CONSTRUCTING OPTIMAL MEDICAL MANAGEMENT AREAS
FOR HEALTH SERVICES RESEARCH
By
Chenxiao Ling

A THESIS
Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Geography
2011

ABSTRACT
CONSTRUCTING OPTIMAL MEDICAL MANAGEMENT AREAS
FOR HEALTH SERVICES RESEARCH
By
Chenxiao Ling
This study constructs optimal medical management areas (MMAs) in the State of Michigan
for the purpose of visualizing and exploring the spatial patterns of two health indicators:
ischemic heart disease (IHD) (ICD-9-CM: 410-414) and diabetes (ICD-9-CM: 250) for the
purpose of assessing population-demand for health services.

Data on IHD and diabetes are

obtained from the Michigan Inpatient Hospital Discharge Database (MIDB) for the year 2008.
MMA boundary definitions are optimized using Automated Zone Matching (AZM) methodology
software. Optimization is conducted by aggregating the residential ZIP Codes of patients
discharged from hospitals with IHD or diabetes, using three constraint parameters: (1) minimum
case threshold, to ensure rate stability; (2) maximum shape compactness, to avoid irregular or
elongated MMAs; and (3) maximum internal homogeneity, to construct MMAs with populations
that demographically similar.

The modifiable area unit problem (MAUP) is examined within

the context of MMA design and epidemiological scale by evaluating IHD and diabetes in relation
to their relevant broader disease groups, diseases of the circulatory system (ICD-9-CM: 390-459)
and endocrine, nutritional and metabolic diseases, and immunity disorders (ICD-9-CM: 240-279).
Following the optimization of AZM-MMAs area-based proportions, crude rates and age-adjusted
rates are calculated to represent the various views of demand for health services.

The

limitations and benefits of using AZM versus traditional ZIP Code boundary definitions to
construct MMAs to assess the demand for inpatient hospital services are discussed for future
applications.

This thesis is dedicated to my parents, without whose support and selfless love,
the completion of this work would not have been possible.

iii

ACKNOWLEDGEMENTS

I would first like to express my deepest gratitude to my advisor, Dr. Sue C. Grady, for your
invaluable guidance, patience and assistance as I learned to conduct this research.
encouragement inspired confidence in me.

Your

It is an honor for me to be one of your students.

Special thanks to the distinguished faculty members who served on my committee: Dr. Ashton M.
Shortridge and Dr. Joseph P. Messina.
building of my thesis.

Your comments and advices greatly helped with the

I feel fortune to have you on my committee.

I would also like to thank

Dr. David J. Campbell and Dr. Bruce Wm. Pigozzi, who provided me with comments and
opinions on thesis writing.
I gratefully acknowledge the use of the AZTool software, which is copyright Dr. David
Martin, Ms. Samantha Cockings and University of Southampton in the UK.

Thanks the

Michigan Department of Community Health for kindly providing the main database.

I also

wish to thank Dr. Arika Ligmann-Zielinska for preparing the shapefile for this study.

Special

thanks to Mr. Jim T. Brown and Mr. Wilson Ndovie, for your technical support to the medical
geography lab and my work.

Thanks are also due to Dr. Richard E. Groop and Dr. Jiaguo Qi,

for bringing me into MSU and this program, and other faculty and staff for assisting and
encouraging me in many ways.
I‟m so grateful to my mom and dad who provide me with this opportunity to study abroad
and conduct this thesis.

I‟d also like to thank Paul, Kristie, Hui, Ziting, Peter and Katie, for

your accompany as lab-mates and friends.

Finally, I wish to express my gratitude to all the

individuals who helped with the completion of this work.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................................... vii
LIST OF FIGURES .................................................................................................................. ix
LIST OF ABBREVIATIONS.................................................................................................... xi
1. INTRODUCTION...................................................................................................................1
2. BACKGROUND ....................................................................................................................5
2.1 Geographic Health Services Research ................................................................................5
2.2 Government Agencies and Health Services Research .........................................................7
2.3 Important Issues in Constructing Medical Management Areas ...........................................8
2.3.1. Small Number Problem ..............................................................................................9
2.3.2. Modifiable Areal Unit Problem (MAUP) .................................................................. 10
2.3.3. Epidemiological Considerations ............................................................................... 10
2.4 Automated Zone Matching (AZM) Methodology ............................................................. 11
2.5 Summary of Literature ..................................................................................................... 20
2.6 Purposes of Study ............................................................................................................ 21
2.7 Objectives ........................................................................................................................ 21
3. DATA AND METHODS ...................................................................................................... 22
3.1 Data ................................................................................................................................. 22
3.2 Methods........................................................................................................................... 23
4. RESULTS ............................................................................................................................. 33
4.1 Descriptive Statistics ........................................................................................................ 33
4.2 Automated zone matching (AZM) methodology output ................................................... 33
4.3 Medical Management Areas (Proportions) ....................................................................... 41
4.4 Medical Management Areas (Crude and Age-Adjusted Rates) ......................................... 51
4.5 Alternative Zone Designs ................................................................................................. 63
5. DISCUSSION ....................................................................................................................... 71
6. CONCLUSIONS AND RECOMMENDATIONS ................................................................. 80
APPENDICES .......................................................................................................................... 82
Appendix 1. Diseases and Injuries Tabular Index. .................................................................. 83
Appendix 2. List of incompatible ZIP Codes. ........................................................................ 84
v

REFERENCES ......................................................................................................................... 86

vi

LIST OF TABLES

Table 1. Summary of literature on zone design. ......................................................................... 11
Table 2. Patient discharge characteristics for Ischemic Heart Disease (IHD) and diabetes in
Michigan, 2008. ................................................................................................................ 33
Table 3. Ischemic Heart Disease (IHD) results from AZM constraint parameter 50 restarts. ...... 35
Table 4. Circulatory diseases results from AZM constraint parameter 50 restarts. ...................... 37
Table 5. Diabetes results for AZM constraint parameter 50 restarts. ........................................... 38
1

Table 6. Endocrine disorders results for AZM constraint parameter 50 restarts. ........................ 40
Table 7. MMAs with high proportions of patients discharged with IHD, Michigan, 2008. ....... 43
Table 8. MMAs with high proportions of patients discharged with circulatory diseases, Michigan,
2008. ................................................................................................................................. 45
Table 9. MMAs with high crude proportions of patients discharged with diabetes, Michigan, 2008.
.......................................................................................................................................... 48
1

Table 10. MMAs with high crude proportions of patients discharged with endocrine disorders ,
Michigan, 2008. ................................................................................................................ 50
Table 11. MMAs with high crude rates of patients discharged with ischemic heart disease,
Michigan, 2008. ................................................................................................................ 52
Table 12. MMAs with high crude rates of patients discharged with circulatory diseases, Michigan,
2008. ................................................................................................................................. 54
Table 13. MMAs with high crude rates of patients discharged with diabetes, Michigan, 2008. 58
1

Table 14. MMAs with high crude rates of patients discharged with endocrine disorders , Michigan,
2008. ................................................................................................................................. 60
Table 15. Statistical outputs of zone designs using alternative methods with simulated annealing.
.......................................................................................................................................... 64
Table 16. Statistical outputs of zone designs using alternative methods without simulated
annealing. .......................................................................................................................... 64
Table 17. Summary of 50 restarts for diseases and disease groups. ............................................ 73
Table 18. List of incompatible ZIP Codes. ................................................................................. 84
vii

1

Includes endocrine, nutritional and metabolic diseases, and immunity disorders

viii

LIST OF FIGURES

Figure 1. IHD: Relative standard errors (RSEs) of proportions by ZIP Code .............................. 27
Figure 2. Diabetes: Relative standard errors (RSEs) of proportions by ZIP Code ....................... 27
Figure 3. Ischemic Heart Disease (IHD) results from AZM constraint parameter 50 restarts. ..... 36
Figure 4. Circulatory diseases results from AZM Constraint Parameters 50 restarts. .................. 37
Figure 5. Diabetes results for AZM constraint parameter 50 restarts. ......................................... 39
Figure 6. Endocrine disorders results for AZM constraint parameter 50 restarts. ........................ 40
Figure 7. Ischemic heart disease: proportions by MMA (n=302), Michigan 2008. ..................... 42
Figure 8. Circulatory diseases: proportions by MMA (n=310), Michigan 2008. ......................... 44
Figure 9. Diabetes: proportions by MMA (n=183), Michigan 2008............................................ 47
Figure 10. Endocrine disorders: proportions by MMA (n=274), Michigan 2008. ....................... 49
Figure 11. Ischemic heart disease: crude rates by MMA (n=302), Michigan 2008. ..................... 51
Figure 12. Circulatory diseases: crude rates by MMA (n=310), Michigan 2008. ........................ 53
Figure 13. Ischemic heart disease: age-adjusted rates by MMA (n=302), Michigan 2008. .......... 55
Figure 14. Circulatory diseases: age-adjusted rates by MMA (n=310), Michigan 2008. ............. 56
Figure 15. Diabetes: crude rates by MMA (n=183), Michigan 2008. .......................................... 57
Figure 16. Endocrine disorders: crude rates by MMA (n=274), Michigan 2008. ........................ 59
Figure 17. Diabetes: age-adjusted rates by MMA (n=183), Michigan 2008. ............................... 61
Figure 18. Endocrine disorders: age-adjusted rates by MMA (n=274), Michigan 2008. ............. 62
Figure 19. Ischemic heart disease: crude rates by MMA (n=307) and their RSE using all HSAs (SA
enabled), Michigan 2008. .................................................................................................. 67
Figure 20. Ischemic heart disease: crude rates by MMA (n=310) without using HSAs (SA enabled),
Michigan 2008. ................................................................................................................. 68
Figure 21. Ischemic heart disease: crude rates by MMA (n=304) using all HSAs (SA disabled),
Michigan 2008. ................................................................................................................. 69
ix

Figure 22. Ischemic heart disease: crude rates by MMA (n=300) without using HSAs (SA
disabled), Michigan 2008. ................................................................................................. 70

x

LIST OF ABBREVIATIONS
AZM

Automated Zoning Matching

AZTool

Automated Zoning Tool

CDC

Centers for Disease Control and Prevention

CI

Confidence Interval

CON

Certificate of Need

EDs

Enumeration Districts

FSA

Facility Sub-Areas

HSA

Hospital System Areas

IAC

Intra-Area Correlation

ICD-9-CM

International Classification of Diseases, Ninth Revision, Clinical
Modification

IHD

Ischemic Heart Disease

MAUP

Modifiable Areal Unit Problem

MDCH

Michigan Department of Community Health

MIDB

Michigan Inpatient Hospital Discharge Database

MMAs

Medical Management Areas

P2A

Perimeter2/Area

RSE

Relative Standard Error

SA

Simulated Annealing

WHO

World Health Organization

ZCTA

ZIP Code Tabulation Areas

xi

1. INTRODUCTION
Health service researchers study health care from „supply‟ and „demand‟ perspectives.

In

this thesis, the „supply‟ perspective refers to the availability of inpatient hospital services for the
entire population or a subset (i.e., the adequacy of the supply to meet the needs of a population)
(Penchansky & Thomas, 1981).

Attributes by which to measure inpatient hospital supply

include: the potential for capacity or number of beds, the skill set of physicians, nurses, and other
health care providers, the services that those providers offer, the length of hospital stay, and the
method(s) of payment and reimbursement.
acquire the available services offered.

Related to supply is accessibility or the ability to

Common barriers to receiving available services include:

low socioeconomic status or poor health insurance coverage, distance in metric or time and hours
of operation (Penchansky & Thomas, 1981).

Finally, inpatient hospital services may be

available and accessible, but not utilized by the population.

Common barriers to utilization

include: fear of diagnosis or treatment, untoward perceptions and prejudices, and language and
cultural barriers (Meade et al., 1988).

Most health service research focuses on the supply

perspective through measurements of availability, accessibility and utilization to understand the
health care system.
Important also is the „demand‟ perspective.
the population for inpatient hospital services.
time.

In this thesis, „demand‟ refers to the need of

The definition of demand/need has evolved over

Bradshaw (1972) for example, defined need as: expressed need, comparative need, and

normative need.

Expressed need refers to “an expression in action of felt need” and

comparative need referred to “the comparison of situations with others.”
comparative needs are subjective definitions.

Expressed and

Normative need on the other hand, represents “an

experts‟ definition or diagnosis”, which could be subjective or objective.
1

Acheson (1978) later

defined demand/need as the “relief from the negative states of distress, discomfort, disability,
handicap, and the risk of morbidity or mortality.”

Acheson (1978) argued that “the demand for

health care is hard to assess quantitatively, because it is really a reflection of perceived health
status.” Health care professionals commonly assess patient‟s perceived health status, to make
their diagnoses in practice.

Over time, however the definition of demand/need took on a more

quantitative meaning, when researcher began to view demand/need in terms of „incidence‟ and
„prevalence‟ of disease.

For example, (Bowling, 2002) stated, “it is reasonable that the spatial

patterns of disease could reflect the „demand‟ for health services, because people with diseases
have the „need‟ to seek healthcare.” (Cromley & McLafferty, 2002) also expressed „need‟ as
“the prevalence of health conditions that should be addressed by health care services.” This
thesis therefore, adopts the prevalence of disease as a measure by which to assess demand of
inpatient hospital services in future analyses.
In 2010, the Michigan Department of Community Health (MDCH) Division of Health
Policy and Access expressed an interest in visualizing the State‟s critical health indicators using
rate-maps to assess the local „demand‟ for inpatient hospital services in those areas.

Critical

health indicators (MDCH, 2009) are defined as high-priority diseases and conditions identified
by the State that also require in-depth public health program monitoring-evaluation and health
care intervention.

In Michigan (MDCH, 2009), heart disease-related deaths and increased

diabetes prevalence were among the most important reported diseases/conditions in the State.
In response to their request, data on the residential ZIP Codes of patients discharged from
hospitals with ischemic heart disease (IHD) (ICD-9-CM: 410-414) and diabetes (ICD-9-CM: 250)
were obtained from the Michigan Inpatient Hospital Discharge Database (MIDB) 2008 to map
local areas of demand for inpatient hospital services.
2

Ischemic heart disease refers to coronary

heart disease (i.e., blood flow and oxygen to the heart muscle is reduced, thereby, increasing the
risk of a myocardial infarction (heart attack) (The Merck Manual 16th edition, 1992).

Diabetes

is an endocrine disorder affecting the pancreas, limiting insulin production, and resulting in
elevated blood glucose levels (The Merck Manual 16th edition, 1992).

