaluate how long it took to lower the severity of
pain and fatigue by a delivered Intervention, the date of contact on which a
symptom was reported to have a severity of 4 or higher was considered the
onset time of the symptom. When patients rated lower severity level (mild or
moderate) compared to the initial severity level (moderate or severe) at onset
that date of contact was defined as the response time.

Two different styles of records for time-to-response will be used in this
stUdy. First, most survival analysis methods10 developed for right censored data
require an actual time to response. Since exact time of onset and response could
not be observed, the date of the scheduled contact was used as a proxy for the

exact time of the events. That is, the number of dates from the contact where a

 

8 The 16 symptoms includes pain, fatigue, nausea, insomnia, distress, difficult to breath, difficult
to remember, poor appetite, dry mouth, vomiting, numbness or tingling, diarrhea, fever, cough,
constipation, and weakness

9 The 5 interference items include emotions, enjoyment of life, relations with others, general daily
activities, and sleep.

1° The implemented survival analysis methods for right censoring in this study includes the log-
rank, Wilcoxon test, Cox proportional hazard model, Lin 8 Wang’s test, Rahbar’s methods, WCM,
and marginal Cox model.

76

severity of pain or fatigue was 4 or higher to the contact where a response to the
symptom was first identified was defined as the actual time to response. Second,
a survival method developed for interval censored data (i.e. the Accelerated
Failure Time model) requires an interval time for symptom response. Consider a
hypothetical situation. Let us say a patient reported onset of pain at 1St contact
and symptom response at 5th contact, and the actual response occurred between
4th and 5th contacts. Therefore, a lower bound of time to response should be the
number of days from 1St to 4th contact, while the upper bound must be the

number of days from 1St to 5th contact.

Independent Variables Patient depression was rated using the Center
for Epidemiologic Studies — Depression (CES-D) scale (125). The CES-D
instrument consists of 20-items rated on a 4 — point Likert-type scale (almost all
of the time, most of the time, some of the time, and little/none of the time) (see
Appendix D). The CES-D scale is a widely used reliable measure of depressive
symptoms with an established cut-off of 16 or greater indicating the potential for
clinical depression (126). Physical function was assessed using the 10-item
physical function subscale from the Short Form 36 (SF-36), a widely used QOL
instrument (see Appendix E). The subscale SF-36 has a standardized score of 0-
100 scale, with higher scores representing better physical function. Patient
comorbidity was derived from patient self-report using Katz instrument (127). To
obtain comorbid conditions, patients were asked “Has a doctor ever told you that

you have (a chronic disease)?” (See Appendix F). Comorbidity was measured by

77

the total number of 15 Chronic conditions including high blood pressure, diabetes,
other cancer, chronic bronchitis or emphysema, heart problem, angina or chest
pains, stroke, emotional problems, arthritis or Rheumatism, fractured hip, surgical
replacement of joint, incontinence, cataract surgery, hearing aid, and other major
health problems at the intake interview. Patient comorbidity was dichotomized at
the median into 0-2 versus 3 or higher categories.

Cancer site was categorized as breast, lung, colon, and others—where
the pattern includes gastrointestinal, gynecological, genitourinary, pancreatic,
non-Hodgkins lymphoma, myeloma, and others. Using information in the medical
record, stage of cancer was categorized according to the tumor-node-metastasis
staging criteria of the American Joint Committee on Cancer. Based on this scale,
stage of cancer was collapsed into early stage (in situ zero, and stage I and II)

and late stage (stage III and IV).

4.3 Data Analysis for Identifying Factors Associated Time to Pain and

Fatigue Response

Data analysis was performed for developing optimal cut-points to define
the level of pain and fatigue severity (mild, moderate, and severe) and testing
consistency of the cut-points. The shifts (‘severe to moderate’, ‘severe to mild’,
and ‘moderate to mild’) were defined as symptom response. Time-to-response
was measured by the number of days from the onset contact to the response

contact. To identify important factors impacting time to response of pain and

78

fatigue, several analysis methods were implemented. First, with the proportional
hazard assumption, the log-rank, Wilcoxon test, and Cox proportional model
were used. Second, the results from the above methods were confirmed by using
the Lin 8 Wang’s Test, WCM, and Rahbar’s methods without the proportional
hazard assumption. Third, using the lower and upper bounds of time to response,
the Accelerated Failure Time (AFT) model was applied. Finally, I tested, using a
marginal Cox model, to determine if the Identified factors in the previous model
were still significant, given the correlation between pain and fatigue symptoms

within a same patient.

4.3.1 Developing Cut-points to Define the Severity Level of Pain and

Fafigue

The first methodological aim of this study is to measure clinically
meaningful changes of pain and fatigue in response to interventions. I developed
optimal cut-points of pain and fatigue severity based on multiple interference
items11 for each symptom.

To use these four interference items (i.e. emotions, enjoyment of life,
relations with others, and general daily activities) for finding cut-points of
symptom severity, an internally consistent reliable interference scale for these
multiple interference items was needed. Patients who reported pain and/or
fatigue at a one or higher on the severity measure were then asked to report

interference with daily activity, emotions, enjoyment of life, and relations with

 

'1 The multiple interference items include emotions, enjoyment of life, relations with others, and
general daily activities.

79

others on the same 0-10 scale with 0 being not present and 10 worst possible.
According to an explanatory factor analysis (123), the four interference items
were highly and positively correlated with each other. The eigenvalues (A) and
the loadings of the four interference items on the first factor are listed in Table
1.The results support the fact that the four interference items are expected by
one dimension and that a single summed score can be used to measure
interference. Also the factor analysis with four items revealed that a single factor
explained about 80% of the total variance for both pain-related interference
(2:327) and fatigue-related interference (A=3.08). All four items in both cases
had approximately equal (high) loadings on a single factor with the largest
eigenvalue. Therefore, a single measure was used in this study by adding the
four interference scores (0 to 40 scale). Using a single summed interference
score to reflect the reactive dimension of symptom experience has been Shown
to be valid and reliable in other cancer studies (34).

Table 1 Factor loadings for the four interference items for each symptom at

 

contact 1
m
Pain Fatigue
Interference with enjoyment of life 0.9138 0.9044
Interference with relations with others 0.8960 0.8558
Interference with general daily activities 0.9058 0.8885
Interference with emotions 0.9004 0.8619

 

 

 

 

To identify and differentiate mild, moderate, and severe categories of
symptom severity, the optimal cut-points were selected by testing the difference
in the summed interference score. In previous studies (4, 80, 92, 128),

80

Multivariate analysis of variance (MANOVA) was used to determine cut-points
categorizing severity levels by maximizing symptom related outcomes (e.g.
interference, emotional status, other functional status). In this study, since the
distribution of interference sum skewed to the right side which is not a normal
distribution, I used the generalized linear model, Let 1<c1<c2 310, where c1 and

C

2 are severity of pain or fatigue at the first contact. Since the distribution of

interference sum has a gamma distribution, a generalized linear model with

gamma distributed errors (129) was used as following;
10g(#)= ,60 + fl151+ ,8252 + ,B3T, (4.1)

where p is the mean of summed interference scores; S1 and S2 are dummy

variables for severe and moderate severity”; and T is total number of other
symptoms at the first contact. This model was repeated 36 times with all possible

combinations of c1 and c2 for each of pain and fatigue. If c1 is 2, then there are
8 possible points for c2 between 3 and 10. In the same way, 7, 6, 5, 4, 3, 2, and

1 points are available for c2 when cl is 3, 4, 5, 6, 7, 8, and 9, respectively. This

model was implemented via PROC GENMOD in SAS version 9.1(130). By
seeking the largest size of the likelihood ratio (LR) of generalized linear model

across all possible cut-points (01,62) for severity categories, optimal cut-points

(c: , c; ) separating moderate from mild and severe from moderate were selected.

 

‘2 S1 (severe) is 1 if c2 5 severity, otherwise 0, and S2 (moderate) is 1 if c1 3 severity< c2,

otherwise 0

81

The distribution of the summed interference score could be influenced by
other symptoms that were not included in the original four interference items. For
instance, if the sample is divided into two groups according to the number of
symptoms other than pain and fatigue, the distribution of the summed
interference score in one group with a small number of symptoms is likely to be
different from the distribution of the summed interference score in the other group
with a large number of symptoms. Positive correlation coefficients between total
number of other symptoms and the summed interference scores were observed
for both pain (r=0.3440, p-value<.0001) and fatigue (r=0.4427, p—value<.0001).
Therefore, the total number of other symptoms was adjusted for in the
generalized linear models.

To provide additional evidence of validity of the cut-points, the summed
interference scores, the duration of a symptom in the past 7 days, and the
physical function (SF-36) were compared by mild, moderate, severe levels of

pain and fatigue based on the selected cut-points.

4.3.2 Consistent Discrimination of Interference by the Cut-points

To use the selected cut-points defined above for measuring symptom
change, the cut-points should reliably differentiate at every intervention contact.
Therefore, I examined if the mild, moderate, and severe categories of symptom
consistently differentiate the interference sums across 6 contacts for pain and
fatigue. Since symptoms and interferences were repeatedly measured during

multiple contacts, a longitudinal model should be used. By including the

82

interaction between time and severity categories (mild, moderate, severe), the
means of the sums for the 4 interference score for three categories were
compared at each contact.

For this analysis, the linear mixed effects (LME) models (131) with
autoregressive covariance structure were employed. The LME model
accommodates multiple missing data points in a longitudinal study. This
consideration was important since several patients did not complete all 6
contacts due to missed contacts or because they dropped out. Further, the LME

model incorporates correlations between contacts within the same patient. Let

c; and c; be the selected cut-points of severity of pain or fatigue at the first

contact. The model incorporating the interaction between the symptom severity
categories (mild, moderate, severe) and time (contact number) was specified as

follows;

y: =flo+fl151t+fl2521+fl3T
+711i +7212 +7313 +7414 +7515

+‘31 151:11 + 51251112 + 51351/3 + 614Su14 + 51551/5

”2132/1 +52252112 + 5235233 + 52452114 + 62552/5

(4.2)

where yt is the mean of summed interference scores at tth contact, Slt

and S2 are dummy variables for severe and moderate severity at tth contact”,

T is total number of other symptoms at the first contact, [1,...,I5 are dummy

 

13 S1 t (severe) is 1 if c severity, otherwise 0, and SZt (moderate) is 1 if c < severity<c

2t 3 1t " 2r

othenrvise 0

83

variables14 for 6 contacts. Parameters fits and y], s are coefficients for main
effects of cut-points (SI: ,S2t) and time ( I,,...,15 ), respectively. Parameters 61.]. s

are coefficients for interaction between cut-points and time. The LME model were
fitted using PROC MIXED in SAS version 9.1 (130).

Least square (LS) means of the summed interference scores by the
interaction terms were calculated from the model. The LS mean of the summed

interference scores for mild, moderate, and severe symptom at tth contact can
be estImated by ’60 + )637‘ + 7t , ,60 + ,637" + 7t + (,61 + 61!) , and ,60 +fl3T + 7t +
(,82 +3”), respectively, where T is the mean number of symptoms. To test if the

mild, moderate, and severe symptoms have different summed interference score

at tth contact, I tested a null hypothesis: fll+r§1t=fi2+321=3 If the null

hypothesis is rejected for all 6 contacts, then the categories of mild, moderate,
and severe may consistently differentiate the summed interference score over
time.

Once consistent differentiation of interference by the cut-points is
confirmed, symptom response can be defined by these cut-points as mentioned
above. Finally time to response for pain and fatigue can be measured by
counting the number of days from onset to response (See Outcome Variable

section in Chapter 4.2 Measures).

 

‘4 It is 1 if a patient was in 1"1 contact, otherwise 0, where t = 1,2,...,5

84

4.3.3 Evaluating Time to Response of Pain and Fatigue

To identify significant factors influencing time to response in the
management of pain and fatigue, the combined data sets from Trial A and B
were used. Since there were differences in gender, cancer site, and physical
function at baseline between the two trials, the factors were tested after adjusting
for these three covariates in multivariable analysis. In this analysis, all covariates
were categorized because some tests are available only for categorized
variables. To avoid multicolinearity between gender and cancer site, I created a
combined variable, categorizing as female 8 Breast cancer, female 8 Lung
cancer, female 8 other cancer, male 8 lung cancer, and male 8 other cancer.
Age (60 or younger VS. older than 60 years old) and comorbidity (less than 3 vs.
3 or more comorbid conditions) were categorized using the median values. Since
CES-D of 16 was considered as an important clinical threshold (126, 132). We
used this value to create a binary variable.

The analyses were performed in the following steps: 1) Univariate analysis
tested the effects of each of the covariates, including age, comorbidity, and
depression without adjusting for any other covariate. 2) Multivariable models
tested the effects of those covariates after adjusting for gender, cancer site,
physical function, and trials (Trial A vs. B). The model selecting methods are
described in next paragraph. 3) I tested the interaction between trials (Trial A and

B) and the covariates.

85

4.3.4 Survival Analysis Incorporating Right-censoring

The first modeling strategy is to evaluate the time-to-response under the
proportional hazard assumption by using the log-rank test, the Wilcoxon test, and
the Cox proportional model. PROC LIFETEST (for the log-rank test and the
Wilcoxon test: Univariate model) and PROC PHREG (for the Cox proportional
hazard model: Multivariable model) procedures, SAS version 9.1, were
implemented. The hazard ratio was presented to measure the effect of a
covariate on time to symptom response.

Although these methods are most commonly used in survival analysis
methods, they are valid only when the proportional hazard assumption is
satisfied. Therefore, it is important to check the proportionality of hazards. To test

the proportionality of hazards for each covariate, I performed the following steps

(105); 1) created a- non-decreasing log function of time ( g(t) = Iog(t/t*), where t

is time to response and t* is the median time to response, 2) added the

interaction term between a covariate and the log function of time into the Cox

. . * *
proportional model given by hi(t)=h0(t)exp(fllxil+fl1xillog(t/t )) for each

covariate x1, and 3) tested if the coefficient of interaction term, fl; , is statistically
different from zero. If ,8: is not zero (i.e. the term is p<0.05), then the

covariate,xl, has non-proportional hazard across time. This test was performed

for both univariate and multivariable analysis.

86

The second modeling strategy is to evaluate time to response when non-
proportional hazards exist by using the Lin 8 Wang’s test, Rahbar’s approach,
and the WCM. The first modeling strategy that is based on the proportional
hazard assumption might not appropriately detect the effect of a covariate on
time-to-response, if the hazard functions are not proportional by the covariate.
Therefore, non-proportional hazard based methods may have more valid results,
since these methods do not require the proportionality of hazards. These
methods are also available, when the proportional hazard assumption Is satisfied.
I investigated how the results of this modeling strategy are different from that of
the first modeling strategy. Since the Lin 8 Wang’s test is available only for two
groups and Rahbar’s approach is restricted to two covariates, these methods
were performed for unadjusted analyses only. Only the WCM was used for a final
multivariable model. For the Lin 8 Wang’s test and Rahbar’s methods, I
developed SAS macros (See Appendix B) and a SAS macro developed by

Heinze and his colleagues was used for the WCM.

4.3.5 Survival Analysis Incorporating Interval-censoring
The first and second modeling strategies can be used for right censored
data, but these modeling strategies are not available when time to response is
observed as an interval of time [L,R], where Ls actual time to response 3 R.
The third modeling strategy is to evaluate time to response when it was observed
as an interval of time via the AFT model with a Weibull distribution. Since

symptoms were monitored at the scheduled intervention contacts in Trial A and B,

87

actual symptom response occurred between the contact periods. Therefore, the
ATF model with interval censoring would be more appropriate method for
assessing this interval censored data. It would show the difference between
methods with right censored15 and interval censored” time data. Because the
AFT model is a parametric model, an appropriate distribution of time-to-response
needs to be selected. The Akaike lnforrnation Criterion (AIC) can be used for
selecting a distribution in the AFT model (105). I compared four distributions: the
Weibull, exponential, Iog-norrnal, and log-logistic distributions using the AIC. The
largest AIC indicates that the best model for both pain and fatigue was based on
the Weibull distributions. PROC LIFEREG, SAS version 9.1, will be used for the
AFT model. Results from the AFT model will be compared that from the Cox

proportional hazard model and the Cox model with weighted estimation.

4.3.6 Survival Analysis for Multiple Events Incorporating Right-

censoring

For the above modeling strategies, the survival analysis models were
performed separately for pain and fatigue. If time to response for pain were
independent from that of fatigue, these separate models for pain and fatigue
would be appropriate. The fourth modeling strategy is to identify the common
effects of covariates on both pain and fatigue, while taking Into account for a
correlation between the two symptoms via the marginal Cox model. I produced a

final multivariable model by using PROC PHREG procedure with the aggregate

 

‘5 The survival analysis methods for right censoring includes the log-rank test, the Wilcoxon test,
the Cox proportional hazard model, the Lin 8 Wang’s test, Rahbar’s methods, and the WCM.
‘6 The survival analysis method for interval censoring includes the AFT model.

88

option in SAS version 9.1. The aggregate option was used to produce the
empirical covariate matrix estimator which accounts for the correlation between

pain and fatigue within an individual. Separate covariate effects for pain ( 3pm.”)
and fatIgue ( ,8 fatigue ) were Included this model. In the equality test

(Ho: flpain = fl fatigue) based on the empIncal covanate matrIx estImator, If the

null hypothesis ( H0) is not rejected, then these two parameters can be replaced

by a single parameter for the overall effect ( flan)"

4.3.7 Diagnostic assessment of the final models

After flnal multivariable models were built, the adequacy of the model was
assessed. In survival analysis, a standardized method of model diagnosis is to
use residuals which are different from that in the linear regression model. A
residual called the Cox-Snell residual (133) can be used to check the adequacy
of the model. The basic idea of this diagnostic test is that a negative log in the

survival function (— log(S(t))) has an exponential distribution when survival time t
is a continuous random variable. Because a survival function S(t) has a uniform

distribution between 0 to 1, W = —log(S(t)) has an exponential distribution. If the

correct model has been fitted, the Cox-Snell residual (—log(.§(t))) has an

exponential distribution. When a cumulative hazard of the Cox-Snell residuals
are plotted against the Cox-Snell residuals, a straight line with a slop of 1 and

ze ro intercept will indicate that the final model is adequate (105).

89

By seeking the significant covariates from the different modeling strategies,
I identified covariates that all consistently recognized as being important factors
for time to response of pain and fatigue. Different results using several other

approaches will be discussed by considering their underlying assumptions

90

CHAPTER 5 RESULTS

This chapter presents the results from the evaluation of pain and fatigue
specially the establishment of optimal cut-points for measuring the severity of
pain and fatigue, and then the application of several different statistical methods
for identifying factors associated with the responses to pain and fatigue. The
analyses were performed to answer two major questions: first, how to define
clinically meaningful changes in the response to symptom management
interventions for pain and fatigue; and, second, how to analyze the time-to-
response of pain and fatigue without violating the model assumptions regarding

proportional hazards.

5.1 Demographic and clinical characteristics of the trials

Table 2 summarizes the characteristics of 601 patients in the two
intervention trials. More women were assigned to Trial B (76.2%) than Trial A
(59.1%) (p-value<0.0001). There was no difference in the age distribution
between the two trials, however, differences in the distribution of cancer sites
was observed between the two trials (p-value<0.0001). More breast-cancer
cases were assigned to Trial B (41 vs. 24.7%) while more lung-cancer cases
were assigned to Trial A (27.3 VS. 15.0%) (See Table 2). More patients had late
stage cancer in Trial A (90.1%) than Trial 8 (82.3%), which is a reflection of the

higher proportion of lung cancer in Trial A which is usually diagnosed later.

91

Based on the CES-D score, approximately 35% of patients qualified as

being at risk for clinical depression (i.e. CES-D216) in either trial. There was no

difference between Trial A and B in CES-D score (p-value=0.4381). There was

also no difference in the number of comorbid conditions between Trial A and B

(p-Value=0.7907). Around 60% of patients reported two or less comorbid

conditions.

Table 2 Characteristics of patients in two intervention trials

m

 

 

 

 

 

 

 

 

 

92

 

 

Trial A Trial B P-values
(IL-(2,2?) (IL-3,2?) (Chi-square Test)
Pafientgender
Male 88 (40.9) 92 (23.8) <.0001
Female 127 (59.1) 294 (76.2)
Pafientage
25 ~ 44 24 (11.2) 57 (14.8)
45 ~ 60 102 (47.4) 178 (46.2) 0.4520
61 ~ 74 70 (32.6) 113 (29.3)
75 + 19 (8.8) 37 (9.6)
Stage of disease
Early 21 (9.9) 68 (17.7) 0.0112
Late 190 (90.1) 316 (82.3)
Site of cancer
Breast 53 (24.7) 160 (41.5)
Lung 63 (29.3) 58 (15.0) <.0001
Other 99 (46.0) 115 (43.5)
CES-D
Less than 16 137 (64.3) 257 (67.4) 0.4381
16 + 76 (35.7) 124 (32.6)
Comorbidity
Less than 3 133 (61.9) 243 (62.9) 0.7907
3 + 82 (38.1) 143 (37.1)

5.2 Meaningful Reductions in Pain and Fatigue among Cancer Patients

To obtain a reliable definition of symptom response, the optimal cut-points
of pain and fatigue will be identified in Section 5.2.1. We will determine if the set
of cut-points consistently differentiate among patient interference over the 6

contacts in Section 5.2.2.

5.2.1 Optimal Cut-points of Pain and Fatigue Severity

To establish the optimal cut-points for differentiating patient interferences
due to pain and fatigue, I explored how the severity of pain and fatigue are
distributed across interference scores at the initial contact. Four of the
interference items17 were highly and positively correlated. We found that sleep
was weakly correlated with the other four items and thus was removed from the
final summed interference scale. The remaining four items were submitted to an
exploratory factor analysis (See Table 1, Chapter 4). As severity of symptoms
increased, the sum of interference score consistently increased. Optimal cut-
points for severity need to be based on clinically important distinctions in
summed interference scores.

Therefore, to establish possible cut-points a generalized linear model with
a gamma distribution function (See Equation 4.1) was used to adjust for the total
number of other symptoms at the first intervention contact. Since the models

were repeated 36 times for all possible combinations of two cut-points (See

 

‘7 The 4 interference items include emotions, enjoyment of life, relations with others, and general
daily activities.

93

Chapter 4.3), 36 Chi-square (Wald test) statistics were produced. The largest Chi-
square statistics for five pairs of two cut-points are listed in Table 3. Larger chi-
square statistic represents better differentiation of interference, and the cut-points
of 2 (for moderate) and 5 (for severe) produced the largest chi-square statistics in
both pain and fatigue. Based on the identified cut-points, the severity levels,
therefore, are defined as “mild” (score of 1), “moderate” (scores of 2 through 4),
and “severe” (score of 5 and greater).

Table 3 Cut-points with five largest chi-square (Wald test) statistics
m

 

 

 

 

 

 

Pain Fatigue
Rank
Cut-points Chi-square Cut-points Chi-square
1 (2, 5) 92.35 (2, 5) 151.68
2 (2, 6) 82.13 (3, 5) 144.80
3 (2, 7) 81.57 (5, 9) 139.11
4 (5, 7) 75.57 (5, 7) 137.23
5 (3, 5) 75.20 (5, 8) 136.80

 

 

 

 

 

 

w

To ensure how appropriately the selected cut-points represent patient
symptom burden, the distributions of interference sums for mild, moderate, and
severe levels of pain and fatigue are compared in Figure 8. The histograms
represent the distribution of interference scores among patients whose
symptoms were classified as mild, moderate, and severe. Interference sums are
distributed around 3 (median) at the mild level, while they are distributed around

8 and 20 (median) at the moderate and severe level, respectively.

94

Figure 8 Distribution of summed interference score (0~40) among mild,

moderate, and severe level of pain and fatigue

 

 

 

 

 

25%

     
   

Moderate Severe

 

 

 

 

 

20%

15%

10%

 

5%

 

0%

     

  

0 8162432400 8162432400 816243240
(a) Distribution of interference sum by level of pain

I Mild Moderate Severe

 

 

 

 

35%

 

 

 

 

30%

25%

20%

15%

10%

 

 

5%

  

    

 

0 8 I6 24 32 40 0 8 16 24 32 40 0 8 I6 24 32 40
(b) Distribution of interference sum by level of fatigue

95

In addition, Table 4 summarizes the cut-points for pain and fatigue. The
means for the summed interference scores, duration of the symptom over the
past seven days prior to delivering the first intervention, patient physical function
(SF-36), and sum of severities of the 14 other symptoms assessed at the
baseline interview are compared across the three severity levels for pain and
fatigue, respectively. Among patients who reported pain or fatigue at the first
contact, 42% and 50% were classified by severe pain and fatigue, respectively.
Only 12% and 6% of patients had mild pain or fatigue, respectively. The means
of the summed interference scores were 3.4, 9.1, and 20.8 for mild, moderate,
and severe pain, respectively. The means of the summed interference scores
were 3.4, 8.8, and 18.3 for mild, moderate, and severe fatigue, respectively.
Greater differences in interference scores between moderate and severe are
observed than that found between mild and moderate. Duration of each symptom
(the number of days in the past week in which patients reported pain or fatigue),
physical functioning score (SF-36), and the sum of symptom severities (i.e. sum
of 14 possible other symptoms) exhibited greater differences between mild and
moderate levels of severity for pain and fatigue than that between moderate and
severe for each symptom. In the case of pain, there is no difference in physical
function scores between moderate and severe severity. These differences
indicate that the established cut-points represent not only interference with the
patient’s lives but also reflect the duration and the impact of pain and fatigue on
their levels of physical function. The difference in physical function scores and

the sum of symptom severities among patients Classified as having mild,

96

moderate, and severe symptoms provide evidence that the established cut-points
reflect real differences in health conditions.