Although IHD-related

deaths are decreasing in Michigan (MDCH, 2011), the prevalence of IHD and diabetes morbidity
are increasing, in part related to an aging population, but environmental risks and lack of
available and accessible high quality health care may also be contributing to this increasing
prevalence.

This research will focus on mapping the prevalence of demand and through

understanding the spatial patterns of diseases, and new causal hypothesis may be generated.
For the purpose of this thesis, the boundaries within which the prevalence rates of IHD and
diabetes are mapped will be referred to as Medical Management Areas (MMAs).
The purpose of this thesis is to (1) construct optimal MMAs by which to (2) visualize and
explore the spatial patterns of IHD and diabetes in the State of Michigan to assist the MDCH
staff with evaluating local areas of demand for inpatient hospital services.

There are however,

known inherent problems with mapping disease rates at the residential ZIP Code level:
specifically ZIP Codes with small case (numerator) or population (denominator) numbers will
result in unstable rates (Washington State Department of Health, 2010); and the modifiable area
unit problem (MAUP), in which there will be changes in disease rates with the modification of
geographic scale and/or zone design (Openshaw, 1984).

Both of these problems are inherently

linked to the epidemiological scale of analysis (i.e., the disease or group(s) of diseases being
studied).
To address these problems, residential ZIP Codes of patient‟s discharged from hospitals with
IHD and diabetes will be aggregated using Automated Zone Matching (AZM) methodology
3

(AZTool) (Cockings et al., 2011) to achieve an adequate case and population count.
AZM-zones will be optimized using three constraint parameters: (1) a minimum case threshold,
to ensure rate stability; (2) maximum shape compactness, to avoid constructing irregular or
elongated MMAs; and (3) maximum internal homogeneity, to construct MMAs of relative
similar demography.

The MMA boundary definitions for IHD and diabetes will be validated by

running AZM 50 times using the same model-constraint parameters and quantifying the „optimal‟
run (i.e., the best output zone design).

The modifiable area unit problem (MAUP) will be

examined within the context of epidemiological scale by evaluating the spatial patterns of IHD
and diabetes in relation to their relevant ICD-9-CM broad disease groups, diseases of circulatory
system (ICD-9-CM: 390-459) (herein, referred to as circulatory diseases) and endocrine,
nutritional and metabolic diseases, and immunity disorders (ICD-9-CM: 240-279) (herein,
referred to as endocrine disorders) in Michigan.

Following the optimization of MMAs,

area-based IHD and diabetes proportions (cases/100 total hospital discharges) and crude and
age-adjusted prevalence rates (cases/1,000 population) will be calculated to visualize and explore
AZM-MMA areas of demand in the State.

It is recognized that these maps will only comprise

those patients who were hospitalized with these diseases and conditions (i.e., chronic, severe or
late-stage disease), further justifying the need to construct optimal MMAs to inform health
services research.

4

2. BACKGROUND
2.1 Geographic Health Services Research
During a yellow fever epidemic on New York City in 18th century, Dr. Valentine Seaman
depicted a map of yellow fever deaths and tried to link them with what he called “putrid eflluvia”
(Seaman et al., 1796) Although his assumption about yellow fever transmission was proved to
be incorrect later, his contribution as the first disease spot map to medical geography remains
important. The most well known historical disease maps were created by John Snow, when he
mapped the residential locations of cholera cases during a cholera epidemic in 1854 in London.
John Snow‟s maps became famous because he was able to show the relationship, i.e., the
geographic proximity of drinking water source and cholera incidence.

Both of these studies

demonstrated the potential use of disease maps to assess demand for inpatient hospital services.
Contemporary health services research appeared in the literature in the 1950s, with an
emphasis on health insurance.

The first national study of health insurance coverage was

undertaken in 1953 by the Health Information Foundation (Institute of Medicine, 1979).

Some

other landmarks of health service research at that time included a five-year study report of
chronic illness by the Commission of Chronic Illness, which highlighted the involvement of
economical concepts as an aide in patient screening and monitoring (Institute of Medicine, 1979).
In terms of health facility research, the emphasis on progressive patient care (i.e., patients are
grouped according to their illness and their need for care) emerged in the late 1950s (Haldeman,
1959).

Studies of the 1960s and early 1970s on health services became more diversified in

terms of the administration of health service, with research topics including regionalization and
rural health care (McNerney & Riedel, 1962), organization of medicine in a sociological context
(Freeman et al., 1979), economies of scale in medical practice (Lorant, 1971), and ambulatory
5

medical care (Walker et al., 1964). In terms of health facility research, health care delivery was
studied using location theories and various spatial models, e.g., central place theory (Shannon &
Dever, 1974) and gravity models.

Location theories are primarily concerned with the

geographic location of economic activity.

For example, central place theory aims to explain the

size and location of human settlements in an urban system (Goodall, 1987).

The gravity model

seeks to simplify the demographic behavior of a large group of people by using the physical
“gravity” model.

When applied to health care studies, these theories were utilized to study

people‟s behavior to seek health care (utilize), locate health care facilities (available) and identify
the locations for future health services.

These theories and their applications in health services

research laid the framework from within which many algorithms and computer-generated
programs were developed and now used today.

Hierarchical location analysis primarily

provided the theoretical foundation for the medical service referral system, such that with
increasing hierarchy each hospital level becomes more specialized (Ghosh & Rushton, 1987).
Spatial interaction issues, including the study of patients‟ travel patterns and the determination of
location and size for health service facilities were both developed with the involvement of
location-allocation models and algorithms (Ghosh & Rushton, 1987).
The use of Geographic Information System (GIS) in health services research emerged in the
1990s to assess health care need, access, and utilization (McLafferty, 2003).

In the past twenty

years, an increasing number of researchers published widely on the topic, including health care
access (McLafferty & Grady, 2005; Wang et al., 2008), health care disparity and inequality in
access (Grady & McLafferty, 2007; McLafferty & Wang, 2009) and health care facility
utilization (Bennett et al., 2010; Statler et al., 2011).
work by utilizing GIS to construct MMAs in Michigan.
6

This thesis will expand on this body of

2.2 Government Agencies and Health Services Research
The Agency for Healthcare Research and Quality (AHRQ) and the Academy for Health
Services Research and Health Policy (AHSR) are federal agencies overlooking the health care
system in the United States.
AHRQ defines health services research as: “the examination of how people acquire access to
health care, how much care costs, and what happens to patients as a result of receiving health
care” (AHRQ, 2002). Within AHRQ the goals of health services research are to (1) identify the
most effective ways to organize, manage, finance, and deliver high quality care; and (2) to
reduce medical errors; and improve patient safety (AHRQ, 2002).

In 2000, the Board of

Directors of AHSR, now the Academy for Health Services Research and Health Policy, adopted a
new definition for the field of health services research: “the multidisciplinary field of scientific
investigation that studies how social factors, financing systems, organizational structures and
processes, health technologies, and personal behaviors affect access to health care, the quality
and cost of health care, and ultimately our health and well-being” (Lohr & Steinwachs, 2002).
The Certificate of Need (CON) legislation is “a representative of public utility regulation”,
which was designed to restrict the expansion of hospitals, particularly in the number of beds and
purchase of expensive equipment (CON, 1978). In 1978, the federal government required that
all states implement CON programs for cardiac care services, meaning that hospitals had to
apply and receive certification prior to implementing a cardiac care program.

The intent of

implementing such as program was to reduce the costs associated with duplicate investments (Ho
et al., 2009).

As hospitals merged and the numbers of facilities declined, some states other than

Michigan, eliminated their CON programs (Ho, et al., 2009).
The Michigan Department of Community Health (MDCH), Division of Health Policy and
7

Access is responsible for managing hospitals through the utilization of a CON Commission in
Michigan.

Hospital regulation is achieved by limiting the number of beds a hospital can use for

inpatient services.

The MDCH assigns hospitals to Hospital System Areas (HSAs) and Facility

Sub-Areas (FSAs) through studying utilization patterns.
HSAs and FSAs (Langley et al., 2010).

Hospital beds are then assigned within

The Michigan implementation of Bed Need

Methodology is unique because it is the only state to perform a bed need methodology at the ZIP
Code level.

This methodology utilizes the annual inpatient records (a.k.a., Michigan Inpatient

Data Base, MIDB) collected by the Michigan Health and Hospital Association (MHA).

In

summary, the methodology calculates a utilization rate for inpatient ZIP Codes to each hospital
subarea in the base year, and multiplies this rate by the projected population (five years after base
year), within each age group and ZIP Code across the state to obtain a total projected bed need
by subarea.

This methodology is a „supply‟ approach to understanding where hospital beds

should be added or reduced. This research will provide information on MMAs for IHD and
diabetes to inform bed need in Michigan.

2.3 Important Issues in Constructing Medical Management Areas
In the construction of MMAs using the residential ZIP Code of patients discharged from
hospitals, it will be important to address small case numbers and the modifiable areal unit
problem (MAUP).

If there are too few cases of disease, the rates calculated will be unstable

and spatial patterns observed will be inaccurate. If the constructed MMAs are not optimized
there will be increased potential for MAUP problems, i.e., less reliable spatial patterns.

In this

study, the epidemiological scale of analysis will also be considered in the design of MMA
construction.

For example, studying diseases at a large epidemiological scale, i.e., primary
8

diagnostic groups there will be more case counts but lower specificity and the ability to
understand the hospital bed need in Michigan.

In contrast, by constructing MMAs using

specific diseases, such as IHD and diabetes, there may be low case counts but increased
specificity in understanding the types of services and beds that are needed in Michigan.

It is

therefore important to construct optimal MMAs that have an adequate case count, are minimally
sensitive to changes in geographic scale and provide meaningful information on diseases and
conditions that can inform future bed need in Michigan.

A brief overview of the small numbers

problem, the MAUP and epidemiological scale are provided below.

2.3.1. Small Number Problem
The Center for Disease Control and Prevention (CDC, 2002) defines stable rates as those
with at least 20 cases in the numerator, which corresponds to a 22% relative standard error (RSE)
of the rate (please see the methods section for the equation to calculate the RSE); also referred to
as the “rule of twenty” (Indiana State Department of Health, 2005).

Likewise, the US Bureau

of the Census suggests having at least 50 population in the denominator to define stable rates
(2002). Thus, having a minimum of 20 cases in the numerator and 50 population in the
denominator is considered a „stable‟ rate. In the construction of MMAs it is also important to
think about what kind of future analytical analyses may be conducted.

For example, in

multilevel modeling it will be important to have at least 30 cases per unit (and 30 units) to
achieve an adequate sample size to model fixed effects; this is also referred to in the literature as
the “30/30 rule” (Kreft, 1996).

9

2.3.2. Modifiable Areal Unit Problem (MAUP)
The MAUP occurs when statistical results are sensitive to changes in the geographic units of
which data are collected (Fotheringham & Wong, 1991).

The results may vary with changes in

the levels of aggregation (scale effect) and the configuration of the zoning scheme (zone effect).
Gehlke and Biehl (1934) first showed that correlation coefficients for variables with absolute
values would increase when contiguous areal units were aggregated because the variation in the
variable(s) decreased as aggregation increased.

The MAUP is also observed with changes in

scale for maps of disease rates, ratios and proportions due to changes in case and/or population
counts with aggregation or de-aggregation.

The zoning effect refers to variation in results when

the units of analysis are reconfigured, e.g., changes in the configuration of ZIP Codes.

2.3.3. Epidemiological Considerations
The International Statistical Classification of Diseases (ICD) and related health problems is
used worldwide to classify diseases and aggregate them into disease groups for diagnostic and
epidemiological purposes (WHO, 2011a).

The MDCH uses the ICD-9-CM version; however,

the ICD-10 version is released and is in use by many US states and counties.

The ICD-9-CM

disease tabulations are organized into 17 primary diagnostic groups and two supplementary
classifications.

A list of these groups is provided in Appendix 1 (WHO, 2011b).

primary disease group, there is a breakdown of sub-groups and specific diseases.

Within each
In this study,

MMAs are constructed for two sub-groups (ischemic heart disease and diabetes) of two primary
diagnostic related groups (diseases of circulatory system and endocrine, nutritional and
metabolic diseases, and immunity disorders) to explore the constraint parameters for optimal
zone design and their meaning for health services research.
10

2.4 Automated Zone Matching (AZM) Methodology
This research will adopt the AZM methodology to address the small case-number problem,
the MAUP and changes in epidemiological scale in the creation of optimal MMAs.

A brief

review of the AZM literature is therefore, provided (Table 1).

Table 1. Summary of literature on zone design.
Author(s)
Purpose
Data

Martin
(2003)

To solve the
problem of
matching
incompatible zonal
geographies

Cocking
and
Martin
(2005)

To demonstrate the
usefulness of zone
designs versus
census boundaries;
explore the MAUP
in traditional versus
new zone designs

Haynes et
al. (2007)

To identify
alternative sets of
neighborhood units
using zone design
and comparing
their characteristics

Haynes et
al. (2008)

Riva et al.
(2008)

To use multilevel
modeling to
identify variations
between subjective
and automated
zone design
neighborhoods
To assess the
ability of census
tracts as units to
measure the active
living potential of
environments

Parameters
Population threshold =
100,
Population target = 250,
Shape = compact,
Homogeneity = tenure
Simulated annealing = Yes

2001 UK
Census
EDs and
tracts
Townsend
score,
self-reporte
d LLTI
(1991 UK
Census)
EDs and
wards

Conclusions
AZM offers an
automated
approach to the
matching
problem.

Purpose-specifi
c automatically
Population target = from
designed zoning
250 to 4500 in the
system is more
increments of 250,
effective than
Population threshold =90%
census
of target value
boundaries
Shape = increasingly
stringent,
Adjacency = railways and
major roads,
Homogeneity = housing
type

Survey,
1991 UK
Census
EDs

Population Target =
larger/medium/smaller,
Shape = compact (weak),
Homogeneity =
Townsend/tenure/house
type

Survey,
1991 UK
Census
EDs
Canadian
Census

Homogeneity = population
density, land use mix, and
geographic accessibility to
proximity services

Disseminati
on areas
(DAs)
11

The
administrative
neighborhood
units were not
an improvement
Subjective
neighborhoods
did not produce
stronger
neighborhood
effects than
computer
generated areas.
Census tracts
are limited for
measuring
active living
potential

Table 1 (cont‟d)

Stafford
et al.
(2008)

To identify area
boundaries using
three methods and
compare the extent
of health
inequalities across
each area

Flowerd
ew et al.
(2008)

To evaluate how
the effect of the
neighborhood on
health differs with
different
neighborhood
definitions

Grady
and
Enander
(2009)

Implement a
methodology by
which to conduct
public health
surveillance for
low birth weight
and infant
mortality in
Michigan

To evaluate
AZTool for
Statistics generating robust
New
statistical output
Zealand zones that fulfill
(2009) pre-specified
optimal
characteristics
To access the
impact of racial
residential
segregation on low
Grady birth weight and
(2010) preterm birth using
optimized
neighborhood
boundary
definitions.

1999 health
survey , 2001
UK Census
Wards, output
areas

Homogeneity = proportion
in rented social housing

Alternative
definitions of
boundaries have
no substantive
effect on the
estimates of
health
inequality.

Population threshold =
2651,
population target = 8136
1991 UK
(average),
Boundaries
Census
Shape = compact (weight 1 matter in health
or 10),
studies.
Wards, EDs
Homogeneity =
employment and tenure,
Simulated annealing = Yes
AZM proved to
be a useful tool
to visualize and
Michigan‟s
Population threshold = 25,
explore the
Vital
Population target = 20,
spatial patterns
Statistics
Shape = compact,
of low birth
Homogeneity = mother‟s
weight and
ZIP Codes
race
infant mortality
for public
surveillance.
AZTool has
Population threshold =
been evaluated
Yes,
to be useful to
2006 area
Population target = Yes,
create new
units,
Shape = Compact,
output
Meshblocks
Homogeneity = population geographies to
or household size
replace the
current ones.
Optimization of
Population threshold = 20, neighborhood
Michigan‟s
Population target = 30,
boundary
Vital
Shape = Compact,
definitions is
Statistics birth Homogeneity = race,
recommended
registry,
rental properties, vacant
for future
properties, and the
studies on
Census tracts presence or absence of a
impacts of
major road or highway
racial
segregation.
12

As Openshaw (1977) points out, the existence of scale and aggregation effects is seen as a
fundamental characteristic of spatial data.
irreversible damage.

They cannot be removed without doing possibly

Thus, the only way to minimize these effects is to control the scale and

aggregation characteristics of spatially aggregated data.

Openshaw then develops a heuristic

procedure that turns scale and aggregation problems to one of optimal-zone design.

This

attempt is made to identify a set of zones, which optimizes an objective function related in some
way to the performance of a model subject to whatever constraints may be relevant. The
development of this automated zone procedure was regarded as the pioneer work to address the
MAUP.

This procedure is revised and improved by Openshaw and Rao (1995).

Later on, different software packages incorporate the principles of automated zone design
originally conceptualized by Openshaw (1977) came to the world.

The relevant packages

include SAGE (Haining et al., 1998; Wise et al., 2001), ZDES (Alvanides et al., 2001), A2Z
(Daras & Alvanides, 2005), AZM (Martin, 2003) and its newer version AZTool (Cockings, et al.,
2011).

There are a small but growing number of studies utilizing zone design software to

evaluate the spatial patterns of health outcomes and local risk factors. These packages offer
different options of parameter input and they all greatly contribute to the development of
software used in zone design.

Martin (2003) presents his early work with AZM, extending

from Openshaw‟s Automated Zone Procedure (AZP).

AZP algorithm is used in order to

maximize the match between two zonal geographies to reconcile incompatible zoning systems.
Most of the studies using zone design software focus particularly on MAUP.

Cockings and

Martin (2005) conducted seminal research using AZM to measure the correlation between
self-reported limiting long-term illness (LLTI) and area-level deprivation at the enumeration
district (ED) and ward scales in Avon, a former county in the UK.
13

This approach took EDs as

building blocks and undertook repeated design of the Avon zoning system at different scales in
order to examine both the scale and aggregation aspects of the MAUP in relation to the
deprivation-health relationship.
from the 1991 Census.

LLTI was measured using the Standard Morbidity Ratio (SMR)

Areal-level deprivation was measured using the Townsend score

involving standardization.

The parameters used in this study were population threshold,

population target and shape.

Population target was set at the values from 250 increasing to

4,500 with step size of 250, covering the range from ED to ward scales.

Population threshold

was set to 90% of the target value to reduce the variation in acceptable zone sizes and thus aid in
the production of alternative zoning systems at predetermined scales.
2

(simple statistics as perimeter /area) was minimized.
constraint specified in the analysis.
analysis.

The shape parameter

Note that there was no homogeneity

The best result from the fifty random restarts is used for the

The correlation coefficients of SMR and deprivation for each set of parameters were

calculated.

The authors concluded that the correlation between variables were markedly

affected by the choice of zoning system, and were strongly associated with the scale of
aggregation.

The authors demonstrated the ability of AZM to explore the influence of

pre-defined and alternative zoning systems and recommended the using of zone design tools as
potentially important role in environmental and health studies.
A study by Haynes et al. (2007) used A2Z software to compare computer-generated zone
design with areal units subjectively defined by local government officers in the city of Bristol,
UK.

They created seven sets of different parameter input.

constraints were applied for the first three sets.
was used in the fourth set.

Three increasingly stringent shape

A railroad and major roads adjacency constraint

The fifth attempted to align zone boundaries along ward boundaries.

The first five zone design all used deprivation as homogeneity constraint.
14

The sixth used a

weak shape constraint, but housing type as a homogeneity constraint; while the seventh also took
account of ward boundaries.

To create sets of neighborhoods at different scales that would be

alternative to the subjectively defined communities, they also created systems of 50, 101 and 150
zones, maximizing the homogeneity of deprivation or housing type in turn, using a weak shape
constraint and no population size requirement. They turned out to find that automated zone
design at different scales could identify much more homogeneous areas than subjectively design
ones, but had less shape compactness.

The authors concluded that in the construction of

optimal zone designs there needs to be balanced between the use of neighborhood homogeneity
constraints and constraints relating to zone shape and boundary alignment.
Following earlier tract, Haynes et al. (2008) used A2Z software to study pre-school children
accidents using multilevel modeling to identify variations between alternative sets of subjective
and automated zone design neighborhoods in southwest England.
sets of “neighborhoods” for the study area.
units in 1991 UK Population Census.

They designed 13 different

One consisted of enumeration districts, which are

The other 12 used enumeration districts as building

blocks and grouped them into larger units at three spatial scales （N = 100, 201, 307）.

Each

automated zone set maximized the homogeneity of selected census characteristics of
Enumeration Districts (EDs) within zones, subject to a weak shape constraint.

Three sets of

census measures (the Townsend composite index of material deprivation, housing tenure, and
housing type) were used in turn within each spatial scale.

Information about accident

occurrence and measures of physical activity, total development and conduct difficulties,
mothers‟ age at delivery, post-natal depression, life events, social support and smoking status
were taken as variables.

Multilevel modeling was used to identify variations between

subjectively defined neighborhoods and computer-generated zones.
15

The risk of accidents to

pre-school children, and most of the characteristics of children and mothers associated with
accident risk, varied significantly between neighborhoods.

Generally, neighborhoods

subjectively defined by planners did not produce stronger effects than computer-generated areas.
In contrast, a study conducted by Riva et al. (2008) intended to assess the soundness of
census tracts as units of analysis for measuring the active living potential for environments,
hypothesized to be associated with walking.

K-mean clustering method (performed in SAS

program) was used to classify smallest areas into clusters (e.g., types of environments).
Through the use of zone design, using the homogeneity constraints population density, land use
mix and accessibility to services, the authors identified seven types of environments within
which varying levels of active living were possible.

Then they compared the census tracts to

the designed zones to evaluate the degree of soundness of census tracts as units of analysis.
The results showed that the soundness of census tracts for measuring active living potential may
be limited.
In the same year, Stafford et al. (2008) used three methods to define area-boundaries and
compare the extent of health inequalities across each drawing on data from the London boroughs
of Camden and Islington.
census ward boundaries.

The first one used administrative boundaries, specifically 2001
The second method drew boundaries using physical and man-made

features of the environment, i.e., roads, railway lines, canals and areas of parkland.

The third

method was designed to maximize the socioeconomic homogeneity of residents using ZDES 3b
software.

Census 2001 output areas were used as the component geography.

in rented social housing was taken as the weighting variable.
perform 10 runs in order to select the best performance.
ensured that shape-compact zones were produced.
16

The proportion

The software was configured to

The selected optimization criterion

The results of the two-level hierarchical

models showed that there was a tendency for slightly larger estimated inequalities across areas
defined by socioeconomic homogeneity compared with other definitions, but differences between
methods were very small. They finally pointed out that, estimates of the extent of variation in
health across neighborhoods - neighborhood inequalities in health - were very similar
irrespective of the way in which the neighborhood boundaries were defined.

Although

administrative area boundaries have little theoretical basis for health study, those studies
indicated that they have no substantive effect. Based on these findings, they can have greater
confidence in the results of the numerous studies which have used administrative boundaries to
define the neighborhood.
While a great number of studies indicate that different sets of boundaries don‟t have a
significant effect on health study outcomes, however, we can still hear the voices that disagree
with this statement.

Using AZTool, Flowerdew et al. (2008) have used British census

Enumeration Districts as building blocks to construct alternative zonal systems using different
sets of criteria, and experiment to see if neighborhoods defined in different ways have similar
implications for health.
of ward.

Population threshold and population target were determined by the size

The first three sets assigned relative weights 1:1, 10:1, and 1:10 to population: shape,

without using any homogeneity constraint. Employment and tenure were used separately as
homogeneity constraint in the fourth and fifth set of parameters.
matter where the boundary was drawn.

They found out that it did

The conclusion indicated that the effect of

neighborhood conditions should be looked at using several different ways to define
neighborhoods, and that the size and composition of the neighborhoods may vary in different
parts of a study area.
Statistics New Zealand (Ralphs & Ang, 2009) published a complete report which evaluates
17

AZTool for generating robust statistical output zones that fulfill pre-specified optimal
characteristics such as compactness of shape, minimum population size, standard mean
population size, and constrained nesting within larger areas.

They find that the new

geographies produced by AZTool substantially out-perform the current geographies across
almost all of the optimization criteria.

The algorithm is stable, and is able to repeatedly

generate high-quality solutions in a timely manner.

They conclude that the ArcGIS/AZTool

toolkit would form the basis of a viable workflow for the automatic production of optimal
geographical areas.
Grady and Enander (2009) investigate the spatial patterns of low birthweight and infant
mortality in the State of Michigan using AZM methodology and minimum case and population
threshold to calculate stable rates and standardized incidence and mortality ratios at the ZIP Code
level.

Applying AZM with a target population of 25 cases and minimum threshold of 20 cases

resulted in the reconstruction of zones with at least 50 births and RSEs of rates 20–22% and
below respectively, demonstrating the stability of these new estimates.

Other AZM parameters

included homogeneity constraints on maternal race and maximum shape compactness of zones to
minimize potential confounding.

With these model parameters the AZM analysis was

conducted by running 50 program restarts with 100 iterations each taking the run (i.e., zone
design) with the most compact shape, the strongest internal homogeneity and lastly the best
target population statistic.

They found that the fifty random restarts were almost equally

optimal in terms of detecting the significant areas (i.e., clusters with elevated rates), and thus
determined to use the initial random aggregation (IRA) as the zone design for the purpose of
public surveillance.

The AZM identified areas with elevated low birthweight and infant

mortality rates and standardized incidence and mortality ratios.
18

The authors concluded that the

AZM proved to be a useful tool for visualizing and exploring the spatial patterns of low
birthweight and infant deaths for public health surveillance.
Following earlier research, Grady (2010) studied the impacts of racial residential segregation
on low birth weight using improved neighborhood boundary definition.
recombine census tracts into new output zones.

AZM was used to

A target population of 30 cases and a minimum

population threshold of 20 cases were set as parameter constraints.

The homogeneity

constraints used were race, rental properties, vacant properties and the presence or absence of a
major road or highway.
used in the study.

The shape constraint which maximized shape compactness was also

Following the new definition of neighborhood boundary, two-stage

hierarchical generalized linear models (the Bernoulli models) were estimated conceptualizing
mothers and infants nested within zones of varying levels of racial isolation, racial clusters and
poverty to assess the effect of high racial isolation and high racial clusters on intrauterine growth
retardation (IUGR) and preterm birth.

The results showed that high racial isolation had

significant impacts on IUGR, while the odds of preterm birth were higher in racially clustered
zones.

MAUP effects were not found in the models.

Optimization of neighborhood boundary

definitions is recommended for future studies on impacts of racial segregation.
Although the conclusions from different studies may vary, the optimized zone design did not
perform worse than the subjectively-defined boundaries and could be obtained easily through
computation using automated zone design.

Since the software packages will enable users to

define their own parameters and the outputs are largely dependent on the input parameters, the
future research could focus on standardization of parameters and therefore to optimize the zone
design outputs.

19

2.5 Summary of Literature
This review of the literature presented some of the major problems that will be encountered
when using the residential ZIP Code of patients discharged with IHD, diabetes, circulatory
diseases and endocrine disorders to construct MMAs to assess the „demand‟ for inpatient hospital
services in Michigan.

AZM is presented as a methodology to address these problems.

The review of the AZM literature shows that the field is still in relatively early development
in terms of modeling zone designs for health and health services research.

For example, very

few studies reported on the full set optional of parameters that are available for use in zone
design.

Previous studies appeared to run the program for a number of times, but some of them

simply used one of the zone designs (e.g., the first restart) without validating the optimal one
within multiple restarts.

This study will advance previous research on AZM zone design by

exploring global optima versus local optima used in previous research to further address the
MAUP (described in more detail in the Methods Section Step 5).

It will also explore different

weighting schemes between the three constraint parameters (minimum case threshold versus
shape compactness versus intra-area correlation coefficients).

Finally, this study will present a

statistical approach to evaluate which of 50 restarts (output generated) is the optimal zone
design.
Furthermore, most of the studies focus only on the aspect of zone design, i.e., geographic
considerations, regardless of epidemiological considerations.

For this study, optimal MMAs

were constructed based on both larger and smaller epidemiological scales for different purposes.
This study will assess zone design in relation to epidemiological scale.
of the diseases studied will be reported for future research.

20

Elevated and low areas

2.6 Purposes of Study
The goals of this study are to (1) design optimal Medical Management Areas (MMAs) for
IHD and diabetes to (2) visualize and explore the spatial patterns of these disease subgroups to
inform future bed need in Michigan.

MMAs of these sub-groups will be compared with MMAs

of the principal diagnoses to explore geographic and epidemiological scale together.