Table 4 Cut-points for severity categories, number of cases reporting each
symptom, unadjusted ~ mean interference scores, duration before first

contact, and physical function at baseline interview

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Severity level of pain III‘IIId M33)“; 5:17:53.
No. of patients N (%) 32 (12.4) 119 (45.9) 108 (41.7)
Interference sum Mean (Std) 3.4 (3.3) 9.1 (7.7) 20.8 (10.3)
Duration18 Mean (Std) 2.9 (2.5) 4.7 (2.2) 5.1 (2.0)
Physical function19 Mean (Std) 63.0 (23.9) 49.5 (25.6) 48.9 (27.3)
Symptom severity sum20 Mean (Std) 29.5 (18.4) 40.7 (19.5) 50.6 (23.8)
Severity level of fatigue “8': M233?“ ?::5?
No. of patients N (%) 34 (6.4) 227 (42.9) 268 (50.7)
Interference sum Mean (Std) 3.4 (3.9) 8.8 (6.7) 18.3 (9.3)
Duration19 Mean (Std) 2.8 (2.0) 4.7 (2.1) 5.5 (1.9)
Physical function20 Mean (Std) 77.0 (21.6) 61.9 (24.6) 48.4 (26.4)
Symptom severity sum21 Mean (Std) 25.1 (22.2) 32.2 (18.1) 43.8 (21.7)
w

 

Taking into consideration the magnitudes of interference for pain and
fatigue categories, and how they might influence symptom response to

management interventions, the stability of these cut—points over time will be

 

‘8 Duration is the number of days when patient experience pain or fatigue in past 7 days prior to
the first contact.

19 Physical function is a standardized score on a 0 to 100 scale from (SF-36 subscale).

2° Symptom severity sum is the sum of severities for the 16 symptoms assessed at baseline.

97

evaluated in the next section. If differences among these cut points for symptom
severity are stable over successive intervention contacts then they may be used
to determine if the management interventions successfully reduce patient burden

of pain and fatigue.

5.2.2 Longitudinal Consistency of Cut-points for Pain and Fatigue

The question under examination is whether, while receiving interventions
to manage pain and fatigue, the established cut-points continue to represent
significantly different interference levels among patients over time. To use these
cut-points for measuring meaningful change in pain and fatigue it is necessary to
establish that these cut-points consistently differentiate among different levels of
interference during the intervention contacts. This section will examine the
magnitude of the difference in summed interference scores between moderate
and mild and severe and moderate categories of pain and fatigue at each of the
6 contacts.

The least square (LS) means of the summed interference scores reflecting
mild, moderate, and severe scores from the linear mixed model (See Equation
4.2) are presented across 6 intervention contacts in Table 5. The mean summed
interference scores for mild pain and fatigue are less than 5 and they are 15 or
greater for severe pain and fatigue across all contacts. In addition, the
examination of the magnitude of the differences between moderate and mild, and
severe and moderate categories consistently Show large differences across all

contacts. Table 5 contains the p-values for testing the equality of the means of

98

summed interference (H0: ,[1 =0)21 among the mild, moderate,

mi,t =’um0,t ='use,t
and severe categories at each intervention contact t. If the null hypothesis (H0)

is rejected, then the three categories can discriminate the summed interference
scores at contact t.

According to the estimated LS means for the summed interference scores
in Table 5, there are consistent differences in scores by severity level across
contacts. The estimated interference means in each severity level are similar
over time. For example, the interference mean in mild, moderate, and severe
fatigue are around 4, 7.5, 15, respectively, at most contact points. These results
indicate that there is a consistent and logical relationship between symptom level
and interference with milder symptom having lower interference scores. The
decline in the mean of summed interference score for the same severity category
is greatest between the first and second contact; and then no further significant
declines in interference occurred between contact 2 through 6. This pattern may
be due to a difference in the absence of intervention between the first contact
and the later contacts. At each contact, patients reported their symptom severity
and interferences first; and then they received interventions based on the
reported symptom severity. Therefore, the symptom severity and interferences
were measured at the first contact before receiving any intervention. Thus it is
possible that the declines observed between contacts 1 and 2 were a function of

the initial interventions. Because patients could receive any interventions after

 

21 [I . , ,1} , and [1 are the LS means of summed interference for mild, moderate,
mz,t mo,t se,t

severe categories at t-th contact

99

reporting their symptoms at the first contact, the intervention could affect the
severity and interference from the second contact. From contact 2 through 6, the
difference in interference among the mild, moderate, and severe categories
remained stable and distinct. However, the weight of evidence provided here
indicates a strong and sustained relationship between interference scores and
their corresponding symptom severity categories at all contacts.

Table 5 Estimated means and standards errors of summed interference

score across 6 intervention contacts by severity level of pain and fatigue*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

* Severity level is determined at each contact point

 

Summed Interference Score
Mean (Standard Error)

Pain Contact 1 Contact 2 Contact 3 Contact 4 Contact 5 Contact 6
Mild 5.5 (3.1) 1.4 (1.8) 5.3 (2.0) 5.7 (2.0) 6.5 (2.1) 5.2 (2.4)
Moderate 10.0 (1.0) 8.1 (0.9) 9.9 (0.9) 8.7 (0.9) 9.3 (0.9) 8.3 (1.0)
Severe 19.5 (0.8) 14.9 (1.0) 16.6 (1.1) 17.2 (1.1) 14.2 (1 .1) 16.5 (1.2)
P-value <.0001 <.0001 <.0001 <.0001 0.0003 <.0001 I
Fatigue Contact 1 Contact 2 Contact 3 Contact 4 Contact 5 Contact 6
Mild 2.3 (2.3) 4.8 (1.2) 3.8 (1.3) 4.2 (1.4) 4.1 (1.5) 2.9 (1.4)
Moderate 10.5 (0.6) 8.0 (0.5) 7.8 (0.5) 7.8 (0.5) 7.5 (0.5) 6.2 (0.5)
Severe 17.3 (0.4) 14.9 (0.5) 14.9 (0.6) 15.0 (0.6) 15.0 (0.6) 15.4 (0.7)

P-value <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

 

To use these categories (mild, moderate, severe) for evaluating change in
pain and fatigue, it is important that individual variations in interference scores
should be small, when patients remained in the same level of severity. I

calculated the individual differences of summed interference scores between the

100

second contact and later contacts when a severity level remained the same.
Because the association between severity and interference at contact 1 is
different than that at later contacts, I compared the summed interference scores
from contact 2 through 6. Figure 9 shows that distributions of differences
between the summed interference score at the second contact and at later
contacts within the same severity category (i.e. mild, moderate, or severe) over
time. The graphs shown in Figure 9 were created from the data that is pooled
across severity levels, however, there distributions were essentially the same
when the data were stratified by severity. The individual differences of
interference are symmetrically distributed around zero over time, when patients
remain at the same severity level. These distributions show that a large number
of patients report small differences in the summed interference scores at the
same levels of severity. The paired t-test was performed to test the equality of
summed interference scores between contacts at the same levels of severity for
each symptom. The test did not reject the null hypothesis that the summed
interference scores are equal at the same level of severity between contacts at
0.05 level of significant.

This consistent difference among mild, moderate, and severe categories
supports the use of these interference based severity cut-points to define
symptom response for three transitions: severe to moderate, severe to mild, and
moderate to mild. The severity of zero (absence of symptoms) was not included
in the mild category at each contact, because interference scores were not

recorded when the symptom was not present. However, additional shifts

101

including severe (2 5) and moderate (2—4) to zero severity should be considered
as meaningful change, and treated as a symptom response. Based on the
defined symptom response categories from this section, I will identify important
factors affecting time-to-response for pain and fatigue. This is presented in
section 5.3. Several survival methods will be implemented to cope with the

methodological problems discussed in Chapter 3.

102

Figure 9 Distributions of individual difference in summed interference

scores (0-40) within the same level of severity for pain and fatigue22

 

 

 

 

 

 

.. l _

25 /,,; N 218 Contact 2 Contact 3
20%J Mean 0.1

15% W

10%

5% _

0%

25%“ N 206 Contact 2 — Contact 4
20%: Mean -0.2

 

 

15%, Std Deviation 6.6

 

10%.
5% .
0% _

 

 

 

 

 

 

 

 

    
   
  
   

 

 

 

25% N 180 Contact2—Contact5
20%;) Mean -0.3

15%,; ”Std Deviation 7.2

10% -

5%

0% l

25% J N 174 Contact2—Contact6
20% I Mean . _ -1.3

15%) Std DeVIatIon 7.0

10%-

5% I

0% I

-40 -32 -24 -16 -8 0 8 16 24 32 40

 

22 Data were generated only among patients who reported the mild, moderate, or severe
categories at the second and each of later contacts

103

5.3 Evaluation of Time-to-Response for Pain and Fatigue Symptoms

Survival analysis is an appropriate technique to evaluate the time-to-
response in pain and fatigue incorporating censored observations due to lost to
follow-up. This section presents the results of unadjusted and adjusted analysis
of the time-to-response for pain and fatigue symptoms using several methods
each with different underlying assumptions. The primary exposure variables in
this research are age, depression, and comorbidity. These variables were tested
after adjusting for the following a priori confounders; gender, cancer site, physical

function, and trial type (A or B).

5.3.1 Estimated Survival Functions for Time-to-Response for Pain

and Fatigue

Among 601 patients who had the first contact, 212 (35%) and 451 (75%)
patients reported a severity of 4 or higher in pain and fatigue sometime between
the first and fifth contacts, respectively. By the end of the intervention contacts,
173 (81.6%) and 344 (76.3%) of these patients, achieved a response to pain and
fatigue (i.e. severe to moderate, severe to mild, or moderate to mild), respectively.
The number of days from the onset to response contact was recorded as time-to-
response. The number of days from onset to last contact without a response was
considered the censoring time.

Figure 10 shows the Kaplan-Meier survival function with 95% confidence

intervals for time-to-response for pain and fatigue in Trial A (dash) and B (solid).

104

The survival functions for pain and fatigue are very similar between the two trials.
Even though 6 intervention contacts were scheduled over 8 weeks, variations
were observed. For example, some patients received intervention contacts for up
to 66 days due to delays in the scheduled contacts. In Figure 10 the two survival
functions for pain (panel a) and fatigue (panel b) have large declines around 1
week after onset. Based on the Kaplan Meier estimates, the median time-to-
response for pain and fatigue are 13 and 14 days, respectively. That is, half of
cases with pain and fatigue responded within 2 weeks. About 10% of pain cases
were censored at the end of follow-up (i.e. these cases had not responded by the
6th contact). Therefore, the overall mean for pain cannot be calculated, and
therefore the restricted mean time23 of 19.5 days was alternatively used for pain
(See Figure 2 & 3 in Chapter 3.1.2). The estimated mean time-to-response in

fatigue is 24.2 days.

 

23 The restricted mean time is obtained by calculating an area under survival curve between zero
time and the maximum time to response.

105

Figure 10 Estimated survival function of time to response of pain and

fatigue24

 

 

10'

0.8‘

0.6*

0.4‘

0.2‘

 

 

 

Survival function of time-to-response

0.0‘. a . e . . .
0 10 20 30 40 50 60 70

1° "1

0.8‘

 

(a) Time to response for pain in days

 

 

0.6J

  

Trial B

   
 

TrialA
0.2j '

0.4‘

 

 

0.0. 2 s , . . . ,
o 10 20 30 40 50 60 70

 

Survival function of time-to-response

(b) Time to response for fatigue in days

 

2‘ Response is defined as a reduction of severity levels (i.e. severe to moderate, severe to mild,
or moderate to mild).

106

5.3.2 Testing for Time-to-Response by Assuming the Proportional
Assumption Holds

This section identifies significant factors associated with time-to-response
in pain and fatigue by assuming the proportional hazard assumption holds. The
log-rank, Wilcoxon test, and Cox proportional hazard model were implemented to
assess both unadjusted and adjusted effects. Patient age, depression, and
comorbidity were first assessed without adjustment for other covariates in
unadjusted analysis. In the multivariable model, each of the three covariates was
tested after adjusting for gender, cancer site, phySical function, and trial. Using
the model selection strategy described in Chapter 4, a final model was developed.

Figures 11, 12, and 13 show the estimated survival functions for time-to-
response for pain by age (60 or younger vs. older than 60), comorbidity (less
than 3 comorbid conditions vs. 3 + comorbid conditions), and depression (CES-D
< 16 vs. 16 +), respectively. In each of these figures, the estimated survival
functions are less than 0.8 after about 7 days, indicating that more than 20% of
subjects in pain responded within 7 days regardless of age, comorbidity, or
depression. None of the survival functions cross one another in Figures 11, 12,
and 13, supporting that the survival functions are likely to be proportional over
time. To test the proportional hazard assumption, an interaction term between
time and each covariate was tested in the Cox proportional hazard model. None
of these tests were statistically significant and therefore the null hypothesis of
proportional hazards for time-to-response in pain was not rejected (See Table 6).

By holding the proportional hazard assumption, Table 6 summarizes tests for

107

equality in survival functions of time-to-response in pain and fatigue by patient
characteristics using the log-rank test, Wilcoxon test, and Cox proportional
hazard model. The median time-to-response and 95% confidence intervals (Cl)
calculated from the Kaplan-Meier survival functions are presented for each level
of each covariate. All three methods identified age and comorbidity, as significant
factors associated with time-to-response for pain. Patients who were older than
60 year old (Median of time-to-response=14 days, 95% Cl=[14, 21]) had longer
time-to-response for pain than younger patients (median of time-to-response =10
days, 95% Cl=[9, 14]). Patients with 3 or more comorbid conditions (median time-
to-response=18 days, 95% Cl=[14, 21]) had a longer time-to-response for pain
compared to those with fewer than three comorbid conditions (median time-to-
response=9, days 95% Cl=[8, 10]). Patients who reported CES-D of 16 or higher
(median time-to-response=14 days, 95% CI=[10, 18]) had a little longer time-to-
response for pain compared with those who reported a less than 16 on CES-D
(median time-to-response=11 days, 95% Cl=[8, 14]), but this depression effect
was not significant in the log-rank test, Wilcoxon test, and the Cox proportional
hazard model.