2.7 Objectives
The objectives of this study include:
1. To demonstrate the need for the use of AZM in the construction of MMAs:
Hypothesis 1a: Mapping disease rates by ZIP Codes will result in a large proportion of
unstable rates.
2. To optimize MMA boundary definitions:
Hypothesis 2a: The shape constraint parameter will be less important than the internal
homogeneity for broad disease groups compared to specific diseases because of the
greater variation in population within the broad disease groups;
Hypothesis 2b: Aggregating on the variables sex, age and race will increase demographic
homogeneity within zones.
3. To visualize disease proportions, crude rates and age-adjusted rates of IHD, diabetes,
circulatory diseases and endocrine disorders:
Hypothesis 3a: The spatial patterns of disease groups will vary by method used to map
the diseases; new information about the prevalence of these diseases in Michigan will be
learned from each method.

21

3. DATA AND METHODS
3.1 Data
Geographic Data
The ZIP Code boundary file that will be used in this analysis will be obtained from ESRI
(2007). ESRI receives these from a private company named Tele Atlas (ESRI, 2011).

The

2007 ZIP Code boundaries (n=900) will be used because it provides the boundary that is closest
to the year of the MIDB 2008.

Due to the requirements of the AZTool, all polygons need to be

contiguous; therefore, the topology of the ZIP Code boundary file will be cleaned by removing
all isolated islands, overshoots and undershoots, and connecting Michigan‟s Upper and Lower
Peninsulas for statewide analysis.

Health Data
The Michigan Inpatient Hospital Database (MIDB) provided by the Michigan Department of
Community Health (MDCH) – Division of Health Policy and Access will be used in this research.
The MIDB is a database containing the inpatients‟ discharge records for all Michigan hospitals
and Michigan residents discharged from hospitals outside of Michigan for a calendar year.

The

MIDBs from 2000 to 2008 were given to researchers in Department of Geography at the
Michigan State University by MDCH for research bed need and health care access within the
State of Michigan.

“Inpatient” refers to a patient who spent as least one night in a hospital.

The data that will be used in this analysis from the 2008 discharge records (n=1,174,862) will
include patients‟ demographic information –i.e., sex, age, race/ethnicity, ZIP Code of residence
and principal diagnosis at time of discharge (ICD-9 code).

Only those records that pertained to

the disease groups to be studied will be used in this analysis, specifically: ischemic heart disease
22

(IHD) (ICD-9-CM: 410-414) (n=58,573), diabetes (ICD-9-CM: 250) (n=17,352), circulatory
diseases (ICD-9-CM: 390-459) (n=214,649) and endocrine, nutritional and metabolic diseases,
and immunity disorders (ICD-9-CM: 240-279) (n=44,057).

Population Data
Although the 2010 census has already released some primary results, detailed population
with age groups at the ZIP Code Tabulation Area (ZCTA) level are not yet available on the
census website to calculate area-based crude and age-adjusted rates.
estimates in 2008 were therefore, obtained from Geolytics, Inc.

Detailed population

(http://www.geolytics.com/).

These data include the total population and population by age-groups (per below) for each ZIP
Code.

3.2 Methods
MMA-zones will be obtained by aggregating ZIP Codes using the optimal zone design
generated by AZTool.

For the health data, proportions (no. cases/total hospital discharges),

crude rates (no. cases/population) and age-adjusted rates will be calculated using the new
MMA-zones.

Those different views of the health data may be used to inform inpatient hospital

services.

Computer Architecture
The data processing and analyses are accomplished on a Sun Microsystems Ultra 20
Workstation, which was running Microsoft Windows XP Professional.

This workstation is

remotely logged into from a Sun Microsystems Fire V40z Server containing MySQL using
23

KRDC. The server runs Sun Solaris 10 (x86).

Additional software used for this research

includes Microsoft Excel 2007, ESRI ArcGIS 9.3, SAS 9.2 and AZTool.

Workflow
Step 1: Database imported into SAS.

The complete database MIDB08 is exported from the

server using a SELECT query (SELECT * FROM endemic.MIDB08;) in MySQL and stored as a
text file on the workstation.

No record or field is removed during this process.

Step 2: Clean the databases.

The original ESRI ZIP Code boundary file is modified by

removing all the slivers and isolated islands and then connecting Upper Michigan and Lower
Michigan.

Thus, every ZIP Code can find at least one contiguous neighbor.

Step 1 is imported into SAS as a new table.
data and to identify outliers.

The text file in

The MIDB data is cleaned to assess any missing

Out of state inpatient records are removed (n=18,078).

The

records containing missing and vague ZIP Codes (e.g., 48400, 48600), are removed as well
(n=236).

MIDB ZIP Codes that don‟t have matched records in the ESRI 2007 ZIP Code

boundary shapefile are recoded according to visual comparison (n=65) (please refer to Appendix
2 for a list of those ZIP Codes that were removed or recoded).

Step 3: Calculate the number of cases by sex, age and race.
from the cleaned SAS table.

The health data was queried

If IHD is to be studied, the records with the corresponding ICD-9

codes are selected from the cleaned database.

Information on sex, age groups (0-14 years old,

15-44 years old, 45-64 years old, 65-74 years old, and 75 years old and older) and race groups
(white, black and others) are recoded and aggregated by residential ZIP Code.
24

Additionally,

using the same age divisions, the total numbers of patient discharges are also aggregated by ZIP
Code to calculate the proportions (no. cases/total number patient discharges) of disease.

The

proportions were calculated in SAS along with their 95% confidence (upper and lower) intervals
(CI) and relative standard errors (RSEs).
The 95% CIs are used to measure the precision around the proportion, i.e., 5% uncertainty
that the proportion occurred by chance.

Since the major factor determining the length of a

confidence interval is the size of the sample, the confidence interval becomes narrower –i.e., the
proportion is more valid when the sample size is getting larger.

Another way of determining if

the proportion is unstable due to small numbers is to calculate the relative standard error.
Below are the formulas used to calculate the RSE and 95% CIs in this thesis (Healthy People
2010 Statistical Note, 2002).

RSE 

SE
 100
rate

SE 

rate

RSE 

cases
rate
cases



1
1
 100 
 100
rate
cases

25

/* IHD */
data IHD_proportion ; set IHD_age_diss ;
proportion = (cases / total_disch) * 1000 ;
RSE = 100 * (sqrt (1/cases)) ;
if cases >= 100 then
do ;
CIL = proportion - (1.96 * proportion * (RSE/100)) ;
CIU = proportion + (1.96 * proportion * (RSE/100)) ;
end ;
else
if cases < 100 then
do ;
if cases = 1 then L = 0.02532 ; else if cases = 2 then L = 0.12110 ; else if cases = 3 then L =
0.20522 ; else if cases = 4 then L = 0.27247 ; else
etc… up to 100 (please see NCHS 2010)
CIL = proportion * L ;
CIU = proportion * U ;
end;
if cases = '.' then cases = 0 ;
if total_disch = '.' then total_disch = 0 ;
if proportion = '.' then proportion = 0 ;
if RSE = '.' then RSE = 0 ;
if CIL = '.' then CIL = 0 ;
if CIU = '.' then CIU = 0 ;

Step 4: Join the health database to the ZIP Code boundary shapefile.

In ArcMAP, the

health database is joined to ESRI 2007 cleaned shapefile using the key ID = ZIP Code.

This

shapefile is exported as a new shapefile ready to be imported into AZTool.

Step 5. Checking the instability of IHD and diabetes proportions by ZIP Codes.

Of 900

ZIP Codes, 276 (30.7%) had fewer than 30 IHD cases and 578 (64.2%) of ZIP Codes had fewer
than 30 cases of diabetes.

These numbers demonstrate that using ZIP Codes as the unit of

analysis will lead to a high proportion of unreliable rates (i.e., high RSEs of the rates) (Figures
1-2) justifying the need for AZM to construct MMAs in Michigan.
26

Figure 1. IHD: Relative standard errors (RSEs) of
1
proportions by ZIP Code

Figure 2. Diabetes: Relative standard errors
(RSEs) of proportions by ZIP Code

1

For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation.

Step 6: Using AZTool to generate MMA-zone assignment files. The cleaned ZIP Code
shapefile is input into AZTool – AZTImport is used to generate intersection (.pat) and contiguity
(.aat) files. A python code is used to make the contents in every column align to the right in
accordance with the requirement of AZTool_Developer.

The intersection and contiguity files

are input into AZTool_Developer to produce optimal zone assignment using the constraint
parameters defined below.
This methodology implements a computationally intensive algorithm that recombines ZIP
Codes from the overall dataset into a smaller set of output zones from within which to calculate
stable proportions and rates.

This is an iterative process, by which one geographic unit is

randomly selected and user-defined constraint parameter(s) (below) are evaluated.
27

If the

parameters are not met, AZM will search contiguous ZIP Codes until it is achieved, thereafter,
aggregating the data and dissolving internal boundaries to create a new zone.

Minimum Population Threshold
The first parameter selected is the minimum population threshold. In this study, the
minimum population threshold is set as 30 cases.
cases from which to calculate stable rates.

Thus, all new zones created have at least 30

The relative weight is set to 100%.

Shape Compactness
2

The second parameter (perimeter /area, P2A) selected is the shape compactness, defined as:
2
1 qk
 4 A
k

Where qk is the perimeter of zone k and Ak is its area.

The automated zone design function is to

minimize the perimeter squared divided by area, which maximizes shape compactness of zones.
In this study it is desirable to have compact zones in order to minimize the potential for local
variability across the zone.

The relative weight is set to 50%.

Internal Homogeneity
The third parameter selected is the homogeneity constraint.

The homogeneity constraint

promotes homogeneity within zones and heterogeneity between zones.
inpatients‟ sex, age and race as homogeneity constraint.

This study uses

Although the theoretical maximum

score for internal homogeneity is 1.0, this will not be found in census areas, and any value above
about 0.05 implies a reasonable degree of homogeneity (Martin & Cockings, 2001).
28

Consider a grouping variable, with k=1,2,…, K categories. This study has K=3 categories
(sex, age, race).

For each category, e.g. sex measure of homogeneity can be obtained using the

intra-area correlation (IAC).

This is calculated as:

1
M
g 1 N g Pkg  Pk 2
1
 k  M 1

N *  1 PK 1  PK 
N * 1



Where,







N * is the mean case size of the ZIP Codes, with an adjustment (Tranmer & Steel,

1998) to take into account variation in the case size of the units.

N *.

In practice,

N * is close to

Ng is the number of cases of a ZIP Code, PK is the overall proportion of the cases in

category K, and Pkg is the proportion in category k in ZIP Code g.

After each variable is calculated, the overall IAC is calculated as:

1 K

 1  Pk  k
K  1 k 1
The overall relative weight is set to 100% for the sub-groups of disease and 150% for the
primary diagnostic groups.

Circulatory diseases and endocrine disorders generally have more

variability in patients within ZIP Codes than IHD and diabetes because of the epidemiological
scale of analysis. Within internal homogeneity each constraint parameter is given equal weight.

Simulated/Synthetic Annealing (SA)
AZTool will be run in SA mode, swaps which cause a deterioration in the overall solution
will be allowed in the first half of the iteration cycle (50 iteration cycles).
29

This enables the

program to search for the global-optima by escaping from the local-optima.

The size of initial

margin is set to 1 (default) in this study.

Region
The last constraint parameter is that the new zones will be constrained within existing
Hospital Service Areas (HSAs).

Because ZIP Codes are not perfectly nested within HSAs, a

ZIP Code is considered to belong to an HSA if the centroid of ZIP Code falls within the HSA.
Constraining zones within HSAs was preferred because these are health services administrative
units from within which, hospital services are managed.

From an administrative perspective it

was therefore, important to create new zones that respected these boundaries.

Optimization
With these parameters, the AZM analysis is conducted by running 100 times with 20
iterations taking the run with the minimum threshold, the most compact shape and the maximum
homogeneity as the optimal AZM-MMA boundary definition.
parameters are described in an .xml file.

All the input route and

A batch mode is utilized to execute a single .xml file

for 50 times for each disease/disease groups. Each output assigns a tract ID (repeatable) for a
ZIP Code, as well as generates a statistical report containing the information about zone number,
zone size, P2A score, IAC score, etc.

Of the 50 outputs, the one with the lowest P2A and

highest IAC is chosen to be the optimal (MMA) zone design.

With the same parameters,

AZTool is conducted by running 50 program restarts with 100 runs and 20 iterations, each of
which takes the most compact shape and maximum IAC.

The optimal output of the program

restarts is identified using Wilcoxon signed-rank test (a paired difference test) to select the lowest
30

P2A and highest IAC score.

Because the P2A score is almost 1 million times larger than the

IAC score, they are not comparable on different orders of magnitude.
direct way will result in simply ranking the P2A score.

To rank the outputs in a

Thus, the IAC score is magnified by

multiplying the ratio of the average of P2A scores to the average of IAC scores.

The modified

IAC score will then be ranked along with the P2A score.

Step 7: Dissolve the ZIP Code boundaries. Join the zone assignment file and second table
generated in step 3 on the boundary shapefile.

Dissolve the boundary using new TractID and

keep the variables of summation of cases, total discharge and total population by age groups.
The attribute table should contain the information with all age groups.
MMA-Zone table back into SAS to calculate proportions and rates.

Bring the new

Herein only the IHD

example is provided.

Step 8: Calculate the proportion of IHD.

The total number of hospital discharges by

MMA-Zone is used in the denominator to calculate the proportions.

 case

i

Proportion =

 total _ disch arg esi

 100

Step 9: Calculate the rates of IHD and diabetes.

The total population is used as the

denominator to calculate the crude rate.

 case
 pop

i

Crude rate =

 100

i

Age-adjustment is a statistical process applied to rates of disease, death, injuries or other
31

health outcomes which allows communities with different age structures to be compared
(NYSDOH, 1999).

A large number of diseases occur at different rates in different age groups.

Most chronic diseases, for example heart diseases, occur more often among older people.
other outcomes, such as injuries, occur more often among younger people.

Some

Thus, an area with

more older people tend to show higher rates of chronic diseases, and similarly an area with more
younger people tend show higher rates of injuries or other youth- susceptible diseases.
high rates don‟t necessarily indicate that population within areas are less healthy.

The

In order to

minimize the effect brought by different age distribution within an area (e.g., zone), the standard
population from a higher political unit (e.g., state) should be used to adjust proportion and rate.
In this study, age standardization (direct method) is used to adjust the proportion and rate using
the statewide population as standard population.



5

Age-adjusted rate =

i 1

agei
 popi
popi
 100 , i=1, 2, …, 5
popi


Step 10: Visualize the proportion and rate maps. Join the proportion, crude and age-adjusted
rates (tables) by MMA-Zone to the dissolved zone-shapefiles and create choropleth maps.
The steps above were repeated for diabetes, the circulatory diseases and endocrine
conditions.