Figures 14, 15, and 16 show the estimated survival functions for time-to-
response for fatigue by age, comorbidity, and depression, respectively. Fairly
similar survival functions were observed by age in Figure 14. The survival
functions by comorbidity categories (Figure 15) show that the median time to
response is 14 days for both levels of comorbidity. After this time point (14 days),

however, the difference between the two survival functions is greater than that

108

before the median time (14 days). The survival functions by depression almost
overlap across time (Figure 16). Tests of the proportional hazard assumption
using the interaction between time and a covariate conclude that all of covariates
satisfied the proportional hazard assumption. Table 6 shows that comorbidity
was the only factor associated with time-to-response in fatigue. Patients who
were 60 years old or younger (median time-to-response=14 days, Cl=[14, 15])
had same median time-to-response for fatigue compared with those who were
older than 60 years old (median time-to-response=14 days, Cl=[14, 21]). Patients
with fewer numbers of comorbid conditions (median time-to-response=14, days
CI=[13, 14]) had a shorter time-to-response compared with those with greater
than three comorbid conditions (median time-to-response=15 days, Cl=[14, 26]).
The comorbidity effect was significant in all three statistical methods despite of
the similarity of median time-to-response. Depression was not significantly
associated with time-to-response for fatigue; median response times were 14

days for all categories of depression.

109

Figure 11 Estimated survival functions of time-to-response in pain by age

 

 

       
    

 

 

 

1.0
0
(D
C
8 r
g 0.8
.6.
g 0.6 .
“5 .
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c - ...........
.2
g 0.2 . """""
g 60 or younger
(0
0.0 .1 . , , . . . .
0 10 20 30 40 50 60 70

Time-to-response for pain in days

Figure 12 Estimated survival functions of time-to-response in pain by

comorbidity
1.0 ‘ L1

0.8 ‘

 

 

0.6 ‘

 
  

"1; Comorbidity: 3+

0.4 4

0.2 .

 

Survival function of time-to-response

 

. . = <
000‘ Comorbidity 3

 

 

0 1'0 {0 30 40 50 60 7'0
Time-to-response for pain in days

110

L.

Figure 13 Estimated survival functions of time-to-response in pain by

depression

 

 

1.0

0.8 ‘

0.6 ‘

     

0.4 « '- -.
-;. CES-D: 16+

0.2. "
CES-D: <16

Survival function of time-to-response

 

0.0

 

 

 

0 1'0 20 3'0 4'0 50 60 70
Time-to—response for pain in days

Figure 14 Estimated survival functions of time-to-response in fatigue by age

 

1.0‘

0.8 ‘

0.6 i

0.44

02 4 60 or younger

 
 

'- .......... ._ . Olderthan 60

Survival function of time-to-response

 

 

0.0 ] .
0 10 20 30 4O 50 6O 70
Time-to-response for fatigue in days

 

111

Figure 15 Estimated survival functions of time-to-response in fatigue by

comorbidity

Survival function of time-to-response

y—a
O

0.8 ‘

0.6 *

0.4 .

0.2 .

0.0

 

 

 

Comorbidity: < 3

 

 

0 1'0 20 50 4'0 50

Time-to-response for fatigue in days

60

70

Figure 16 Estimated survival functions of time-to-response in fatigue by

depression

Survival function of time-to-response

1.0‘

0.8 '

0.6 4

0.4 .

0.2 ,

0.0

 

 

 

CES—D: <16

 

 

' 0 '10 '20 '30 '40 50
Time-to-response for fatigue in days

112

70

Table 6 Median time to response and unadjusted tests for time-to-response

for pain and fatigue by the log-rank, Wilcoxon, and Cox proportional model

M Wilcoxon Cox PH Test for

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

edian Log-
Time-to-Response in Pain (days) rank Model PH25
( 95% Cl ) P-value P-value P-value P-value
60 or younger 10 (9, 14)
Age .0190 .0293 .0293 .7476
Older than 60 14 (14, 21)
Less than 3 9 (8, 10)
Comorbidity <.0001 <.0001 <.0001 .1321
3 + 18 (14, 21)
Less than 16 11 (8, 14)
CES-D .0896 .1698 .1140 .9361
16 + 14 (10, 18)
. . Median Log- Wilcoxon Cox PH Test for
Tlme-tg-aliieslp:nse m (days) rank Model PH24
9 ( 95% Cl ) P-value P-value P-value P-value
60 or younger 14 (14, 15)
Age .6939 .4658 .7144 .3105
Older than 60 14 (14, 21)
Less than 3 14 (13, 14)
Comorbidity .0031 .0140 .0060 .4584
3 + 15 (14, 26)
Less than 16 14 (1'3, 15)
CES-D .3641 .6801 .3967 .4161
16 + 14 (14, 21)

 

 

 

25 They are the results of testing whether the hazards are proportional for each covariate.

113

The multivariate models for time-to-response in pain and fatigue are
shown in Table 7. The main effects including age, Comorbidity, and depression
are tested after controlling for a priori confounders such as gender, cancer site,
physical function, and trial in the final model. Only comorbidity remained as a
significant covariate for both pain (HR=1.70, 95% Cl=[1.18, 2.46]) and fatigue
(HR=1.32, 95% Cl=[1.02, 1.701). Patients who had lower number of comorbid
conditions (< 3) reported shorter time-to-response for both pain and fatigue.

. To see if there exists any covariate that has a different effect between
Trial A and B, I examined interaction effects between trial and each main effect in
both final models. None of the interactions were significant. In addition, the final
models were performed separately for Trail A and B. In the separate models, the
hazard ratios for other covariates including gender, cancer site, and physical
function were close to 1. The hazard ratios for comorbidity were greater than 1.3

in both models.

114

Table 7 Final models of time-to-response in pain and fatigue in the Cox

proportional hazard model

a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cox Proportional Hazard Model
Time-to-response in pain H.333? 95% Cl p-value
Age (60 yrs or less vs. > 60 yrs) 1.35 0.95, 1.90 .0909
Comorbidity (<3 vs. 3+) 1.70 1.18, 2.46 .0045
CES-D (<16 vs. 216) 1.18 0.83, 1.67 .3572
Gender (Male vs. Female) 1.21 0.80, 1.83 .3650
Cancer (Breast vs. Other) 0.94 0.63, 1.40 .9313
(Lung vs. Other) 0.94 0.62, 1.41
Physical function26 1.00 0.99, 1.01 .7651
Trial (Trial B vs. Trial A) 1.03 0.73, 1.43 .8778
Time-to-response in fatigue Higgtaigd 95% Cl p-value
Age (60 yrs or less vs. > 60 yrs) 0.92 0.73, 1.17 .4938
Comorbidity (<3 vs. 3+) 1.32 1.02, 1.70 .0359
CES-D (<16 vs. 216) 1.00 0.78, 1.27 .9831
Gender (Male vs. Female) 0.99 0.75, 1.31 .9698
Cancer (Breast vs. Other) 0.97 0.74, 1.28 .2738
(Lung vs. Other) 0.78 0.57, 1.06
Physical function 26 1.00 0.99, 1.01 .1635
Trial (Trial B vs. Trial A) 0.94 0.75, 1.17 .5637

 

 

 

 

 

5.3.3 Testing for Time-to-Response without Assuming the
Proportional Hazards assumption holds
Although the proportional hazard assumption holds for three main effects

of interest (age, comorbidity, and depression) in this data, this section will explore

 

26 It is 1 unit change in a standardized physical function score on a 0 to 100 scale from (SF-36
subscale).

115

to see how the results are changed when using alternative survival analysis
methods which do not require this assumption. Three recently proposed
methods: including the Lin 8 Wang’s test, a Cox model with weighted estimation
(WCM), and the Rahbar’s method were implemented to evaluate time-to-
response. The first 2 methods are available only for univariate analysis, but WCM
can be applied to multivariable analysis models. The three models, including the
Lin & Wang’s test, the WCM, and the Rahbar’s method, are available for both
proportional and non-proportional hazards. Since the proportional assumption
was satisfied, the Cox proportional hazard model appears to be valid, therefore
the WCM had the same result as the regular Cox proportional hazard model.
Table 8 summarizes the results of unadjusted tests for time-to-response
for pain and fatigue by the Lin & Wang’s test, the WCM, and the Rahbar’s
method. Interestingly, the Lin & Wang’s test produced fairly large p-values, but
failed to detect significant effects on time-to-response for pain and fatigue for
most covariates except comorbidity. The WCM produces results similar to those
produced by the Cox proportional hazard model in Table 6. The Rahbar’s method
produced different results than the other methods. This test identified age (p-
value=0.0004), comorbidity (p-value<.0001), and depression (p-value =0.0001)
as significant factors associated with time-to-response in pain. Rahbar’s test also
identified more significant covariates associated with time-to-response for fatigue
including age (p-value=0.0304), comorbidity (p-value =<.0001), and depression

(p-value=0.0014).

116

The smaller p-values generated by Rahbar’s test may occur due to
differences in the mean time-to-response. For example, in Figure 16 the
estimated survival functions of time-to-response for fatigue by depression level
are very close to each other until around 30 days. However, about 18% of
patients, who had a CES-D of less than 16, are censored at 55 days, while more
than 10% of patients, who had high depression, responded after 55 days. This
difference results in a smaller mean time-to-response in fatigue in patients with
low depression compared with those with high depression, and produces a
significant p-value in the Rahbar’s test.

The final multivariable WCM is not presented in this section, because the
WCM is essentially identical to the Cox proportional hazard model when all

covariates have proportional hazards.

117

Table 8 Unadjusted tests for time-to-response in pain and fatigue by the Lin

& Wang's test, the WCM, and the Rahbar's method

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Median .
Time-to-Response in Pain (days) US$33? 532?: Pail“: e
( 95% Cl )
60 or younger 10 (9, 14)
Age .6599 .0004 .0425
Older than 60 14 (14, 21)
_ . Less than 3 9 (8, 10)
Comorbidity <.0001 <.0001 <.0001
3 + 18 (14, 21 )
Less than 16 11 (8, 14)
CES-D .8106 .0001 .2023
16 + 14 (10, 18) -
Time-to-Response in “3:33? Lin&Wang Rahbar WCM
Fatigue ( 95% Cl ) P-value P-value P-value
60 or younger 14 (14, 15)
Age .9343 .0304 .521 1
Older than 60 14 (14, 21 )
Less than 3 14 (13, 14)
Comorbidity .4697 <.0001 .0206
3 + 15 (14, 26)
Less than 16 14(13, 15)
CES-D .2830 .0014 .6976
16 + 14 (14, 21 )

5.3.4 Testing for Time-to-Response of Pain and Fatigue with Interval
Censoring Type

In Section 5.3.2 and 5.3.3, all the methods account for right-censoring for

time-to—response. However, since patients were monitored over two weeks at

scheduled contact times, the date of contact during which patients reported

response to the symptom may not correspond to the exact date of the response.

Because the symptom response occurred between the prior contact and the

current contact, time-to-response has an interval form. Thus, there is a question

118

as to how the findings from methods using right-censored data differ from those
that account for interval censored time. To answer this question, the Accelerated
Failure Time (AFT) model was implemented with interval time-to-response in
pain and fatigue.

The results from the final multivariable models are summarized in Table
9. In contrast to the results of the Cox proportional model, age (TR=0.67, 95%
CI=[0.46, 096]) and comorbidity (TR=0.56, 95% CI=[0.38, 0.821) have significant
effects in the final multivariable AFT model for pain. In this model, not only low
comorbidity, but also younger age is associated with shorter time-to-response for
pain. The AFI' model of time—to-response for fatigue shows similar results to the
Cox proportional model. Only comorbidity is significantly associated with time-to-
response.

To test for differential effects between Trial A and B, I examined the
interaction effect between trial and the three main effects on time-to-response for
pain and fatigue in these AFT models. None of these interactions was significant
which indicates that the identified effects did not differ between the two trials.
Furthermore, when two separate models were generated for Trial A and B, the
effects of the covariates are similar to the results shown in Table 9. Therefore,
the difference between Trial A and B did not influence the results from the final

multivariable AFT model.

119

in the AFT model with interval censoring

Table 9 Final multivariable models of time-to-response in pain and fatigue

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Accelerated Failure Time Model
Time-to-response in pain 2318:2222: 95% Cl p-value
Age (60 yrs or less vs. > 60 yrs) 0.67 0.46, 0.96 .0289
Comorbidity (<3 vs. 3+) 0.56 0.38, 0.82 .0031
CES-D (<16 vs. 216) 0.68 0.47, 0.98 .0405
Gender (Male vs. Female) 0.63 0.41, 0.97 .0343
Cancer (Breast vs. Other) 0.87 0.55, 1.37 .7862
(Lung vs. Other) 0.89 0.59, 1.34
Physical function27 1.00 0.99, 1.01 .6637
Trial (Trial B vs. Trial A) 1.05 0.74, 1.51 .7722
Time-to-response in fatigue 1:38:33; 95% Cl p-value
Age (60 yrs or less vs. > 60 yrs) 1.18 0.91, 1.53 .2030
Comorbidity (<3 vs. 3+) 0.75 0.56, 0.99 .0411
CES-D (<16 vs. 216) 0.92 0.70 1.20 .5274
Gender (Male vs. Female) 0.95 0.70, 1.20 .7597
Cancer (Breast vs. Other) 0.90 0.67, 1.22 .4979
(Lung vs. Other) 1.13 0.82, 1.57
Physical function28 1.00 0.99, 1.00 .2303
Trial (Trial B vs. Trial A) 1.11 0.87, 1.41 .4098

 

 

 

 

5.3.5 Testing for Time-to-Response in Pain and Fatigue while
considering the correlation between the two symptoms

Effect of comorbidity was statistically significant in the three different

modeling strategies in Sections 5.3.2, 5.3.3, and 5.3.4. The previous models

were developed separately for pain and fatigue. Because of the correlations

 

27 It is 1 unit change in a standardized physical function score on a 0 to 100 scale from (SF-36
subscale).

120

between pain and fatigue within an individual, the subjects included in the models
for pain and fatigue are not independent. The validity of the statistical inference
for the two Cox proportional hazard models for pain and fatigue could therefore
be questioned because these time-to-response outcomes are correlated. Th
marginal Cox model is able to account for the correlations between outcomes
within an individual. The main advantage of the marginal Cox model is that it
avoids the inflation of type I errors that occurs when running two separate models
for pain and fatigue. Therefore, the marginal Cox model incorporating the
correlation between pain and fatigue within an individual was used. The marginal
Cox model can include multiple outcomes (i.e., response for pain and fatigue) for
each patient and accounts for the correlation between pain and fatigue (See
Chapter 3.5).

Because the marginal Cox model includes coefficients of each covariate
for both pain and fatigue, the difference in the covariates between pain and
fatigue can be tested. Based on the results of an equality test in the adjusted
models, age (p-value=0.0848), comorbidity (p-value=0.1237), and depression (p-
value=0.3541) were not significantly different and thus do not have significant
different effects on the time-to-response for pain and fatigue. Therefore, using
one coefficient for each covariate in the final model was appropriate strategy.
The coefficients in Table 10 represent the common effect of each covariate on
time-to-response on both pain and fatigue. This model also indicates that only
comorbidity (HR=1.36, 95% Cl=[1.11, 1.67]) is significantly associated with time-

to-response.

121

Table 10 Final model of time-to-response in the marginal Cox model

fl

 

 

 

 

 

 

 

 

 

 

 

 

 

”[323.“ Corfig/eonce p-value
atlo Interval

Age (60 yrs or less vs. > 60 yrs) 0.96 0.79, 1.17 .7183

Comorbidity (<3 vs. 3+) 1.36 1.11, 1.67 .0030

CES-D (<16 vs. 216) 0.96 0.79, 1.17 .7115

Gender (Male vs. Female) 1.04 0.82, 1.33 .7391

Cancer (Breast vs. Other) 0.99 0.79, 1.24 .4475

(Lung vs. Other) 0.86 0.68, 1.09
Physical function28 1.00 0.99, 1.01 .1440
Trial (Trial B vs. Trial A) 0.94 0.77, 1.13 .5045

E

In the final mode, none of the other covariates (gender, cancer site,
physical function, and trial) representing differences between Trial A and B are
significant. Additionally, I also examined interactions between the indicator
variable for trial (Trial A vs. B) and each covariate, and none was significant. In
separate models for Trial A and B, the magnitude of the comorbidity effect
(HR=1.42, 95% Cl=[1.11, 1.821) in Trial A is not seriously different from that

(HR=1.34, 95% CI=[0.98, 1.831 ) in Trial 8.

 

28 It is 1 unit change in a standardized physical function score on a 0 to 100 scale from (SF-36
subscale).

122

5.3.6 Diagnostic assessment of the final model

To undertake a diagnostic assessment of the final multivariable models
including the Cox proportional hazard model, the AFT model, and the marginal
Cox model, Cox-Snell residuals were estimated (See Chapter 4.3.7). The
residual plots from the Cox proportional hazard model, the marginal Cox model,
and the AFT model are presented in Figure 17 (panel a, b, and c), respectively.
Because the plots are very similar for pain and fatigue for the same models, I am
presenting only plots for pain. The Cox proportional model (panel a) and marginal
Cox model (panel b) have a faidy straight line with a slope of one and zero
intercept. These residual plots indicate that these two models fit the data fairly
well. Although the plot of Cox-Snell residuals for the AFT model (panel c) is not
straight as much as the Cox proportional hazard model and marginal Cox model
(panel a and b), it is fairly linear line with a slope of one and zero intercept.

Therefore, the results from the AFT model is also acceptable.

123

Figure 17 Cumulative hazard plot of the Cox-Snell residuals for three final

models

Cumulative hazard of residual

Cumulative hazard of residual

 

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Cox-Snell Residual

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(b) Marginal Cox model

124

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(c) AFT model with interval censoring

5.3.7 Recurrence of pain and fatigue

In this study, a symptom response is defined as the first episode of lower

response for pain and fatigue.

However, symptoms can obviously revert after an initial response (i.e.

125

symptom severity level after onset (i.e. severe to moderate, severe to mild, or
moderate to mild). That is, time-to-response was measured from time of onset to
time of first response. As the results from several survival models show, we

found that low comorbidity is significantly associated with shorter time of first

recurrence). For example, a patient who responded to pain at third contact could
have severe pain again (i.e. recurrence of pain) at next contact. Thus this patient
could have two episodes of response during the follow-up period. In this study,

we ignored recurrent episodes thus the main effects were assessed only for the

first episode of response. The effects of multiple episodes on the results are
unkown and would require a new analysis.

Table 11 is a summary of recurrence by covariates and the results of
testing (Chi-square test), if recurrent cases are associated with any covariate.
Thirty-four (16%) and eighty five (19%) of patients reported recurrence of pain
and fatigue symptoms, resepectively, after initially responding. There is no
significant difference in the recurrence of pain and fatigue between Trial A and B.
Although a little more recurrences of pain occurred in younger and lower
comorbidity groups, there is no significant difference in any of the covariates.
Therefore, the recurrent symptoms would not seriously affect the covariate

effects on time-to-response.

126

Table 11 Recurrence of pain and fatigue after responding to first episode of

 

 

 

 

 

 

 

 

 

 

 

 

 

pain or fatigue
Recurrence No recurrence P-values
Pain N=34 N=178 .
. (N (%)) (N (%)) (Chi-square Test)

Age

< 60 yrs 26(19.0) 111 (81.0) 01148
60 yrs + 8 (10.7) 67 (89.3) '
Comorbidity

Less than 3 23 (19-3) 96 (80.7) 0 1398
3 + 11 (11.8) 82 (88.2) '
Depression

Less than 16 16 (13.8) 100 (86.2)

16 + 18 (18.7) 78 (81.3) 03276
Trial

Trial A 21 (17.5) 99 (82.5)

Trial B 13 (14.1) 79 (85.9L 0'5076

Recurrence No recurrence P-values
Fati ue N=85 N=366 .
9 (N (%)) (N (%)) (Chi-square Test)

Age

< 60 yrs 50 (17.9) 230 (82.1) 0 4916
60 yrs + 35 (20.5) 136 (79.5) '
Comorbidity

Less than 3 52 (18-8) 225 (81-2) 0 9593
3 + 33 (19.0) 141 (81.0) '
Depression

Less than 16 54 (13-4) 239 (18-6) 0 7578
16 + 31 (19.6) 127 (80.4) '

Trial

Trial A 56 (19.9) 226 (80.1)
___Trial B 29 17.2 140 82.8 0'4782

 

In summary, comorbidity has a strong independent effect on time-to-
response in pain and fatigue among cancer patients undergoing chemotherapy.
This result is consistent across different survival analysis methods. The
proportional hazard models, including both the Cox proportional hazard model
and the marginal Cox model, had a good model fit. The AFT model which
handles interval censoring detected additional significant variable (i.e. age) on
time-to-response for pain. The marginal Cox model provided an estimate of the
overall effect of comorbidity (HR=1.36, 95% Cl=[1.11, 1.671) on time-to-response
for both pain and fatigue when considering correlation between the two
symptoms for each patient. In this data, low comorbidity was consistently
associated with shorter time-to-response for both pain and fatigue with and
without adjustment. Younger age was also statistically associated with shorter
time-to-response for pain in both adjusted and unadjusted models. However,
because younger age is associated with lower comorbid conditions, the effect of
age was less significant when adjusting for comorbidity. Therefore, younger
cancer patients who have a fewer comorbid conditions respond to their pain and

fatigue in shorter time while they receive symptom managements.

128

CHAPTER 6 DISCUSSION

This research identified important factors associated with time-to-response
for pain and fatigue among cancer patients undergoing chemotherapy. When
assessing change in symptoms, it is important to know how to evaluate clinically
meaningful changes in symptoms and what criteria to apply to assess which
survival analysis methods are more appropriate in evaluating symptom response.
This study demonstrates a process for evaluating clinically meaningful responses
of pain and fatigue and compared alternative surviVal analysis models to
evaluate time-to-response. In this chapter, I will discuss and summarize the
following points: 1) potential biases associated with combining data sets from two
trials 2) evaluation of clinically meaningful changes in the severity of each
symptom, 3) use of survival analysis to asses time-to-response among
symptoms and conclude with an assessment of the conditions under which each

survival technique would be appropriate for use.

6.1 Considering Potential Bias from Combining Data Sets

Although pain and fatigue are relatively prevalent symptoms among
cancer patients, the number of patients with symptoms reaching threshold
(severity of 4 or greater) in pain and fatigue was not large in each of the trials. To
gain larger sample size for increasing the statistical power, I used cases of pain

and fatigue from two trials. The two trials were performed with identical timelines

129

and study designs. However, Trial A required the presence of a caregiver as one
of entry criteria. More male patients were assigned to Trial A because mene were
more likely to have a spouse who could act as a caretaker. More female patients
were assigned to Trial B because they were less likely to have a spouse at home.
Thus as a consequence of the different entry criteria, the higher proportion of
male patients in Trial A increased the number of lung cancer patients in Trial A,
and the higher proportion of women in Trial B resulted in more breast cancer
patients being assigned in Trial B. The differences in cancer types between the
trials resulted in more males and lower physical functioning in Trial A. These
differences can lead to different survival functions for time-to-response for pain
and fatigue between the two trials, which, also, may call into question the wisdom
of combining data from the two trials.

Survival distributions for pain and fatigue were very similar between Trial
A and B, and the coefficients for the trials (Trial A vs. B) were not significantly
different in any of the survival models. This indicates that patterns of response in
pain and fatigue are not different between Trial A and B. Only small changes in
the hazard ratios and response time ratios were observed after controlling for site
of cancer and other covariates. In addition, it was useful to compare the stratified
hazard ratios by sites of cancer. The hazard ratios and their confidence intervals
largely overlapped among patients with breast, lung, and other cancer sites (This
is not presented in the result section.) For example, the hazard ratios for
comorbidity for response in fatigue are 1.31 (95% CI=[0.87, 1.971) for breast

cancer, 1.45 (95% CI=[0.84, 2.491) for lung cancer, and 1.20 (95% CI=[0.83,

130

1.741) for other sites. Thus, despite differences in gender, site of cancer, and
physical function between Trial A and B, these factors were not significantly
associated with time-to-response for pain and fatigue. Further, there is no
evidence that these factors modified or confounded the effects of age,
comorbidity, and depression on time-to-response. Because the similar patterns of
survival curves were observed between two trials in this study, it would be
enough to examine the covariate effects after adjusting for the difference

between trials.

6.2 Evaluating Clinically Meaningful Change on Symptom Severity

In this section, I discuss the first research question (Aim 1); can clinically
meaningful changes in pain and fatigue symptoms be measured using the four
dimensions of interference to define clinically meaningful cut-points that separate
levels of symptom severity. To evaluate the effectiveness of symptom
management it is important to use appropriate measures that are sensitive to
detecting meaningful changes in symptoms. Kirshner and Guyatt (134) provided
a guideline that create such measures in clinical medicine or the social science.
They classified three types of measures by their purposes including
discrimination, prediction, and evaluation. They define an “evaluative measure”,
as an instrument used to measure the individual or group change in a dimension
of interest overtime. Based on their guideline (134), I will review the categories

of symptom severity (mild, moderate, severe) as an evaluative measure in terms

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of item selection, item scaling, internal consistency, reliability, validity, and
responsiveness.

First, an instrument should include items that represent clinically
meaningful effects of interventions (item selection). The categories of mild,
moderate, and severe are constructed using a combined interference score to
separate severity measures into clinically meaningful categories. In the trials from
which these data were drawn interventions were delivered to patients to reduce
symptom severity. Successful reductions in symptom severity should lower
interference with respect to patients’ daily lives (135). That is, the changes in
these interference items can represent the effect of interventions on reducing the
severity of symptoms. Therefore, all items used satisfy the criterion for an
evaluative measure.

Second, a scale should be sensitive to clinically important improvement or
deterioration (item scaling). Usually a finer scale (0 to 10) than the threefold
classification (mild, moderate, severe) is preferred as a evaluative measure (134).
However, the absolute differences on a 0 to 10 scale of severity may not always
represent an equal level in improvement or deterioration in interferences (80).
Therefore, it is possible that there is no significant improvement in interferences
while a patient lowers the severity of symptoms from 9 to 7. Although a 0 to 10
scale is more sensitive than the threefold classification, it does not have a clear
threshold to identify clinically meaningful changes. According to Table 4 in
Chapter 5, this threefold classification successfully discriminates the physical

functioning, severities of other symptoms, as well as the summed score for

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comparing the four items of the interference scale. The categories of mild,
moderate, and severe may be sufficiently sensitive to clinically important
changes and provide clear definitions and interpretations.