32

4. RESULTS
4.1 Descriptive Statistics
Table 2 shows the descriptive statistics for IHD and diabetes in Michigan.
were 1,174,862 hospitalized patients in Michigan.
discharged with IHD and 17,352 (1.5%) with diabetes.
were male compared with 51.6% for diabetes.

In 2008, there

Of these, 58,573 (5.0%) were patients
Of patients discharged with IHD 60.1%

Almost all patients discharged with IHD were

over 44 years of age; however, a substantial proportion of patients with diabetes were less than
44 years of age.

Of patients discharged with diabetes, 33.9% were Blacks compared with

13.0% for IHD.
Table 2. Patient discharge characteristics for Ischemic Heart Disease
(IHD) and diabetes in Michigan, 2008.
IHD
Diabetes
No.
%
No.
%
1
Sex
Male
35,200
60.1
8,951
51.6
Female
23,367
39.9
8,401
48.4
Age
0-14
3
<1.0
906
5.2
15-44
2,812
4.8
5,389
31.1
45-64
22,972
39.2
6,224
35.9
65-74
14,566
24.9
2,215
12.8
75+
18,220
31.1
2,618
15.1
Race
White
50,141
85.6
11,069
63.8
Black
7,624
13.0
5,874
33.9
Others
808
1.4
409
2.4
Total
58,573
100.0
17,352
100.0
1

Data variable missing = 6

4.2 Automated zone matching (AZM) methodology output
The optimal zone design in this study met the requirements of a minimum case threshold of
33

30, maximum shape compactness (P2A) and maximum internal homogeneity (IAC) (patient‟s
sex, age and race). Based on the statistical results from these constraint parameters the optimal
zone design was selected from 50 program restarts (20 runs with 100 iterations in each restart).
Tables 3-6 display the statistical results from the constraint parameters (P2A and IAC) for each
of the 50 restarts.

Thus, most optimal restart was that with the combination of a low P2A and

high IAC scores.

However, the lowest P2A and highest IAC scores do not necessarily occur in

the same „restart‟.

Therefore, to select the optimal zone design the Wilcoxon signed rank test

was used to prioritize the 50 restarts.

The Wilcoxon signed rank test is a method used to

compare two repeated measurements on a single sample.

In this study it was used to rank the

P2A and IAC output from the 50 restarts.
The direct method of Wilcoxon signed rank simply ranks the difference between the P2A
and IAC scores from the lowest to the highest in order to get a relatively small P2A and IAC
combination score (4th column).

However, the P2A score was over 100,000 times larger than

the IAC score, and therefore the variation of IAC score (±
0.1) was negligible compared to the
variation of P2A score (±
400~500).

Thus, this method appeared to rank only the P2A score.

In order to make the IAC score more comparable to the P2A score, the IAC score was
magnified by multiplying the ratio of the average of P2A scores to the average of IAC scores.
The new IAC score (5th column) was then used to conduct the Wilcoxon signed rank along with
the raw P2A score. The final signed rank is shown in the last column of each table.
Comparing the results from the two ranking methods the „top restarts‟ are identical for IHD,
diabetes, circulatory diseases and endocrine disorders, although the other restarts are not the
same.

Thus this top restart (zone design) was used to construct the MMAs.

the scatter charts of P2A and IAC scores.

Figures 3-6 show

The marked pair of P2A and IAC in each table is the
34

one that was chosen.
For the 50 restarts for IHD, the P2A score ranged from 12159.985 to 13097.956 and the raw
IAC score ranged from 0.101 to 0.104. There was no certain order or obvious pattern for the 50
restarts.

For this disease the optimal run was the run 50.

In order to validate that the 51st or

later runs would not offer a better solution AZM was run for an additional 10 restarts. A better
solution was not found within the additional 10 restarts (results not shown).

Table 3. Ischemic Heart Disease (IHD) results from AZM constraint parameter 50 restarts.
#
P2A
IAC
direct
IAC
signed
sign
xi-yi
|xi-yi| rank
Restart
Score
Score
rank
Score*
rank
1
2
3
4
5
6
7
8
9
10
.
.
40
41
42
43
44
45
46
47
48
49
50

12706.433
12578.864
12587.606
12665.61
12650.174
12311.717
12659.281
12530.21
12479.754
12702.271

0.102
0.103
0.101
0.103
0.102
0.102
0.103
0.102
0.102
0.102

32
18
19
27
25
4
26
17
14
31

12581.069
12704.413
12457.725
12704.413
12581.069
12581.069
12704.413
12581.069
12581.069
12581.069

1
-1
1
-1
1
-1
-1
-1
-1
1

125.364
-125.549
129.881
-38.803
69.105
-269.352
-45.132
-50.859
-101.315
121.202

125.364
125.549
129.881
38.803
69.105
269.352
45.132
50.859
101.315
121.202

25
26
28
7
17
44
9
11
21
23

25
-26
28
-7
17
-44
-9
-11
-21
23

12406.211
12422.611
12516.299
12606.672
12667.231
12445.146
12731.338
12632.239
12829.676
12412.041
12159.985

0.102
0.101
0.102
0.103
0.103
0.101
0.102
0.103
0.103
0.102
0.103

8
11
16
21
28
13
34
22
42
10
1

12581.069
12457.725
12581.069
12704.413
12704.413
12457.725
12581.069
12704.413
12704.413
12581.069
12704.413

-1
-1
-1
-1
-1
-1
1
-1
1
-1
-1

-174.858
-35.114
-64.770
-97.741
-37.182
-12.579
150.269
-72.174
125.263
-169.028
-544.428

174.858
35.114
64.770
97.741
37.182
12.579
150.269
72.174
125.263
169.028
544.428

35
5
15
20
6
1
32
18
24
34
50

-35
-5
-15
-20
-6
-1
32
-18
24
-34
-50

35

Figure 3. Ischemic Heart Disease (IHD) results from AZM constraint parameter 50 restarts.

For circulatory diseases the 50 restarts showed the P2A scores ranging from 12290.7 to
13180.417 and the IAC scores ranged from 0.105 to 0.107. The P2A score was slightly higher
than that of IHD but the IAC score was also slightly higher than that of IHD.

This finding

suggests that the internal homogeneity of MMAs for circulatory diseases is better than IHD, but
at the cost of shape compactness.
schemes (150% versus 100%).
restarts.

These findings were the result of the different weighting

Again there was no certain order or obvious pattern for the 50

For circulatory diseases the best run occurred at the 44th restart.

36

Table 4. Circulatory diseases results from AZM constraint parameter 50 restarts.
#
P2A
IAC
direct
IAC
sign
xi-yi
|xi-yi| rank
Restart
Score
Score
rank
Score*
1
2
3
4
5
6
7
8
9
10
.
.
40
41
42
43
44
45
46
47
48
49
50

signed
rank

12698.642
12814.638
12817.251
13180.417
12833.441
12882.058
12587.874
12653.838
13142.169
12886.871

0.106
0.106
0.106
0.107
0.106
0.106
0.106
0.105
0.107
0.105

11
19
21
50
24
31
7
9
49
32

12830.206
12830.206
12830.206
12951.245
12830.206
12830.206
12830.206
12709.166
12951.245
12709.166

-1
-1
-1
1
1
1
-1
-1
1
1

-131.564
-15.568
-12.955
229.172
3.235
51.852
-242.332
-55.328
190.924
177.705

131.564
15.568
12.955
229.172
3.235
51.852
242.332
55.328
190.924
177.705

32
8
6
43
2
19
44
20
41
38

-32
-8
-6
43
2
19
-44
-20
41
38

12852.792
12510.993
12586.063
13113.917
12290.7
12465.152
12939.848
12874.901
12825.617
12997.182
12994.496

0.106
0.106
0.105
0.106
0.105
0.106
0.106
0.106
0.106
0.107
0.107

27
3
6
47
1
2
37
29
23
42
41

12830.206
12830.206
12709.166
12830.206
12709.166
12830.206
12830.206
12830.206
12830.206
12951.245
12951.245

1
-1
-1
1
-1
-1
1
1
-1
1
1

22.586
-319.213
-123.103
283.711
-418.466
-365.054
109.642
44.695
-4.589
45.937
43.251

22.586
319.213
123.103
283.711
418.466
365.054
109.642
44.695
4.589
45.937
43.251

11
48
29
46
50
49
28
16
3
17
15

11
-48
-29
46
-50
-49
28
16
-3
17
15

Figure 4. Circulatory diseases results from AZM Constraint Parameters 50 restarts.
37

For diabetes the P2A scores ranged from 7723.661 to 8382.684 and the IAC scores ranged
from 0.113 to 0.115.

Both P2A and IAC scores performed better than those of IHD, indicating

that MMAs for diabetes has an overall more compact shape and higher levels of internal
homogeneity.

The best run was the 42nd restart.

Table 5. Diabetes results for AZM constraint parameter 50 restarts.
#
P2A
IAC
direct
IAC
sign
xi-yi
Restart
Score
Score
rank
Score*
1
2
3
4
5
6
7
8
9
.
40
41
42
43
44
45
46
47
48
49
50

|xi-yi|

rank

signed
rank

8199.467
7958.955
8229.87
8073.524
8201.623
8115.091
8010.526
8122.558
8103.236

0.114
0.114
0.114
0.113
0.115
0.115
0.113
0.114
0.115

41
9
45
22
42
28
12
32
25

8081.797
8081.797
8081.797
8010.904
8152.690
8152.690
8010.904
8081.797
8152.690

1
-1
1
1
1
-1
-1
1
-1

117.670 117.670
-122.842 122.842
148.073 148.073
62.620
62.620
48.933
48.933
-37.599 37.599
-0.378
0.378
40.761
40.761
-49.454 49.454

36
37
44
26
19
14
1
17
20

36
-37
44
26
19
-14
-1
17
-20

8143.834
8127.077
7723.661
8054.704
8101.63
7779.17
8226.145
7986.754
8184.887
8029.364
8024.535

0.115
0.114
0.114
0.114
0.114
0.114
0.114
0.114
0.114
0.113
0.114

36
33
1
20
24
2
44
10
40
15
13

8152.690
8081.797
8081.797
8081.797
8081.797
8081.797
8081.797
8081.797
8081.797
8010.904
8081.797

-1
1
-1
-1
1
-1
1
-1
1
1
-1

-8.856
45.280
-358.136
-27.093
19.833
-302.627
144.348
-95.043
103.090
18.460
-57.262

3
18
50
8
7
49
42
31
34
6
22

-3
18
-50
-8
7
-49
42
-31
34
6
-22

38

8.856
45.280
358.136
27.093
19.833
302.627
144.348
95.043
103.090
18.460
57.262

Figure 5. Diabetes results for AZM constraint parameter 50 restarts.

Finally for endocrine disorders the P2A scores ranged from 11205.813 to 12094.776 and the
IAC scores ranged from 0.105 to 0.108.

The shape compactness is better than for IHD and

circulatory diseases, but not as good as diabetes.

The internal homogeneity of endocrine

disorders (0.105-0.108) is similar to circulatory diseases (0.105-0.107), which is between IHD
(0.101-0.104) and diabetes (0.113-0.115).

The 45th restart was the best.

39

Table 6. Endocrine disorders results for AZM constraint parameter 50 restarts.
#
P2A
IAC
direct
IAC
sign
xi-yi
|xi-yi|
Restart
Score
Score
rank
Score*
1
2
3
4
5
6
7
8
9
10
.
.
42
43
44
45
46
47
48
49
50

rank

signed
rank

11978.361
11708.393
11372.357
11772.844
11544.485
11775.188
11811.23
11330.497
11478.534
11449.538

0.108
0.106
0.106
0.107
0.107
0.107
0.107
0.106
0.106
0.106

28
32
6
37
17
38
39
3
13
11

11818.119
11599.265
11599.265
11708.692
11708.692
11708.692
11708.692
11599.265
11599.265
11599.265

1
1
-1
1
-1
1
1
-1
-1
-1

160.242
109.128
-226.908
64.152
-164.207
66.496
102.538
-268.768
-120.731
-149.727

160.242
109.128
226.908
64.152
164.207
66.496
102.538
268.768
120.731
149.727

30
20
40
10
31
11
18
46
23
28

30
20
-40
10
-31
11
18
-46
-23
-28

11563.882
11418.243
11836.446
11205.813
11528.659
11376.88
11900.819
11731.725
11372.179

0.106
0.107
0.107
0.106
0.106
0.106
0.107
0.106
0.106

21
9
41
1
16
7
47
34
5

11599.265
11708.692
11708.692
11599.265
11599.265
11599.265
11708.692
11599.265
11599.265

-1
-1
1
-1
-1
-1
1
1
-1

-35.383
-290.449
127.754
-393.452
-70.606
-222.385
192.127
132.460
-227.086

35.383
290.449
127.754
393.452
70.606
222.385
192.127
132.460
227.086

5
47
24
50
12
39
38
26
41

-5
-47
24
-50
-12
-39
38
26
-41

Figure 6. Endocrine disorders results for AZM constraint parameter 50 restarts.

40

4.3 Medical Management Areas (Proportions)
Following automated zone design the number of ZIP Codes was reduced from 900 to 274
zones for IHD (Figure 7), 310 zones for circulatory diseases (Figure 8), 183 zones for diabetes
(Figure 9) and 274 zones for endocrine disorders (Figure 10).
calculated within the optimal zone designs.

Their proportions were

Each zone had at least 30 cases and therefore met

the case threshold for stable proportions.
Figure 7 and Table 7 shows the MMAs of crude proportions for IHD. The spatial patterns
show MMAs with high proportions (11.8, 95% CI 9.3, 14.7) of patients discharged from
hospitals in Au Gres and the northwestern portion of the state (hospital system area) (HSA=6)
with IHD.

High proportions of discharges are also observed near the southern portion of the

state (9.3, 95% CI 8.3, 10.4) (HSA=2) bordering with Indiana and Ohio and in western Michigan
(10.6, 95% CI 7.6, 14.3) (HSA=4).