Third, Kirshner and Guyatt (134) suggest that all items in an evaluative
instrument be internally consistent. The four interference items (emotion,
relationship with others, daily activities, and enjoyment life) have consistently
high correlations overtime. The internal consistency among these items can be
proved using the Cronbach’s alpha”. Very high Cronbach’s alpha (around 0.9)
was observed at each of the 6 contacts. That is, it can be interpreted that about
90% of variance in the hypothetical measure (i.e., overall interference with
patient’s life) would be explained by these observed items. Therefore, the four
interference items satisfy the criterion of internal consistency for evaluative
measure.

Fourth, the replicated observations on each individual patient should
remain stable over time (reliability). The evaluative measures need to remain
small in magnitude on the within-patient variance (individual variance of repeated
measures), while the discriminative measures focus on maximizing the between-
patient variance. Figure 9 in Chapter 5 shows the distributions of differences in
interference sums within patients whose severity category are very similar
compared with previous contacts. These distributions which are symmetric
around zero indicate small differences in interferences within a patient. That is,

the expectation of differences in interference sum is zero when patients retain the

 

29 Cronbach’s alpha is a statistic on a 0 to 1 scale used to measure the consistency of multiple
items in an instrument. When items are highly consistent, Cronbach's alpha is close to 1.

133

same level of severity. However, some large differences are observed in
relatively small numbers of patients. These large differences occur, because
interference may be associated with not only symptom severity but also with
other psychological or environmental factors. In this study, these large
differences are not associated with age, gender, cancer type, comorbidity, and
depression at baseline. Further research needs to assess what other factors
might explain these changes in interference that occur within patients overtime.
Fifth, Kirshner and Guyatt (134) suggest that the measures need to be
compared with some global standard methods for validity. The categories of mild,
moderate, and severe are constructed by modifying the globally used
instruments (Brief Pain Inventory (BPI) and Brief Fatigue Inventory (BFI)) whose
validity has been proved (4, 88). This study proposed the severity of 2 and 5 as
cut-points for categorizing mild, moderate, and severe in both pain and fatigue. In
previous studies, Serlin et al. (80) proposed the cut-points of 5 and 7 for the
categories in pain, and Mendoza et al. (4) proposed the cut-points of 4 and 7 for
the categories in fatigue in cancer patients. These higher cut-points may be
explained by the fact that these methods used the multivariate analysis of
variance (MANOVA) to find the cut-points of severity in symptoms. This analytical
technique assumes a normal distribution of interference items. In this study,
however, interference sums were highly skewed to right and thus the generalized
linear model with a gamma distribution was used to take into account the skewed
distribution. This difference could lower the cut-points in this study below those of

previous studies.

134

In this research the interference scale developed to establish interference
based cut-points across the ten-point severity scale meet all five evaluation
criteria set out by Kirshner and Guyatt (134). As a result, this scale represents a
psychometrically sound indicator for separating meaningful interference based
categories for defining severity, and its change (response) to interventions for

managing pain and fatigue.

6.3 Applying Survival Analysis in the Assessments of Symptom

This study demonstrates application of survival analysis techniques in the
assessment of pain and fatigue among cancer patients. Unlike survivorship or
resolution of disease, more considerations and limitations exist, when using
survival analysis models in symptom assessments. In this section, I discuss
research questions (Aim 2 to 5) regarding the applications of survival analysis

techniques.

Survival analysis under the proportional hazard assumption

There is the question as to which factors are predictors of time-to-
response in pain and fatigue among cancer patients when using survival analysis
techniques that require the assumption of proportional hazards (Aim 2). To obtain
an answer for this question, we need to examine the proportional hazard
assumption and to understand the distinctions among the three survival analysis

methods which require the proportional hazard assumption.

135

In this study, the proportional hazard assumption was examined by
assessing the interaction between time and each covariate in the Cox
proportional hazard model. However, there are other methods for examining the
proportional hazard assumption using graphical comparison and residuals rather
than the interaction between time and each covariate in the Cox proportional
hazard model (105, 136—139). The graphical method plots the cumulative hazard
functions between groups. If the proportional hazard holds, then the log-
cumulative hazard functions between groups with different levels of a covariate
are parallel across log of time-to-response. Also, GrambSch and Themeau (140)
proposed the use of Schoenfeld residuals for testing the proportionality. In recent
research, Ng'andu (138) compared the power of detecting non-proportional
hazard with these methods and found that the method using the interaction
between time and covariate have equally reliable power compared to the other
methods.

As long as the proportional hazard assumption holds, we need to
understand the distinctions among the log-rank test, the Wilcoxon test, and the
Cox proportional hazard model. In this study these three survival analysis
methods had fairly consistent results that found significant effects of age and
comorbidity on time-to-response for pain and comorbidity effects on the time-to-
response for fatigue. In univariate analysis, the log-rank test is essentially the
same as the partial likelihood function for the Cox proportional hazard model
when there are no individuals having exactly the same time-to-event (105). In

this study, fairly similar p-vales were obtained for the log-rank test and Cox

136

proportional hazard model. Ignorable differences in the p-values between the two
methods may be due to the fact that several patients reported symptom
responses at exactly the same time. It is known that the Wilcoxon test is more
sensitive to differences in survival functions as time-to-response closes to zero
(more number of individuals at risk) (105). However, the Wilcoxon test also
produced similar p-values with the two methods. If investigators are more
interested in the difference of time-to-response within relatively short periods
then, the Wilcoxon test would be a better option. Regardless of these differences,
the same results were obtained from these three methods using the univariate
analysis.

In this study, the proportional hazard assumption holds for all covariates
and only comorbidity has significant effect on time-to-response for both pain and
fatigue in the final multivariable Cox proportional hazard model. It is possible that
comorbidity is one of mediators between age and time-to-response for pain and
fatigue. Based on the definition of a mediator that Baron and Kenny described
(141), we can assess possibility of a mediation effect of comorbidity between age
and time-to-response for pain. Baron and Kenny proposed that a mediator
variable should satisfy the following conditions; 1) the predictor (i.e. age) causes
the mediator variable (i.e. comorbidity), 2) the predictor is significantly associated
with the outcome (i.e. time-to-response) without the mediator, 3) the mediator is
significantly associated with the outcome without the predictor, 4) the predictor
has smaller effect on the outcome in the model adjusting for the mediator than

the model not adjusting for it. In several previous studies, it has been observed

137

that elderiy patients are more likely to have high risk of comorbid conditions and
late stage cancer (53, 58, 59). The significant effects of age and comorbidity on
time-to-response for pain were observed in univariate analysis. The age effect
was not significant after adjusting for comorbidity. Tein and Mackinnon (142)
propose a method for estimating mediation effect with survival data. However,

more research is needed to obtain a reliable confidence interval for this estimator.

Survival analysis ignoring the proportional hazard assumption

Second, the next question (Aim 3) was; whether findings based on
survival analysis techniques that were appropriate for the proportional hazards
assumption hold when using alternative survival techniques (the Lin & Wang’s
test, the Rahbar’s test, and the Cox model with weighted estimation (WCM)) that
do not require the proportional hazard assumption. Because the proportional
hazard assumption holds for all covariates, it is not necessary to use these
alternative methods in this study. The proposed methods (the Lin & Wang’s test,
the Rahbar’s test, and the WCM) are available for both proportional and non-
proportional hazards. It is worthy to discuss how differently these methods result
compared to the log-rank, Wilcoxon, and Cox proportional hazard model.

Because the proportional hazard assumption held in this study, there was
no difference between the Cox proportional hazard model and WCM. Because
the WCM is a generalized form of the Cox proportional model to allow for the
inconsistent hazard rates, the WCM produced similar results to the Cox

proportional hazard model.

138

The Lin & Wang’s test and Rahbar’s method are available for both
proportional and non-proportional hazards. However, there are some restrictions
using these methods to assess our data. The Lin & Wang’s test did not identify
any significant effect of covariates (i.e’. age, comorbidity, and depression) while
the Rahbar’s method and the WCM found significant effects of age and
comorbidity. It is because large variances occur when large numbers of events
(responses) occur at exactly same time. This negative aspect of Lin & Wang’s
test was not identified in their original study (107). The Rahbar’s test had
relatively very small p-values compared to other methods, because this method
tests for mean survival time while other methods tests for survival functions. Test
of mean survival time is relatively sensitive to small numbers of subjects with
extremely long time-to-response (outliers) compared with that of survival function.
The survival functions between age groups (Figure 14) or depression groups
(Figure 16) are not significantly different until 55 days. Approximately 15% of the
patients who were older or more depressed reported a response to their fatigue
or were censored between 55 and 65 days. However, the patients who were
younger or less depressed were censored at around 55 days. That is, the
differences of survival functions were observed only between 55 and 65 days.
The Rabhar’s method is sensitive to this difference while other methods ignore
that. Therefore, the Rabhar’s method produced smaller p-values than others.
Regardless of these differences, the significant comorbidity effect on time-to-
response for pain and fatigue and the significant age effect on time-to-response

for pain were observed using these alternative methods.

139

Survival analysis for interval censoring

The third, question was; whether the findings based on survival analysis
techniques that were appropriate for right censoring hold when the Accelerated
Failure Time (AFT) model is used that accounts for interval censoring. In this
study, patients reported their experience with symptoms, such as severity,
duration, and interference, during the past 7 days. Given that, the exact time of
response cannot be observed, the time-to-response is observed at intervals. For
example, if one patient reports severe pain over 3 weeks and reports mild pain at
the 4th week, then the time of response occurs between the 3ml and 4th week from
the onset of the symptom. The AFT model incorporating interval censoring was
used for this study and the finding was similar to the Cox proportional hazard
model. One reason for the similar results between the AFT model and the Cox
proportional hazard model is thatthe lengths of interval censoring are equal
around 7 days in most cases due to prescheduled contacts. The other reason is
the length of interval censoring is relatively small compared with the mean time-
to-response. For example, the estimated restricted means of time-to-response
are around 20 and 24 days for pain and fatigue, respectively. Therefore,
difference within a length of interval censoring (one week) may not change the
covariate effect compared to the Cox proportional hazard model with right-
censored data. If the length of time between contacts is longer or is not
scheduled on a consistent time interval, then in future research, it is worthy to
compare the results from the Cox proportional hazard model and AFT model

incorporating interval censoring.

140

Survival analysis for correlated events

Finally, the last question was; whether the findings from the separate
models of pain and fatigue (the Cox proportional hazard model, the Cox model
with weighted estimation, and the Accelerated Failure Time model) hold when
using the Cox marginal model that accounts for the correlation between the two
symptoms (pain and fatigue). Because pain and fatigue are highly correlated, the
response for pain may be very close to that for fatigue within the same individual.
For example, when a patient has a response to pain, he/she may, subsequently,
experience a lower level of fatigue. Therefore, the time-to-response varies by
individual characteristics rather than type of symptoms (pain or fatigue), and this
trend resulted in fairly similar final models between pain and fatigue. The
marginal Cox model determined if individual characteristics differentially affect
time-to-response for pain and fatigue when considering a correlation between the
two symptoms. This model consistently showed that comorbidity has a significant
effect on time-to-response for both pain and fatigue with larger sample size.

In these data, I did not see considerable limitations from the non-
proportional hazard or interval censoring models. Therefore, the marginal Cox
model can provide the most reliable final model by incorporating the correlation
between pain and fatigue. Although the limitations regarding survival analysis
(Aims 2 to 5) did not seriously affect the final models in these data, this study
shows what important assumptions need to be considered to use survival
analysis techniques for assessing symptom response and what restrictions the

used survival analysis methods have. The final models revealed a consistently

141

strong effect for comorbidity on time-to-response for pain and fatigue under the
different conditions in terms of proportional hazard, interval censoring, and
correlation between pain and fatigue. In these data shorter time-to-response for
pain and fatigue among cancer patients who had fewer comorbid conditions
could be due to less severe pain, fatigue, and other symptoms (21, 43) and more
adherence to treatments (52, 65, 66) than those patients with more comorbid
conditions. Because cancer patients who had fewer comorbid conditions may
have fewer other symptoms that need to be managed, their responses to
management strategies for pain and fatigue are less likely to be interfered with
due to the lower overall symptom burden compared with patients who had
several comorbid conditions. Patients who had fewer comorbid conditions could
continue to follow strategies that the nurses or coach provided while the patients
who had more comorbid conditions might have greater difficulty adhering to the
larger numbers of interventions. Assuming the effectiveness of symptom
management in achieving symptom responses, more comorbid conditions may
interfere with adherence to symptom management thus reducing their
effectiveness in producing symptom response. These differences could result in
more effectively responding for pain and fatigue among patients with fewer
comorbid conditions.

There is a potential that patients’ age can be a confounding factor
between comorbidity and time-to-response for pain and fatigue. However, the
hazard ratios for comorbidity were not changed before and after adjusting for age.

The hazard ratios for comorbidity without adjusting for age are 1.81 (95%

142

Cl=[1.26, 2.591) and 1.28 (95% Cl=[2;01, 1.641) in pain and fatigue, respectively.
After adjusting for age, the hazard ratios are 1.70 (95% Cl=[1.18, 2.461) and 1.32
(95% Cl=[1.02, 1.701) which are quite similar to the hazard ratios prior to
adjustment. Therefore, comorbidity appears to be a main effect and is not altered
to any appreciable extent by age as a confounding effect. Symptom management
for pain and fatigue in cancer patients needs to consider more intensive

strategies for older patients who experience more comorbid conditions.

143

Appendix A The Symptom Assessment at Intervention Contact (Example
for Pain)
PATIENT SYMPTOMS - PT VERSION

The next questions ask about the symptoms you have experienced in the past 7
days due to cancer or its treatment, and how they may have affected you.

1. During the past 7 days. on how many days did you experience pain?

(If 0 skip to question 2)
0 1 2 3 4 5 6 7
Not present days

A. On a scale of 0=not present to 10=the worst it could be. how severe is pain

(for you)? .
0 1 2 3 4 5 6 7 8 9 10
Not present worst possible

B. Please rate your pain by telling me the one number that best describes your
pain at its WORST in the past 7 days.
0 1 2 3 4 5 6 7 8 9 10
No pain as bad as you can imagine

C. Please rate your pain by telling me the one number that best describes your
pain at its LEAST in the past 7 days.
0 1 2 3 4 5 6 7 8 9 10
No pain as bad as you can imagine

D. Please rate your pain by telling me the one number that best describes your
pain at its AVERAGE in the past 7 days.
0 1 2 3 4 5 6 7 8 9 10
No pain as bad as you can imagine

E. In the past seven days, how much reliefs have pain treatments or
medications provided? Please tell me the one percentage that most
represents how much reliefs you have received.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
No relief complete relief

F. On a scale of 0=did not interfere to 10=completely interfered, overall, how
much did pain interfere in your life?
0 1 2 3 4 5 6 7 8 9 10
Did not interfere completely interfered

144

. Tell me the one number that describes how, during the past 7 days, pain has
interfered with your GENERAL ACTIVITIY

0 1 2 3 4 5 6 7 8 9 10
Did not interfere completely interfered

. Tell me the one number that describes how, during the past 7 days, pain has

interfered with your MOOD
0 1 2 3 4 5 6 7 8 9 10
Did not interfere completely interfered

Tell me the one number that describes how, during the past 7 days, pain has
interfered with your WORKING ABILITY

0 1 2 3 4 5 6 7 8 9 10
Did not interfere completely interfered

. Tell me the one number that describes how, during the past 7 days, pain has

interfered with your NORMAL WORK (includes both work outside the home
and housework)

0 1 2 3 4 5 6 7 8 9 10
Did not interfere completely interfered

. Tell me the one number that describes how, during the past 7 days, pain has
interfered with your RELATIONS WITH OTHER PEOPLE

0 1 2 3 4 5 6 7 8 9 10
Did not interfere completely interfered

. Tell me the one number that describes how, during the past 7 days, pain has

interfered with your SLEEP
0 1 2 3 4 5 6 7 8 9 10
Did not interfere completely interfered

. Tell me the one number that describes how, during the past 7 days, pain has
interfered with your ENJOYMENT OF LIFE
0 1 2 3 4 5 6 7 8 9 10

Did not interfere completely interfered

145

Appendix B SAS macros

SAS Macro for the log-rank, Wilcoxon, and Ling 8. Wang’s test

%Macro LinTest(Var=,Symptom=);

DATA Sample; Set Main(Keep= timet &VAR CENSOR Symptom
where:(Symptom="&Symptom"));

KEEP 2 D G;

Z=time1;

D=Censor;

G=&Var;

PROC RANK DATA=SAMPLE 0UT=SAMPLES TIES=LOW;
VAR z; RANKS Kz; RUN;

PROC FREQ DATA=SAMPLES NOPRINT;
WHERE 6:1; TABLE KZ / NOPERCENT 0UT=T1 OUTCUM;

DATA T1;SET T1; KEEP KZ N1;N1=COUNT; RUN;

PROC FREQ DATA=SAMPLES NOPRINT;

WHERE G=2; TABLE KZ / NOPERCENT OUT=T2 OUTCUM;
DATA T2;SET T2; KEEP KZ N2;N2=COUNT; RUN;

PROC FREQ DATA=SAMPLES NOPRINT;

WHERE G=1 AND D=1; TABLE KZ / NOPERCENT 0UT=01 OUTCUM;
DATA D1;SET 01; KEEP KZ 01;01=COUNT; RUN;

PROC FREQ DATA=SAMPLES NOPRINT;

WHERE G=2 AND D=1; TABLE KZ / NOPERCENT 0UT=02 OUTCUM;
DATA 02;SET D2; KEEP KZ D2;D2=COUNT; RUN;

DATA COM;MERGE T1 T2 D1 02; BY KZ;

ARRAY 0[4] N1 N2 01 02;

00 1:1 T0 4; IF 0[I]=. THEN 0[I]=0;END;
DROP I;

RUN;

PROC IML;
use COM;

146

READ ALL VARc INTO N1;
READ ALL VARD INTO N2;

READ ALL VAR{'D1'} INTO D1;
READ ALL VAR{'D2'} INTO D2;
N=NROW(N1);

M1=N1 [+1];

M2=N2l+ili

$1=REPEAT(M1,N,1);
$2=REPEAT(M2,N,1);

K =REPEAT(1,N,1);

D0 I=1 T0 N-1;

$1[I+1,11=S1[I,11-N1[1,1];
$2[I+1,1]=S2[I,11-N2[I,1];

END;

v=31||D1||S2||D2;
C={'N1','DI','N2','D2'};
CREATE SAM FROM v [COLNAME=C];
APPEND FROM v;

RUN;
QUIT;

DATA CAL;SET SAM;

SumN=SUM(N1,N2);SumD=SUM(Dt,02);
IF SumN=1 THEN DELETE;

RUN;

DATA CAL;SET CAL;

/*** Log Rank Test ***************************************l

logE=D1-N1*SumD/SumN;
logV=N1*N2*SumD*(SumN-SumD)/(SumN*SumN*(SumN-1));

/*** Wilcoxon Test ***************************************/

WxE=SumN*(D1-N1*SumD/SumN);
WxV=SumN*SumN*N1*N2*SumD*(SumN-SumD)/(SumN*SumN*(SumN-1));

/*** Lin—Test Statistic *************************************/

E1=N1*SumD/SumN;
V=N1*N2*SumD*(SumN-SumD)/(SumN*SumN*(SumN-1));
E2=V+E1*E1;

IF SumD>=3 THEN C31=COMB(SumD,3);ELSE C31=0;

147

IF N1>=3 THEN 032=COMB(N1,3);ELSE cs2=0;
IF SumN>=3 THEN C33=COMB(SumN,3);ELSE C33=0;

E3=3*E2-2*E1+GAMMA(4)*C31*032/(C33+.000000001);

IF SumD>=4 THEN C41=COMB(SumD,4);ELSE 041:0;
IF N1>=4 THEN C42=COMB(N1,4);ELSE 042:0;
IF SumN>=4 THEN C43=COMB(SumN,4);ELSE 643:0;

E4=6*E3-11*E2+6*E1+GAMMA(5)*C41*C42/(C43+.000000001);

DELTA=(D1-E1)**2;

EDELTA=V;
VDELTA=E4-4*E3*E1+6*E2*(E1*E1)-3*(E1**4)-V*V;
RUN;

PROC MEANS DATA=CAL NOPRINT;

VAR LogE LogV WxE WxV DELTA EDELTA VDELTA;

OUTPUT 0UT=LinTest SUM=;

RUN;

DATA LinTest ;SET LinTest;
TestLogRank=LogE*LogE/LogV;
TestWilcoxon=WxE*WxE/va;
TestLin=(DELTA-EDELTA)/SQRT(VDELTA);
LogRank=ROUND(1-CDF('CHISQUARE',TestLogRank,1),.0001) ;
Wilcoxon=ROUND(1-CDF('CHISQUARE',TestWilcoxon,1) ,.0001) ;
Lin=ROUND(2*(1-CDF('NORMAL',ABS(TestLin))),.0001) ;

RUN;

PROC PRINT DATA=LinTest;
TITLE 'P-VALUES FOR HOMOGENIETY TEST FOR MEAN SURVIVAL TIME';
VAR TestLogRank LogRank TestWilcoxon Wilcoxon TestLin Lin;
RUN;
%MEND;

%Liniest(Var=pSEX,Symptom=Pain);
%Linfest(Var=AGE,Symptom=Pain);
%Linfest(Var=StageCat,Symptom=Pain);
%Linfest(Var=Comorbidity,Symptom=Pain);
%Ljn768t(Var=CESD,Symptom=Pain);
%Lin763t(Var=ChemoStart,Symptom=Pain);

148

%Ljniest(Var=pSEX,Symptom=Fatigue);
%Ljnfest(Var=AGE,Symptom=Fatigue);
%Linrest(Var=StageCat,Symptom=Fatigue);
%Ljnfest(Var=Comorbidity,Symptom=Fatigue);
%Ljnfest(Var=CESD,Symptom=Fatigue);
%L1nfest(Var=ChemoStart,Symptom=Fatigue);

SAS Macro for a nonparametric test for equality of mean survival
time (Rahbar’s Method)

%MACRO NEWTEST(G);
DATA SAM&G;SET SAMPLE;WHERE G=&G;J=1;
PROC RANK DATA=SAM&G OUT=SAM&G DESCENDING TIES=LOW;
BY J;
VAR Z;
RANKS KZ;
RUN;
PROC SORT DATA=SAM&G ;BY J Z;RUN;
PROC LIFETEST DATA=SAM&G NOPRINT OUTSURV=SURV&G;
TIME Z*D(O);
BY J;
DATA SURV&G ;SET SURV&G;
LZ=LAG(Z);
LSURVIV=LAG(SURVIVAL);
BASE=Z-LZ;
M=BASE*LSURVIV;
IF SURVIVAL=. THEN M=.;
RUN;
PROC SORT DATA=SURV&G ;BY J 2;
DATA SURV&G ;MERGE SAM&G SURV&G ;BY J 2;
K22=LAG(KZ);
IF K22=KZ THEN DELETE;
RUN;
DATA UME&G ;SET SURV&G ; BY J;
IF FIRST.J THEN TOTAL=O;
TOTAL+M;

RUN;

149

PROC MEANS DATA=UME&G NOPRINT;
VAR M;
OUTPUT OUT=SUM&G SUM=UE&G ;
BY J;
RUN;
DATA UME&G ;MERGE UME&G SUM&G;BY J ;
AZ=UE&G -TOTAL;
IF Z=O THEN AZ=O;
SIGMA&G =(1-_CENSOR_)*((AZ/KZ)**2);
IF _CENSOR_=. THEN DELETE;
RUN;
PROC SORT DATA=UME&G ; BY J;
PROC MEANS DATA=UME&G NOPRINT;
VAR SIGMA&G;
BY J;
OUTPUT OUT=S&G SUM=;
RUN;
DATA UE&G ;MERGE SUM&G S&G;BY J;
KEEP J UE&G SIGMA&G _FREO_;
RUN;
PROC MEANS DATA=SAM&G NOPRINT;
VAR KZ;
OUTPUT OUT=NUM&G MAX=N&G;
RUN;
DATA UE&G ;MERGE UE&G NUM&G;
SIGMA&G =N&G*SIGMA&G;
STD&G =SORT(SIGMA&G/N&G);
G=&G;
LABEL G='Negative';
RUN;
PROC MEANS DATA=UE&G MEAN MAXDEC=4;
VAR 6 N86 UE&G SIGMA&G;
RUN;
%MEND;

/**** Test for Two Groups ****/

%Macro Rahbar(Var=,Symptom=);
DATA Sample;Set Main(Keep= time1 &VAR CENSOR Symptom
where:(Symptom="&Symptom"));

KEEP Z O G;

Z=time1;

150

D=Censor;
G=&Var;

%NEMVEST(1);
enruvrsvrz);

DATA UES;MERGE UE1 UE2;RUN;

PROC DELETE DATA=UE1;PROC DELETE DATA=UE2;
PROC MEANS DATA=UEs N MEAN STD MAXDEC=4;
VAR UE1 SIGMAI UE2 SIGMA2;

RUN;

DATA ESTIMATE;SET UES;
/***** COMBINED ESTIMATE *****/
SUM1=SIGMA1*N1+SIGMA2*N2;
L1=SIGMA1*N1/SUM1;
L2=SIGMA2*N2/SUM1;

CE1=L1*UE1+L2*UE2;
CE2=L1*UE1+L2*UE2;

N=N1+N2;
0M11=N1/N;0MI2=N2/N;

RHOI=SIGMA1IOMII;
RH02=SIGMA2/OM12;

COMBINE=RH01*L1*L1+RH02*L2*L2;
STDCIMB=SQRT(COMBINE/N);

/*** LAMBDA ***/

DI=(UE1-CE1);
D2=(UE2-CE2);

SUMD=SQRT(N)*D1+SQRT(N)*D2+SQRT(N);

GAMMA1=((1-L1)**2)*RHO1+(L2**2)*RH02;
GAMMA2=(L1**2)*RH01+((1-L2)**2)*RH02;

GAMMA12=~L1*RH01-L2*RH02+COMBINE;

151

RUN;