41

Figure 7. Ischemic heart disease: proportions by MMA (n=302), Michigan 2008.
(statewide proportion: 5.0 per 100 discharges)

42

1

Table 7. MMAs with high proportions of patients discharged with IHD,
Michigan, 2008.
#
MMA
316
627
42
557
210
412
170
36
535
468
393
52
381
151
573
302
18

2

3

4

Cases

total

crude proportion

95% CI

RSE

77
57
75
39
42
136
167
87
268
112
159
297
57
36
289
83
38

654
504
679
365
398
1,293
1,598
857
2,713
1,166
1,658
3,183
613
388
3,150
909
426

11.8
11.3
11.0
10.7
10.6
10.5
10.5
10.2
9.9
9.6
9.6
9.3
9.3
9.3
9.2
9.1
8.9

9.3, 14.7
8.6, 14.7
8.7, 13.8
7.6, 14.6
7.6, 14.3
8.8, 12.3
8.9, 12
8.1, 12.5
8.7, 11.1
7.8, 11.4
8.1, 11.1
8.3, 10.4
7, 12
6.5, 12.8
8.1, 10.2
7.3, 11.3
6.3, 12.2

11.4
13.2
11.5
16.0
15.4
8.6
7.7
10.7
6.1
9.4
7.9
5.8
13.2
16.7
5.9
11.0
16.2

1

High crude proportions are marked as red areas in the maps.
Proportion: cases per 100 discharges
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

Figure 8 shows the MMAs of crude proportions of patients discharged with circulatory
diseases.

These spatial patterns are somehow similar to that of IHD.

The northeast and

northwestern sides of Lower Michigan (HSA=7), MMAs near the southern border (HSA=2) and
some scattered areas of the Upper Peninsula.

The highest crude proportion was 30.5 per 100

discharges (95% CI 23.6, 38.7) in Black River and Spruce (Table 8).

Those large urban areas,

such as Detroit, Lansing, Grand Rapids and Marquette, tended to have low proportions of
hospital discharges for circulatory diseases, which conforms to the pattern of IHD.

43

Figure 8. Circulatory diseases: proportions by MMA (n=310), Michigan 2008.
(statewide proportion: 18.3 per 100 discharges)

44

1

Table 8. MMAs with high proportions of patients discharged with circulatory diseases,
Michigan, 2008.
2
3
4
# MMA Cases
total
crude proportion
95% CI
RSE
781
28
466
484
533
753
763
463
500
774
386
495
559
811
713
343
426
694
593
262
618
354
37
166
585
652
379
165
624
512
48
660
802

67
206
98
61
96
71
166
117
644
267
188
370
410
42
1210
424
144
58
173
64
36
416
549
906
248
171
61
100
150
387
143
238
101

220
679
327
219
354
262
613
433
2,473
1,026
728
1,437
1,598
164
4,748
1,671
576
233
695
258
146
1,692
2,241
3,728
1,021
704
252
416
625
1,616
598
999
425

30.5
30.3
30.0
27.9
27.1
27.1
27.1
27.0
26.0
26.0
25.8
25.7
25.7
25.6
25.5
25.4
25.0
24.9
24.9
24.8
24.7
24.6
24.5
24.3
24.3
24.3
24.2
24.0
24.0
23.9
23.9
23.8
23.8

23.6, 38.7
26.2, 34.5
24.3, 36.5
21.3, 35.8
22, 33.1
21.2, 34.2
23, 31.2
22.1, 31.9
24, 28.1
22.9, 29.1
22.1, 29.5
23.1, 28.4
23.2, 28.1
18.5, 34.6
24, 26.9
23, 27.8
20.9, 29.1
18.9, 32.2
21.2, 28.6
19.1, 31.7
17.3, 34.1
22.2, 26.9
22.4, 26.5
22.7, 25.9
21.3, 27.3
20.6, 27.9
18.5, 31.1
19.3, 28.8
20.2, 27.8
21.6, 26.3
20, 27.8
20.8, 26.9
19.1, 28.4

1

High crude proportions are marked as red areas in the maps.
Proportion: cases per 100 discharges
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

45

12.2
7.0
10.1
12.8
10.2
11.9
7.8
9.2
3.9
6.1
7.3
5.2
4.9
15.4
2.9
4.9
8.3
13.1
7.6
12.5
16.7
4.9
4.3
3.3
6.4
7.6
12.8
10.0
8.2
5.1
8.4
6.5
10.0

Figure 9 shows the MMAs of crude proportions of patients discharged with diabetes.
Different from previous maps of MMAs for IHD and circulatory diseases, the MMAs with high
and low proportions of diabetes were more dispersed.

Those large cities, such as Detroit,

Lansing, Grand Rapids Kalamazoo, Saginaw, Muskegon and Flint, tended to have high
proportions of patients discharged with diabetes, which was opposite to the pattern of IHD.
The highest crude proportion was 3.4 per 100 discharges (95% CI 2.9, 3.9) in Detroit (Table 9).
Suburban and rural areas were more likely to have lower proportions of patient‟s discharged with
diabetes that urban areas.

46

Figure 9. Diabetes: proportions by MMA (n=183), Michigan 2008.
(statewide proportion: 1.5 per 100 discharges)

47

1

Table 9. MMAs with high crude proportions of patients discharged with diabetes, Michigan,
2008.
2
3
4
# MMA
cases
total
crude proportion
95% CI
RSE
343
250
323
199
344
40
182
154
10
241
2
228
298
297
252
169
331
167
108
235
43
311
332
270
306
341
334

194
421
175
968
214
208
669
103
280
277
112
36
163
40
114
75
128
246
123
111
212
246
103
127
154
118
124

5,712
14,410
6,379
36,453
8,078
7,870
25,883
3,988
10,965
10,899
4,448
1,442
6,779
1,668
4,812
3,224
5,568
10,932
5,470
4,957
9,528
11,060
4,718
5,835
7,228
5,581
6,033

3.4
2.9
2.7
2.7
2.6
2.6
2.6
2.6
2.6
2.5
2.5
2.5
2.4
2.4
2.4
2.3
2.3
2.3
2.2
2.2
2.2
2.2
2.2
2.2
2.1
2.1
2.1

2.9, 3.9
2.6, 3.2
2.3, 3.1
2.5, 2.8
2.3, 3
2.3, 3
2.4, 2.8
2.1, 3.1
2.3, 2.9
2.2, 2.8
2.1, 3
1.7, 3.5
2, 2.8
1.7, 3.3
1.9, 2.8
1.8, 2.9
1.9, 2.7
2, 2.5
1.9, 2.6
1.8, 2.7
1.9, 2.5
1.9, 2.5
1.8, 2.6
1.8, 2.6
1.8, 2.5
1.7, 2.5
1.7, 2.4

1

High crude proportions are marked as red areas in the maps.
Proportion: cases per 100 discharges
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

48

7.2
4.9
7.6
3.2
6.8
6.9
3.9
9.9
6.0
6.0
9.4
16.7
7.8
15.8
9.4
11.5
8.8
6.4
9.0
9.5
6.9
6.4
9.9
8.9
8.1
9.2
9.0

Figure 10 is the map of crude proportions of patients discharged with endocrine disorders.
The spatial pattern is generally similar to diabetes, which seldom has large clusters.

Urban

areas like Detroit, Lansing, Muskegon, Kalamazoo and Midland, as well as some other areas
show MMAs with elevated proportions of hospital discharges with endocrine disorders in the
Upper Peninsula and Lower Michigan.

The highest crude proportion of discharges with

endocrine disorders was 6.16 per 100 discharges (95% CI 4.27, 8.61) in Munith (Table 10).

Figure 10. Endocrine disorders: proportions by MMA (n=274), Michigan 2008.
(statewide proportion: 3.8 per 100 discharges)
49

1

Table 10. MMAs with high crude proportions of patients discharged with endocrine disorders,
Michigan, 2008.
2
3
4
# MMA Cases
total
crude proportion
95% CI
RSE
29
365
107
453
499
369
8
186
508
391
518
539
23
143
424
416
417
316
410
129
510
229
310
80
169

34
30
67
1,319
90
570
456
56
627
620
786
44
35
114
218
166
481
653
130
50
41
31
60
69
373

552
519
1,186
24,355
1,668
10,578
8,633
1,068
12,195
12,086
15,545
878
704
2,300
4,448
3,431
9,986
13,565
2,705
1,052
868
659
1,283
1,480
8,078

6.2
5.8
5.6
5.4
5.4
5.4
5.3
5.2
5.1
5.1
5.1
5.0
5.0
5.0
4.9
4.8
4.8
4.8
4.8
4.8
4.7
4.7
4.7
4.7
4.6

4.3, 8.6
3.9, 8.3
4.4, 7.2
5.1, 5.7
4.3, 6.6
4.9, 5.8
4.8, 5.8
4, 6.8
4.7, 5.5
4.7, 5.5
4.7, 5.4
3.6, 6.7
3.5, 6.9
4, 5.9
4.3, 5.6
4.1, 5.6
4.4, 5.2
4.4, 5.2
4, 5.6
3.5, 6.3
3.4, 6.4
3.2, 6.7
3.6, 6
3.6, 5.9
4.1, 5.1

1

High crude proportions are marked as red areas in the maps.
Proportion: cases per 100 discharges
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

50

17.1
18.3
12.2
2.8
10.5
4.2
4.7
13.4
4.0
4.0
3.6
15.1
16.9
9.4
6.8
7.8
4.6
3.9
8.8
14.1
15.6
18.0
12.9
12.0
5.2

4.4 Medical Management Areas (Crude and Age-Adjusted Rates)
Figure 11 shows the MMAs of crude rates of patients discharged with IHD in the population
using the optimal zone design.

The spatial patterns showed that high rates of IHD in the

population did not scatter evenly throughout the state. The northeast and southern portions of
Lower Michigan (HSA=2,6,7) showed elevated crude rates of discharges with IHD.

The

highest crude rate was 24.2 per 1,000 population (95% CI 19.1, 30.3) and the age-adjusted rate
was 17.2 in Au Gres (Table 11).

Figure 11. Ischemic heart disease: crude rates by MMA (n=302), Michigan 2008.
(statewide rate: 5.8 per 1,000 population)
51

1

Table 11. MMAs with high crude rates of patients discharged with ischemic heart disease,
Michigan, 2008.
#
2
3
4
2
cases
population
crude rate
95% CI
RSE
age-adjusted rate
MMA
316
170
151
573
468
412
535
55
557
336
36
302
182
354
393
627
150
52
202
585
70

77
167
36
289
112
136
268
38
39
469
87
83
502
180
159
57
39
297
177
516
50

3,180
9,888
2,307
19,283
7,535
9,331
18,437
2,685
2,844
34,425
6,411
6,124
37,945
13,811
12,252
4,560
3,130
23,928
14,323
41,988
4,144

24.2
16.9
15.6
15.0
14.9
14.6
14.5
14.2
13.7
13.6
13.6
13.6
13.2
13.0
13.0
12.5
12.5
12.4
12.4
12.3
12.1

19.1, 30.3
14.3, 19.5
10.9, 21.6
13.3, 16.7
12.1, 17.6
12.1, 17
12.8, 16.3
10, 19.4
9.8, 18.7
12.4, 14.9
10.9, 16.7
10.8, 16.8
12.1, 14.4
11.1, 14.9
11, 15
9.5, 16.2
8.9, 17
11, 13.8
10.5, 14.2
11.2, 13.3
9, 15.9

11.4
7.7
16.7
5.9
9.4
8.6
6.1
16.2
16.0
4.6
10.7
11.0
4.5
7.5
7.9
13.2
16.0
5.8
7.5
4.4
14.1

17.2
10.8
8.5
10.1
10.9
13.5
11.8
8.6
11.1
12.9
10.7
10.5
12.3
10.3
11.7
11.4
10.9
12.2
11.6
10.3
7.8

1

High crude proportions are marked as red areas in the maps.
Rate: cases per 1,000 population
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

Figure 12 shows the MMAs of crude rates of patients discharged with circulatory diseases
using the optimal zone design.

The spatial pattern still showed MMAs with high proportions of

patient‟s discharged with IHD throughout the state.

A large cluster of high proportion of

discharges with circulatory diseases was located in northeast of Lower Michigan (HSA=6,7) and
two large clusters of low proportion were located in southwest and southeast of Lower Michigan.

52

The highest crude rate was 54.7 per 1,000 population (95% CI 44.4, 66.7) and its age-adjusted
rate was 34.15 in Comins and Fairview (Table 12).

Figure 12. Circulatory diseases: crude rates by MMA (n=310), Michigan 2008.
(statewide rate: 21.2 per 1,000 population)

53

1

Table 12. MMAs with high crude rates of patients discharged with circulatory diseases,
Michigan, 2008.
#
MMA

cases

population

crude
2
rate

95% CI

3

RSE

466
774
152
343
618
713
753
781
533
593
559
671
694

98
267
1,558
424
36
1,210
71
67
96
173
410
1,587
58

1,790
5,886
34,638
9,777
848
29,171
1,747
1,663
2,383
4,385
10,511
41,622
1,593

54.7
45.4
45.0
43.4
42.5
41.5
40.6
40.3
40.3
39.5
39.0
38.1
36.4

44.4, 66.7
39.9, 50.8
42.7, 47.2
39.2, 47.5
29.7, 58.8
39.1, 43.8
31.7, 51.3
31.2, 51.2
32.6, 49.2
33.6, 45.3
35.2, 42.8
36.3, 40
27.6, 47.1

10.1
6.1
2.5
4.9
16.7
2.9
11.9
12.2
10.2
7.6
4.9
2.5
13.1

1

High crude proportions are marked as red areas in the maps.
Rate: cases per 1,000 population
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

54

4

age-adjusted
2
rate
34.1
34.8
43.9
29.7
23.2
26.5
30.4
24.7
20.2
25.1
25.5
34.6
24.2

Figure 13 shows the age-adjusted rates of MMA-IHD.

IHD age-adjusted rates were still

generally high in the northwest portion of the state and other rural areas.
age-adjusted rate was 17.2 per 1,000 population in Flint (MMA 316).

The highest

MMAs that had high

age-adjusted rates also included Kingsley and Buckley (MMA 452: 10.7 per 1,000 population)
and Monroe (MMA 388: 10.1 per 1,000 population).

In contrast, some other areas seem not to

have very high rates in this map, such as Glennie, compared to the map of crude rates.

Figure 13. Ischemic heart disease: age-adjusted rates by MMA (n=302), Michigan 2008.
55

Figure 14 shows the age-adjusted rates of patient‟s discharged with circulatory diseases.
The spatial pattern of discharges with circulatory diseases was somehow similar to that of IHD.
Compared to the map of crude rates, areas with high and low age-adjusted rates were even more
scattered.

Areas with high age-adjusted rates generally scattered in the Lower Michigan.

The

highest age-adjusted rate was 43.9 per 1,000 population in Detroit (MMA 152). Some other
urban areas, such as Battle Creek (MMA 337: 33.5 per 1,000 population) and Flint (MMA 654:
39.5 per 1,000 population), showed elevated age-adjusted rates as well.

Figure 14. Circulatory diseases: age-adjusted rates by MMA (n=310), Michigan 2008.
56

Figure 15 shows the crude rates of discharges with diabetes using the optimal zone design.
The spatial pattern of diabetes was more evenly distributed throughout the state than IHD.