PROC IML;
USE ESTIMATE;
READ ALL VAR{'D1'} INTO 01;
READ ALL VAR{'DZ'} INTO 02;
READ ALL VAR{'N'} INTO N ;
READ ALL VAR{'GAMMAI'} INTO GAMMA1 ;
READ ALL VAR{'GAMMAZ'} INTO GAMMA2 ;
READ ALL VAR{'GAMMA12'} INTO GAMMA12 ;
THETA=D1||DZ;
C1=GAMMA1||GAMMA12;
02=GAMMA12||GAMMA2;
V=C1‘||C2‘;
V0=GINV(V);
L=N*THETA*VO*THETA‘;
C={'LAMBDA'};
LA=L;
CREATE LAMBDA FROM LA [COLNAME=C];
APPEND FROM LA;
RUN;
OUIT;

DATA PVALUE;SET LAMBDA;

CHI=CINV(0.95,1);

NEWTEST=ROUND(1-CDF('CHISOUARE',LAMBDA,1) ,.0001) ;
PROC MEANS DATA=ESTIMATE MEAN MAXDEC=3;

VAR N1 UE1 STDI N2 UE2 STD2 CE1 SIGMAI SIGMA2 GAMMA1 GAMMA2
GAMMA12; _
RUN;
PROC MEANS DATA=PVALUE N MEAN MAXDEC=4;

VAR LAMBDA NEWTEST;

RUN;
%MEND;
%flahbar(Var=pSEX,Symptom=Pain);
%flahbar(Var=AGE,Symptom=Pain);
%flahbar(Var=StageCat,Symptom=Pain);
%flahbar(Var=Comorbidity,Symptom=Pain);
%flahbar(Var=CESD,Symptom=Pain);
%flahbar(Var=ChemoStart,Symptom=Pain);

%flahbar(Var=pSEX,Symptom=Fatigue);
152

%flahbar(Var=AGE,Symptom=Fatigue);
%flahbar(Var=StageCat,Symptom=Fatigue);
%flahbar(Var=Comorbidity,Symptom=Fatigue);
%flahbar(Var=CESD,Symptom=Fatigue);
%flahbar(Var=ChemoStart,Symptom=Fatigue);

/**** Tests for Three Groups ****/

*Macro Rahbar3(Var=,Symptom=);
DATA Sample;Set Main(Keep= time1 &VAR CENSOR Symptom
where=(Symptom="&Symptom"));

KEEP 2 D G;

Z=time1;

D=Censor;

G=&Var;

%NEM7E3T(I);
smruvzsrtz);
%NEW7£SV(3);

DATA UES;MERGE UE1 UE2 UE3;RUN;

PROC DELETE DATA=UE1;PROC DELETE DATA=UE2;PROC DELETE DATA=UES;
PROC MEANS DATA=UES N MEAN STD MAXDEC=4;

VAR UE1 SIGMA1 UE2 SIGMA2 UE3 SIGMA3;

RUN;

DATA ESTIMATE;SET UES;
/***** COMBINED ESTIMATE *****/
SUM1=SIGMA1*N1+SIGMA2*N2+SIGMA3*N3;
L1=SIGMA1*N1/SUM1;
L2=SIGMA2*N2/SUM1;
L3=SIGMA3*N3/SUM1;

CE1=L1*UE1+L2*UE2+L3*UE3;
CE2=L1*UE1+L2*UE2+L3*UE3;
CE3=L1*UE1+L2*UE2+L3*UE3;
CE4=L1*UE1+L2*UE2+L3*UE3;
N=N1+N2+N3;

0MI1=N1/N;0M12=N2/N;OMI3=N3/N;

153

RHO1=SIGMA1IOMI1;
RH02=SIGMA2/OM12;
RH03=SIGMA3IOMI3;

COMBINE=RH01*L1*LI+RH02*L2*L2+RH03*L3*L3;
STDCIMB=SORT(COMBINE/N);

/*** LAMBDA ***/

DI=(UE1-CE1);
D2=(UE2-CE2);
03=(UE3-CE3);

SUMD=SQRT(N)*DI+SORT(N)*02+SQRT(N)*DS;

GAMMA1=((1-L1)**2)*RH01+(L2**2)*RH02+(L3**2)*RH03;
GAMMA2=(L1**2)*RHO1+((1-L2)**2)*RH02+(L3**2)*RH03;
GAMMA3=(L1**2)*RHO1+(L2**2)*RHO2+((1-L3)**2)*RH03;

GAMMA12=-L1*RH01-L2*RH02+COMBINE;
GAMMA13=-L1*RHO1-L3*RH03+COMBINE;
GAMMA23=-L2*RH02-L3*RH03+COMBINE;

S1=SORT(SIGMA1);

$2=SORT(SIGMA2);

S3=SQRT(SIGMA3);
RUN;

PRDC IML;

USE ESTIMATE;

READ ALL VAR{'D1'} INTO D1;

READ ALL VAR{'DZ'} INTO D2;

READ ALL VAR{'D3'} INTO D3;

READ ALL VAR{'N'} INTO N ;

READ ALL VAR{'GAMMA1'} INTO GAMMA1 ;
READ ALL VAR{'GAMMAZ'} INTO GAMMA2 ;
READ ALL VAR{'GAMMAS'} INTO GAMMAS ;
READ ALL VAR{'GAMMA12'} INTO 6AMMA12 ;
READ ALL VAR{'GAMMA13'} INTO GAMMA13 ;
READ ALL VAR{'GAMMA23'} INTO GAMMA23 ;

THETA=DI||D2||D3;

154

CI=GAMMA1||GAMMA12||GAMMA13;
C2=GAMMA12||6AMMA2||6AMMA23;
C3=6AMMA13||GAMMA23||6AMMA3;

V=C1‘||CZ‘||03‘;

V0=GINV(V);

L=N*THETA*VO*THETA‘;

C={'LAMBDA'};

LA=L;

CREATE LAMBDA FROM LA [COLNAME=C];
APPEND FROM LA;

RUN;

QUIT;

DATA PVALUE;SET LAMBDA;
CHI=CINV(O.95,2);
NEWTEST=ROUND(1-CDF('CHISOUARE',LAMBDA,2) ,.0001) ;
PROC MEANS DATA=ESTIMATE MEAN MAXDEC=3;
VAR N1 UE1 STDI N2 UE2 ST02 N3 UE3 ST03 CE1
SIGMA1 SIGMA2 SIGMA3
S1 82 $3
GAMMA1 GAMMA2 GAMMA3
GAMMA12 GAMMA13 GAMMA23 ;
RUN;
PROC MEANS DATA=PVALUE N MEAN MAXDEC=4;
VAR LAMBDA NEWTEST;
RUN;
*mend;
9sflahbar3(Var=Cance r , Symptom=Pain) ;
%flahbar6(Var=Cancer,Symptom=Fatigue);

155

Appendix C The MD Anderson Symptom Inventory (MDASI) (143)
MD. Anderson Symptom Inventory (MDASI) Core Items

Part I. How severe are your symptoms?

People with cancer frequently have symptoms that are caused by their disease
or their treatment. We ask you to rate how severe the following symptoms have
been in the last 24 hours. Please fill in the circle below from O (symptom has
not been present) to 10 (the symptom was as bad as you can imagine it could
be) for each item.

1. Your pain at its WORST?
0 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

2. Your fatigue (tiredness) at its WORST?
O 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

3. Your nausea at its WORST?
O 1 2 3 4 5 6 7 8 9 10
Not present ' as bad as you can imagine

4. Your disturbed sleep at its WORST?
O 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

5. Your feelings of being distressed (upset) at its WORST?
0 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

6. Your shortness of breath at its WORST?
0 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

7. Your problem with remembering things at its WORST?

0 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

156

8. Your problem with lack of appetite at its WORST?
O 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

9. Your feeling drowsy (Sleepy) at its WORST?
0 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

10.Your having a dry mouth at its WORST?
O 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

11.Your feeling sad at its WORST?
0 1 2 3 4 5 6 . 7 8 9 10
Not present as bad as you can imagine

12. Your vomiting at its WORST?
0 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

13.Your numbness of tingling at its WORST?
0 1 2 3 4 5 6 7 8 9 10
Not present as bad as you can imagine

Part II. How have your symptoms interfered with your life?

Symptoms frequently interfere with how we feel and function how much have
your symptoms interfered with the following items in the last 24 hours:

14. General activity?
0 1 2 3 4 5 6 7 8 9 10

Do Not Interfere Interfered Completely
1 5. Mood?

O 1 2 3 4 5 6 7 8 9 10

Do Not Interfere Interfered Completely

16.Work (including work around the house)?
0 1 2 3 4 5 6 7 8 9 10
Do Not Interfere Interfered Completely

157

17. Relations with other people?
0 1 2 3 4 5 6 7 8 9 10

Do Not Interfere Interfered Completely
18.Walking?

0 1 2 3 4 5 6 7 8 9 10

Do Not Interfere Interfered Completely

19. Enjoyment of life?
0 1 2 3 4 5 6 7 8 9 10
Do Not Interfere Interfered Completely

158

Appendix D The Center for Epidemiologic Studies - Depression (CES-D)
scale (125)
Depression (CESD) Questions Your Feelings

These questions are about how you feel and how things have been with you
within the past month. Please note the answer that comes closest to the way you
have been feeling during the past month. The answer choices are “almost all of
the time,” “most of the time,” “some of the time,” “rarely or none of the time.”
During the past month, how much of the time:

0) rarely/none of the time 1) some of the time 2) most of the time 3) all of the time
1. Were you bothered by things that usually don’t bother you?

2. Have you not felt like eating; had a poor appetite?

3. Have you felt that you could not shake off the blues, even with the help of
family or friends?

Have you felt that you were just as good as other people?

Have you had trouble keeping your mind on what you were doing?

Have you felt depressed?

Have you felt that everything you did was an effort?

Have you felt hopeful about the future?

999°N9’91P

Have you thought your life has been a future?
10. Have you felt fearful?

11.Have your Sleep been restless?
12.Were you happy?

13. Have you talked less than usual?

14. Have you felt lonely?

15.Were people unfriendly?

16. Have you enjoyed life?

17. Have you had crying sells?

18. Have you felt sad?

19. Have you felt that people dislike you?
20. Could you not get going?

159

Appendix E The Short Form — 36 (SF-36) Physical Functioning Sub Scale

The following questions are about the activities you might do during a typical day.

1. Does your health limit your ability to do activities? If so, how much?
a. Vigorous activities, such as running, lifting heavy objects, participating
in strenuous sports?
Currently, does your health limit you in ?
---- Yes, limited a lot.
------ Yes, limited a little.
------ No, not limited at all.

 

b. Moderate activities, such as moving a table, pushing a vacuum cleaner,
bowling, or playing golf? .
Currently, does your health limit you in ?
----- Yes, limited 3 lot.
------ Yes, limited a little.
------ No, not limited at all.

 

c. Lifting or carrying groceries?
Currently, does your health limit you in ?
----- Yes, limited a lot.
------ Yes, limited a little.
------ No, not limited at all.

 

d. Climbing several flights of stairs?
Currently, does your health limit you in ?
------ Yes, limited a lot.
------- Yes, limited a little.
------- No, not limited at all.

 

e. Climbing one flight of stairs?
Currently, does your health limit you in ?
------- Yes, limited a lot.
------- Yes, limited a little.
------ No, not limited at all.

 

160

9.

Bending, kneeling, or stooping?
Currently, does your health limit you in
------ Yes, limited a lot.

------- Yes, limited 3 little.

------- No, not limited at all.

Walking more than a mile?

Currently, does your health limit you in
----- Yes, limited a lot.

------ Yes, limited a little.

------ No, not limited at all.

Walking several blocks?

Currently, does your health limit you in
----- Yes, limited a lot.

----- Yes, limited a little.

------- No, not limited at all.

Walking one block?

Currently, does your health limit you in
------ Yes, limited a lot.

------ Yes, limited a little.

------ No, not limited at all.

Bathing or dressing yourself?
Currently, does your health limit you in
------ Yes, limited a lot.

------ Yes, limited a little.

------ No, not limited at all.

161

 

 

 

 

 

Appendix F The Assessment for Comorbid Conditions (127)

HEALTH CONDITIONS
1. Has a doctor ever told you that you have high blood pressure of
hypertension?
a. Yes b. No

2. Do you have diabetes?
a. Yes D. No

3. Has a doctor ever told you that you have cancer or a malignant tumor,
other than the cancer for which you currently are being treated?
a. Yes b. No

4. Not including asthma, has a doctor ever told you that have chronic lung
disease such as Chronic bronchitis or emphysema?
a. Yes b. No

5. Have a doctor ever told you that you had a heart attack, coronary heart
disease, angina, congestive heart failure, or other heart problems?
a. Yes b. No

6. Have you recently had any angina or chest pains due to your heart?
a. Yes D. No

7. Has a doctor ever told you that you had a stroke?
a. Yes b. No

8. Have you ever seen a doctor for emotional, nervous, or psychiatric
problems?
a. Yes D. No

9. During the last 12 months, have you seen a doctor specifically for arthritis
or rheumatism?
a. Yes b. No

10. Have you ever fractured your hip?

a. Yes b. No

162

11.Have you ever had surgical replacement of a joint?
a. Yes D. No

12. During the last 12 months, have you lost any amount of urine beyond your
control?
a. Yes b. No

13. Have you ever had cataract surgery?
a. Yes b. No

14. Do you ever wear a hearing aid?
a. Yes b. No

15. Do you have any other major health problems, which you haven’t told me
about?
a. Yes D. No

 

Specify

163

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