The

highest crude rate was 6.31 per 1,000 population (95% CI 5.42, 7.2) and the age-adjusted rate
was 6.46 in Detroit (Table 13).

There are two more high areas in Detroit too.

The other

obviously elevated crude rate (in the middle of the map) was 4.62 per 1,000 (95% CI 4, 5.24) and
its age-adjusted rate was 5.12.

Most of the state seems to have medium to low rates.

Figure 15. Diabetes: crude rates by MMA (n=183), Michigan 2008.
(statewide rate: 1.7 per 1,000 population)
57

1

Table 13. MMAs with high crude rates of patients discharged with diabetes,
Michigan, 2008.
#
MMA

cases

population

crude rate

343
154
250
344
40
10

194
103
421
214
208
280

30,733
20,273
86,598
46,337
46,155
70,276

6.3
5.1
4.9
4.6
4.5
4.0

2

95% CI

3

5.4, 7.2
4.1, 6.1
4.4, 5.3
4, 5.2
3.9, 5.1
3.5, 4.5

RSE

4

7.2
9.9
4.9
6.8
6.9
6.0

age-adjusted rate

2

6.5
5.0
4.9
5.1
4.7
4.5

1

High crude proportions are marked as red areas in the maps.
Rate: cases per 1,000 population
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

Figure 16 shows the crude rates of discharges with endocrine disorders.

The spatial pattern

of endocrine conditions were scattered throughout the state. The highest crude rate was 9.54
per 1,000 population (95% CI 9.02, 10.05) and the age-adjusted rate was 10.14 still in Detroit
(Table 13).

There are a couple more high areas all over the state as well, including Saginaw,

Lansing, Flint and west and east corners of the Upper Michigan.
are more likely to have low crude rates.

58

The suburban and rural areas

Figure 16. Endocrine disorders: crude rates by MMA (n=274), Michigan 2008.
(statewide rate: 4.4 per 1,000 population)

59

1

Table 14. MMAs with high crude rates of patients discharged with endocrine disorders,
Michigan, 2008.
# MMA

Cases

population

crude rate

95% CI

RSE

age-adjusted
2
rate

453
499
169
369
518
508
365
8
107
417
487
535
30
23

1,319
90
373
570
786
627
30
456
67
481
215
390
487
35

138,325
10,868
46,337
72,281
99,998
80,461
3,908
60,885
8,966
64,926
29,113
55,949
70,276
5,367

9.5
8.3
8.0
7.9
7.9
7.8
7.7
7.5
7.5
7.4
7.4
7.0
6.9
6.5

9, 10.1
6.7, 10.2
7.2, 8.9
7.2, 8.5
7.3, 8.4
7.2, 8.4
5.2, 11
6.8, 8.2
5.8, 9.5
6.7, 8.1
6.4, 8.4
6.3, 7.7
6.3, 7.5
4.5, 9.1

2.8
10.5
5.2
4.2
3.6
4.0
18.3
4.7
12.2
4.6
6.8
5.1
4.5
16.9

10.1
9.1
8.9
8.2
8.5
8.1
6.0
8.2
5.8
8.1
7.7
6.9
8.0
6.6

2

3

4

1

High crude proportions are marked as red areas in the maps.
Rate: cases per 1,000 population
3
95% CI: 95% Confidence Interval
4
RSE: Relative Standard Error
2

The map of age-adjusted rates for diabetes is shown in Figure 17.

Besides Saginaw, which

also had an elevated crude rate, Flint, Pontiac, Lansing, Kalamazoo and Detroit all had high
age-adjusted rates.
(MMA 343).

The highest age-adjusted rate was 6.5 per 1,000 population in Detroit

Direct age-standardization generally makes the rates higher than crude ones.

60

Figure 17. Diabetes: age-adjusted rates by MMA (n=183), Michigan 2008.
The map of age-adjusted rates for endocrine disorders is shown in Figure 18.

This map is

very similar to the map of crude rates, except rates become higher after age-standardization.
The highest age-adjusted rate was 10.1 per 1,000 population still in Detroit (MMA 453). Those
areas that popped up in the map of crude rates seem not to be apparent in this map, such as Battle
Creek and two other areas in the Upper Michigan.
lower age-adjusted rates than urban areas.
61

Rural and suburban areas still tend to have

Figure 18. Endocrine disorders: age-adjusted rates by MMA (n=274), Michigan 2008.

62

4.5 Alternative Zone Designs
Following the implementation of the AZM constraint parameters listed in the Methods
Section it was observed that zones constrained within the HSAs may also be prone to the MAUP
thus, reducing the quality of the overall zone design via simulated annealing by achieving
regional optima.

To examine the differences in these possible effects, three different ways to

use regions were implemented one by one.

The first model conformed to the previous zone

design, i.e., using all the HSAs as regions and respect the region boundary.
disenabled the region option, i.e., didn‟t respect any region boundary.

The second model

The third model ran the

program within each HSA, i.e. took HSAs one by one as a region, and merged the eight HSA
outputs.

All the other constraint parameters (minimum case threshold, maximum shape

compactness and maximum internal homogeneity), weighting scheme and simulated annealing
option, remained the same as in previous zone designs.

To target the specific diseases that are

representative, IHD and diabetes were used in this part.

Due to limited time, the AZTool

program only ran each method once (i.e., one restart) and compare the outputs of the three zone
designs.

The zone designs and statistical outputs are shown in Table 15.

The second concern while constructing the optimal MMAs is whether simulated annealing
improved the overall zone design.

Since the zone design improvements by using simulated

annealing is still controversial (Ralphs & Ang, 2009), this study attempted to further understand
the impact of simulated annealing with and without regional constraints.

The AZTool program

was operated again without enabling simulated annealing to supplement earlier results.
zone designs and statistical outputs are shown in Table 16.

63

The

Table 15. Statistical outputs of zone designs using alternative methods with simulated annealing.
IHD
Diabetes
Region
Zones
Zones
IAC score P2A score
IAC score P2A score
No.
No.
Statewide with HSA
307
0.102
12706.400
192
0.114
8199.470
Statewide without HSA 310
0.101
12156.900
191
0.114
8002.900
With each HSA
296
0.105
12221.575
184
0.117
7568.432
HSA 1
79
0.114
2387.320
74
0.121
2311.410
HSA 2
28
0.033
1286.960
15
0.083
669.343
HSA 3
34
0.033
1545.980
20
0.055
940.288
HSA 4
45
0.045
1952.860
23
0.063
1038.820
HSA 5
14
0.127
696.123
10
0.096
456.856
HSA 6
41
0.083
1597.520
22
0.113
922.021
HSA 7
33
0.015
1645.530
12
0.047
767.508
HSA 8
22
0.044
1109.280
8
0.031
462.185

Table 16. Statistical outputs of zone designs using alternative methods without simulated
annealing.
IHD
Diabetes
Region
Zones
Zones
IAC score P2A score
IAC score P2A score
No.
No.
Statewide with HSA
304
0.105
12153.600
191
0.117
7892.021
Statewide without HSA 300
0.105
11692.740
190
0.117
7684.949
With Each HSA
294
0.105
12122.198
187
0.120
7907.426
HSA 1
77
0.114
2319.089
77
0.127
2457.142
HSA 2
27
0.032
1175.123
14
0.085
726.182
HSA 3
31
0.032
1288.262
19
0.054
893.580
HSA 4
45
0.048
2035.757
26
0.068
1255.703
HSA 5
12
0.121
554.482
9
0.095
432.163
HSA 6
43
0.085
1769.000
22
0.118
934.050
HSA 7
36
0.015
1859.815
12
0.043
712.513
HSA 8
23
0.041
1120.669
8
0.028
496.092

The first model conformed to the previous zone design, i.e., using all the HSAs as regions
and respect the region boundary.
respect any region boundary.

The second model disenabled the region option, i.e., didn‟t

The third model ran the program within each HSA, i.e. took

HSAs one by one as a region, and merged the eight HSA outputs.
64

The results from these analyses showed that the differences between the first and second
models (statewide with/without HSAs) in terms of the number of zones were not substantially
different (n=307 versus 310); however, the numbers of zones using each HSA as the region
constraint (the sum of number of zones in each HSA – third model) was slightly less (n=296).
The IAC was similar across all three models demonstrating that the zones had similar levels of
demographic homogeneity regardless of the different number of zones and whether or not the
zones where constrained within HSAs.

These results indicate that the number and size of zones

across the three alternative methods are generally similar.
Since the P2A and IAC scores vary greatly by HSA, only the overall zone design which
merged the eight HSAs is compared to the other two statewide methods.

The overall internal

homogeneity generated by merging HSAs appear to be better than the other two methods using
statewide geographic units for both IHD and diabetes.

Again, the differences of internal

homogeneity between the two methods using statewide geographic units with or without HSA
are not substantial.

In contrast to internal homogeneity, it‟s too early to conclude anything from

the shape compactness scores.

The unclear results of shape compactness possibly result from

their lighter relative weights compared to case threshold and maximum homogeneity.

The

shape constraint parameter might be sacrificed to obtain better results of the other two.

Two

statewide maps showing the crude rates and selected RSE values with and without using HSA
(SA enabled) are shown in Figure 19 and Figure 20.
Comparing the output results of enabling and disabling simulated annealing, it is interesting
to observe that the three zone design models using simulated annealing do not appear to perform
better than the three zone design models without simulated annealing as evidenced by the similar
number of zones and slightly lower IAC and higher P2A scores.
65

Thus simulated annealing does

not seem to be an important parameter in the construction of new zones.

This finding was

similar to that reported in research conducted in New Zealand (Ralphs & Ang, 2009).

Future

research should continue to explore the use of simulated annealing in AZM research.
Another approach to examining how constraining new zones impacts the overall study
results is to assess the RSE of rates on each side of regional boundaries.

Statewide maps

showing the crude rates and selected RSE values for the three models are shown in Figure 21 and
Figure 22.

Note that these maps use the optimal zone design from the first random start, rather

than the „best‟ from 50 random restarts.

Future research should also use multiple restarts to

prioritize the zone design and comparing the effects of regional constraints and simulated
annealing based on the zone construction.
The assessment of RSE‟s on each side of HSA boundaries show that all rates are stable (i.e.,
RSEs < 20%) and do not demonstrate substantial differences, suggesting that regional constraints
do not impact the local rate results.

66

Figure 19. Ischemic heart disease: crude rates by MMA (n=307) and their RSE using all HSAs
(SA enabled), Michigan 2008.

67

Figure 20. Ischemic heart disease: crude rates by MMA (n=310) without using HSAs (SA
enabled), Michigan 2008.

68

Figure 21. Ischemic heart disease: crude rates by MMA (n=304) using all HSAs (SA disabled),
Michigan 2008.

69

Figure 22. Ischemic heart disease: crude rates by MMA (n=300) without using HSAs (SA
disabled), Michigan 2008.

70

5. DISCUSSION
The goals of this study were to (1) design optimal Medical Management Areas (MMAs) for
IHD and diabetes to (2) visualize and explore the spatial patterns of these disease subgroups to
inform future bed need in Michigan.

MMAs of these sub-groups were compared with MMAs

of the principal diagnoses to explore geographic and epidemiological scale together.
The objectives of this study included and the results from the analyses are provided below.

Objective 1: To demonstrate the need for the use of AZM in the construction of MMAs.
Hypothesis 1a: Mapping disease rates by ZIP Codes will result in a large proportion of unstable
rates.
Much health services research focuses on the „supply‟ perspective. This thesis provided a
detailed methodology by which demand could also be measured to inform inpatient bed need in
Michigan.

The methodology was justified after constructing rate maps of the diseases being

studied using ZIP Codes and identifying large areas across the state with unstable rates defined
by the RSE > 20%.

By creating the RSE maps, this study finds hypothesis 1a to be true and

further illustrates that it is inappropriate to map disease rates using ZIP Codes in Michigan.
Therefore, AZM, as a program to provide new zones that ensure the stability of rates, is needed
to construct optimal MMAs to show the demand of health services.

Objective 2: To optimize MMA boundary definitions.
Hypothesis 2a: The shape constraint parameter will be less important than the internal
homogeneity for broad disease groups compared to specific diseases because of the greater

71

variation in population within the broad disease groups. Since when a couple of ZIP Codes are
aggregated into a zone, the population is becoming larger which results in more homogeneity.
Table 17 is a summary of the AZM outputs for IHD, circulatory diseases, diabetes and
endocrine disorders.

Note that generally the best restart occurred between 40 and 50 restarts.

These best restarts met the constraint parameter requirements of the minimum case threshold,
maximizing the shape compactness and maximizing the internal homogeneity.

This study

advanced earlier research by exploring different weighting schemes for the constraint parameters
and finally using the combination of minimum threshold (100%), shape compactness (50%), IAC
(sex, age, race) for IHD and diabetes (100%) and circulatory diseases and endocrine disorders
(150%).

In other words, the IAC was modeled according to the epidemiological scale of

analysis (i.e., twice as important as the shape constraint for IHD and diabetes and three times as
important for circulatory disease and endocrine disorders).

The IAC was considered more

important than the shape constraint in order to ensure greater demographic-homogeneity within
zones, which conceptually should be helpful when assessing bed need in areas.

At a lower

epidemiological scale, a lower IAC weight was needed because the patients discharged with IHD
or diabetes were expected to be more similar than patients discharges with diagnoses within the
primary diagnostic related groups, circulatory diseases and endocrine disorders.

Interestingly,

all sets of MMAs constructed had a similar number of zones in the their output demonstrating the
success of the modeling because if the IAC had been weighted similar to shape compactness
there would have been fewer and more heterogeneous zones which would have been less
informative to the inpatient bed need in Michigan.

The reason that IHD has a lower IAC score

is probably due to the great variety of etiology within IHD.
diabetes has higher level of internal homogeneity.
72

More specific disease such as

Thus the internal homogeneity of population

discharged with certain diseases is dependent on the specificity of diseases.

Objective 2 of

optimizing MMA boundary has been completed and thus hypothesis 2a stating that the shape
constraint parameter will be less important than the IAC for broad disease groups compared to
specific diseases is found to be partly true.
Table 17. Summary of 50 restarts for diseases and disease groups.
Best
restart

Cases
No.

Zones
No.

P2A
Score

IHD

50

58,573

302

12160-13098 0.101-0.104

0.109

Circulatory diseases

44

214,649

310

12291-13180 0.105-0.107

0.112

Diabetes

42

17,352

183

Endocrine disorders

45

44,057

274

7724-8383

IAC
Score

ZIP Code
IAC Score

0.113-0.115

0.127

11206-12095 0.105-0.108

0.113

Objective 2: To optimize MMA boundary definitions.
Hypothesis 2b: Aggregating on the variables sex, age and race will increase demographic
homogeneity within zones.
The results showed that as the zones get larger, they become more similar and therefore the
differences between zones become smaller, i.e., less heterogeneous.

That explains why the ZIP

Code level homogeneity is better than the MMA level. Therefore, hypothesis 2b is found to be
true.

This study also advanced the AZM approach by applying the Wilcoxon signed-rank

method to prioritize the top „restart‟ out of the 50 restarts conducted.

While the Wilcoxon

signed rank may not be the only test available to prioritize the restarts it applied nicely to this
study and is recommended for use in future AMZ modeling because of it is relatively easy to
automate and implement.

Other related approaches to prioritize the 50 restarts could be

explored and compared in the future.

73

Region
The use of HSA boundary as region constraint parameter doesn‟t appear to have adverse
effect on the overall zone design because the statewide zone outputs with and without HSA
boundary have similar numbers of zones, P2A scores and IAC scores.

That greatly reduces that

possibility that using HSAs as regions will result in sub-optimal zone design.

Thus in the main

section, there is no significant effect to use region constraint.

Simulated Annealing (SA)
Finally, this study used simulated annealing (SA) in the construction of MMAs, which is not
documented in previous studies.

Theoretically, SA helps to achieve the better global-optima,

which would be an ideal solution to reduce bias associated with the MAUP.

However, only one

research (Ralphs & Ang, 2009) had done the experiment to compare the results between running
AZM in a SA mode or not and the conclusion is that SA didn‟t improve the performance of
AZM significantly in terms of the population target, and also at the cost of shape compactness.
This study also tested the SA effect and found that running AZM in a SA mode didn‟t produce
better zone designs.

Since there isn‟t any final conclusion yet, this could be a promising topic

for future research.

Objective 3: To visualize disease proportions, crude rates and age-adjusted rates of IHD, diabetes,
circulatory diseases and endocrine disorders:
Hypothesis 3a: The spatial patterns of disease groups will vary by method used to map the
diseases; new information about the prevalence of these diseases in Michigan will be learned
from each method.
74

Area-based proportions of patient discharges, crude rates and age-adjusted rates of patient
discharges in the population were calculated using the new MMAs and their spatial patterns were
visualized.

Some of the interesting findings and interpretation of those findings is presented

below.

Ischemic Heart Disease
Generally, MMAs that showed elevated proportions of discharged patients represented
demand for inpatient hospital services in Michigan.

If more people were discharged from

hospitals with IHD in 2008, it could be assumed that people would still have that demand in the
near future.

The medical information of proportion is especially useful for local health

department and hospitals, because they would know that the amount and quality of health
facilities and equipment should meet the demand of patients with IHD.
On the map showing proportions of patients discharged with IHD, HSA 6 and 7 showed
elevated proportions. The highest proportion was also located in HSA 6.

The general pattern of

crude map is similar to that of proportion map, indicating that patients attended hospitals were
fairly representative of the total population.

Since the areas with elevated rates and proportions

were mostly rural areas where people were less rich, people with IHD should be taken better care
of by providing availability and accessibility of health services to them.
reasons that those areas showed elevated rates remain unknown.

However, the true

For example, doctors might

refer quite a lot of patients to those areas where high-quality health care services were offered in
local hospitals and clinics.

Thus it might be too early to conclude that people were less healthy

over in those areas.
From the legend of maps showing age-adjusted rates and crude rates, it is found that
75

age-adjustment reduced the overall rates significantly.

The highest rates reduced from 24.2 to

17.2 per 1,000 population, indicating the elder people could largely contribute to the high rates.
However, even after age-adjustment, the rate maps still showed that HSA 6 and 7 and other
scattered MMAs had elevated age-adjusted rates. This illustrates that more elder people is not
the only factor causing the high crude rates, and other factors (e.g., more doctors‟ referral, more
health insurance coverage, high socioeconomic states) could also contribute to the high rates.
Future research should continue to explore the factors that are associated with the high rates.
The circulatory diseases always show similar patterns as IHD‟s, no matter proportion maps
or rate maps.

Since IHD is the main cause of heart diseases and even circulatory diseases, it‟s

not surprising to see similar patterns.

As a broad disease group, circulatory diseases show the

demand of health services from people with more various characteristics.

Diabetes
The proportion maps of patients discharged with diabetes and endocrine disorders are less
similar than IHD and circulatory diseases, although of all people discharged with endocrine
disorders, the cases of diabetes were more than one third in 2008.

Thus, if the spatial pattern of

diabetes is the solely one to be studied, using its broader group (i.e., endocrine disorders) to
obtain more cases will not be a wise idea.

But one thing in common for these two maps is, the

high proportions of patient discharges are mostly located in urban areas, indicating that people
with endocrine disorders sought more health services or their physicians were more likely to
admit them to hospitals than in rural areas.
The age-adjustment doesn‟t reduce the rate of patients discharged with diabetes in urban
areas.

These findings suggest that the population of diabetic patients is relatively similar to the
76

state‟s population.

It is worth noting that the highest crude rate and the highest age-adjusted

rate were located in the same metropolitan area – Detroit.
reason of high rates in Detroit.

More elderly people might not be the

Thus, it will be interesting to explore the causes of high rates

over there.
Another important point is, diabetes is usually less severe and harmful than IHD, and thus
there may be a substantial number of outpatients throughout the state.
not be fully aware of their state of diabetes.

Moreover, people may

Because diabetes is an all-age disease, young

people may not have health insurance coverage, which impedes their ability to access health care.
People living in rural areas may not be able to see a doctor because hospitals are hardly
accessible or affordable.

Those factors should be taken into consideration while make decisions.

Future research should target on the causes of high rates or low rates to explore the actual
reasons of certain spatial patterns.

Limitations
Though AZM offered an optimal zone design for health service study, some limitations are
still inevitable.

First, using simulated annealing, the aggregation of contiguous ZIP Codes is

random until there is not random ZIP Code left and then selection criteria begins.

Although the

number of zones and IAC/P2A coefficients were similar for each restart, the ways that ZIP
Codes were aggregated were completely different.

AZM cannot produce two set of zones with

exactly the same design within a finite number of running.
might be slightly different in each restart.

As a result, the disease patterns

But the optimal zone design could always be selected

meeting the criteria of strongest IAC and smallest P2A coefficients to reduce the uncertainty.
Future study should continue to evaluate the global versus local optima (with the local optima
77

the optimal selection occurs first increasing the likelihood that the boundary definitions will
appear similar) and simulated annealing.

While previous studies (Flowerdew, et al., 2008;

Martin, 2003; Riva, et al., 2008) largely tested the zone effect by conducting analysis at different
scales, a further step may also consider the scale effect.
Second, this study didn‟t test how different weights would have influences on AZM zone
output.

While a set of parameters was recommended in this study, weights of parameters were

determined more on an empirical basis.

It is highly possible that changing the weights could

result in different zone design outputs and different number of zones.

David Martin also

suggested that great attention should be paid while determining the weights (Atkinson & Martin,
2000).

Further study could focus on choosing the optimal weight for each parameter based on

knowledge of how it may relate to the disease in question.
Third, for the maximum homogeneity parameter, only sex, age and race were used because
of the data limitation.

However, the choices of parameters should depend on the specific need.

However, as implemented, only a limited number of variables (i.e., a maximum of 12 variables)
could be taken into homogeneity parameter.
Another limitation in the mapping process is that we used multiple data sources.
collected data from patients who usually reported their USPS ZIP Codes.

MIDB

Population estimates

from the private company Geolytics were originally derived from census 2000 which used
ZCTAs.

The boundary used in this study is from ESRI 2007 who appeared to use USPS ZIP

Codes.

As is known to people, the USPS ZIP Codes and ZCTAs do not align very well.

Although recoding has been performed, some of the boundaries are still inaccurate.

It might

lead to the misinterpretation if population was misallocated due to approximate matching of

78

geographic units.

Future research should perform analysis and make maps based on the same

geographic boundary.
Finally, natural break was the classification method used in the choropleth maps because a
good distribution of data is preferable.

However, a different classification scheme (e.g.,

quantiles) may have a substantial visual impact on the perceived spatial patterns of the diseases.
Since quantile was proven to be suitable for showing health data on choropleth maps (Brewer &
Pickle, 2002) because it keeps the same number of units in each class, it should be explored in
future research with the knowledge that interesting data outliers may be smoothed over.
Besides quantile, equal interval also provides the possibility to compare different maps.

Future Research
In this analysis health service demand was assessed by constructing Medical Management
Areas to visualize and explore the proportions, crude rates and age-adjusted rates of IHD and
diabetes. Similarities and differences between these measures were analyzed. Future research
could explore underlying mechanisms associated with high or low level of patient discharges to
further inform health service researchers and also future epidemiological research. Sociologists
and public health researchers may further examine the disparities of health service demand
between urban and rural areas, and between younger and elder people in the state of Michigan.
These methods may also be applied in other states to assess hospital demand in those areas.

79

6. CONCLUSIONS AND RECOMMENDATIONS
Ischemic heart disease (IHD) and diabetes, as two of the critical health indicators in the state
of Michigan, receive substantial attention from the Michigan Department of Community Health
(MDCH). MDCH is interested to know the spatial patterns of the critical health indicators for
the purpose of health service regulation from demand perspective. This study illustrates that the
spatial patterns of IHD and diabetes derived from administrative units (i.e., ZIP Codes), can
result in a substantial number of units with high RSEs and therefore unstable rates throughout the
state when the numbers of cases within units are small. One of the methods to solve this small
number problem is to aggregate ZIP Codes into larger zones to obtain more cases within
zones. In this study, AZM dissolves the boundaries of ZIP Codes with less than 30 cases, and
constructs new MMAs with maximum shape compactness and maximum internal
homogeneity. The corresponding broader groups of IHD and diabetes in ICD-9-CM (circulatory
diseases and endocrine disorders) are also utilized to construct MMAs for the comparison with
IHD and diabetes. Choropleth maps serve as the media to represent the spatial patterns of those
diseases and disease groups. Proportions (cases per 100 discharges), area-based crude rates
(cases per 1,000 population) and age-adjusted rates are shown as different health views. MMAs
with high and low prevalence are informative to health care regulators and are useful to assist
decision-making and health service management. AZM is therefore an efficient tool that could
be used in health service research to explore health care demand.
While AZM is useful in constructing MMAs for health service studies, future researchers
should be aware that the construction of zone designs are a relatively subjective process. The
output of this program is significantly influenced by the purposes of study, data availability and
the input parameters. Researchers should therefore, be careful with the selection of input
80

parameters in the optimization of new zones. With these issues considered, AZM is still
recommended for future health service and geographic-epidemiological research.

81

APPENDICES

82

Appendix 1. Diseases and Injuries Tabular Index.
1. INFECTIOUS AND PARASITIC DISEASES (001-139)
2. NEOPLASMS (140-239)
3. ENDOCRINE, NUTRITIONAL AND METABOLIC DISEASES, AND IMMUNITY DISORDERS
(240-279)
4. DISEASES OF THE BLOOD AND BLOOD-FORMING ORGANS (280-289)
5. MENTAL DISORDERS (290-319)
6. DISEASES OF THE NERVOUS SYSTEM AND SENSE ORGANS (320-389)
7. DISEASES OF THE CIRCULATORY SYSTEM (390-459)
8. DISEASES OF THE RESPIRATORY SYSTEM (460-519)
9. DISEASES OF THE DIGESTIVE SYSTEM (520-579)
10. DISEASES OF THE GENITOURINARY SYSTEM (580-629)
11. COMPLICATIONS OF PREGNANCY, CHILDBIRTH, AND THE PUERPERIUM (630-679)
12. DISEASES OF THE SKIN AND SUBCUTANEOUS TISSUE (680-709)
13. DISEASES OF THE MUSCULOSKELETAL SYSTEM AND CONNECTIVE TISSUE (710-739)
14. CONGENITAL ANOMALIES (740-759)
15. CERTAIN CONDITIONS ORIGINATING IN THE PERINATAL PERIOD (760-779)
16. SYMPTOMS, SIGNS, AND ILL-DEFINED CONDITIONS (780-799)
17. INJURY AND POISONING (800-999)
SUPPLEMENTARY CLASSIFICATION OF FACTORS INFLUENCING HEALTH STATUS AND
CONTACT WITH HEALTH SERVICES (V01-V89)
SUPPLEMENTARY CLASSIFICATION OF EXTERNAL CAUSES OF INJURY AND POISONING
(E800-E999)

83

Appendix 2. List of incompatible ZIP Codes.
Table 18. List of incompatible ZIP Codes.
Incompatible ZIP Codes
48028
48033
48138
48139
48143
48168
48190
48193
48243
48434
48437
48476
48620
48627
48630
48633
48638
48710
48724
48758
48824
48852
48853
48874
48894
48896
49027
49104
49115
49119
49282
49289
49312
49335
49406
49434
49458
49519
49534
49611
49626
49627

Operation
removed
divided into 48033, 48034
removed
recode to 48189
recode to 48169
divided into 48167, 48168
recode to 48191
divided into 48192, 48193
removed
recode to 48465
recode to 48458
recode to 48429
removed
recode to 48653
recode to 48629
recode to 48632
divided into 48603, 48638
divided into 48706, 48710
recode to 48604
removed
divided into 48823, 48824
recode to 48829
recode to 48879
recode to 48871
recode to 48835
recode to 48858
recode to 49056
divided into 49103, 49104
recode to 49125
recode to 49128
recode to 49233
recode to 49279
recode to 49309
recode to 49348
recode to 49453
recode to 49423
recode to 49402
divided into 49509, 49519
divided into 49534, 49544
recode to 49659
recode to 49660
recode to 49648

84

Table 18 (Cont‟d)
49628
49634
49666
49674
49722
49748
49757
49764
49775
49782
49791
49793
49796
49805
49808
49852
49863
49864
49871
49872
49901
49915
49917
49918
49922
49929
49934
49955
49959
49660
49961
49963
49971

recode to 49635
recode to 49660
recode to 49649
removed
recode to 49770
recode to 49728
removed
removed
removed
removed
recode to 49721
recode to 49780
recode to 49713
recode to 49950
recode to 49814
removed
removed
removed
recode to 49866
recode to 49878
recode to 49950
recode to 49935
recode to 49913
recode to 49913
recode to 49945
recode to 49953
recode to 49930
recode to 49916
recode to 49911
recode to 49953
recode to 49967
recode to 49905
recode to 49953

85

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