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SPATIAL TRENDS OF WEST NILE VIRUS IN DETROIT, MICHIGAN 2002
By

Kevin Patrick McKnight

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

MASTER OF ARTS
Department of Geography

2006

ABSTRACT

SPATIAL TRENDS OF WEST NILE VIRUS IN DETROIT,
MICHIGAN 2002

By

Kevin Patrick McKnight

West Nile Virus is vector-home flavivirus that affects mainly birds, horses, and
humans. The disease emerged in the United States in 1999 and by 2001 had reached
Michigan. Currently, the virus has been reported in all 48 contiguous states. In clinical
human cases, the most common symptoms are fever, weakness, nausea, headache, and
changes in mental state. The crow is the most common wildlife host in the life cycle of
the virus. The state of Michigan, through the Michigan Department of Community
Health, collected the spatial locations of dead birds (Corvidae). Statewide, during 2002,
there were over 8,000 reports. The large number of samples made spatial and temporal
hotspot detection possible. However, the volunteer reporting method produced a dataset
with a direct correlation between the numbers and locations of the dead birds and
population density. Therefore, accurately identifying hotspots remains a challenge.
Extensive cleaning was required to insure the data points were spatially accurate. The
dataset was then modeled using Ripley’s K, Moran’s I, Oden’s 1(p0p), Local Moran’s I,
Kulldorff’s Spatial Scan, and the Geographic Analysis Machine. These statistical models
identified overall spatial structure and local clustering in the dataset. Identification of
hotspots was confounded by limited information about the collection procedures, data

availability, and the limitations of each method.

Dedicated to my parents:
This would not have been possible
without your support.

iii

Special Thanks to:
Edward F. Hartwick and Beth M. Clute

I would also like to thank my advisor, Dr. Joseph Messina, and my committee members,
Drs. Bruce Pigozzi and Ashton Shortridge. Your advice throughout this research was
invaluable.

iv

TABLE OF CONTENTS

LIST OF TABLES .................................................................................. vii
LIST OF FIGURES ................................................................................ viii
1 INTRODUCTION ...................................................................................................... l
1 . 1 Introduction ......................................................................................................... 1
1.2 Literature Review ................................................................................................ 6

2 METHODOLOGY ................................................................................................... 14
2.1 Data ................................................................................................................... 14
2.1.1 Dead Crow Data ............................................................................................... 14
2.1.2 Census Data ..................................................................................................... 18
POPULATION DENSITY BY BLOCK GROUP ............................................................ 20
2.2 Global Statistics ................................................................................................ 21
2.2.1 Ripley’s K ........................................................................................................ 21
2.2.2 Moran’s I .......................................................................................................... 23
2.2.3 Oden’s I(pop) ................................................................................................... 27

2.3 Local Statistics ................................................................................................. 30
2.3.1 Anselin’s Local Moran (LISA) ........................................................................ 30
2.3.2 Kulldorff’s Spatial Scan Statistic ..................................................................... 31
2.3.3 Geographic Analysis Machine (GAM) ............................................................ 33

2.4 Data Preparation/ Methods for Statistical modeling ........................................ 34
2.4.1 Ripley’s K ........................................................................................................ 34
2.4.2 Moran’s I and Local Moran (LISA) ................................................................. 35
2.4.3 Oden’s I(pop) and Kulldorffs Scan Method ................................................... 38
2.4.4 Geographic Analysis Machine ......................................................................... 39

3 RESULTS & ANALYSES ....................................................................................... 42
3.1 7 Results from Global Methods ........................................................................... 42
3.1.1 Ripley’s K ........................................................................................................ 42
3.1.2 Moran’s I .......................................................................................................... 47
3.1.3 Oden’s Ipop ...................................................................................................... 48

3.2 Local Models ................................................................................................... 50
3.2.1 Anselin’s Local Indicator of Spatial Autocorrelation ...................................... 50
3.2.2 Kulldorff .......................................................................................................... 67
3.2.3 GAM ................................................................................................................ 72

4 DISCUSSION AND CONCLUSIONS .................................................................... 86
4.1 Overview .......................................................................................................... 86
4.2 Discussion of Results ....................................................................................... 88
4.2.1 Global Tests ..................................................................................................... 88
4.2.2 Local Models ................................................................................................... 91

4.3 Future Research ............................................................................................... 95

APPENDIX 1 .................................................................................................................... 98

Moran’s I: 100 X 100 Grid Results ............................................................................... 98
Moran’s I: 10 X 10 Grid Results ................................................................................. 101
APPENDIX 2 .................................................................................................................. 104
Oden’s I(pop): 10 X 10 Grid Results .......................................................................... 104
WORKS CITED ............................................................................................................. 107

vi

LIST OF TABLES

Table 1. Bird records, human population, and ratio of birds to humans by county ........... 15
Table 2. Bird records by month ......................................................................................... 16
Table 3. Oden’s I(pop) Monte Carlo assumption results ................................................... 49

vii

Fig.
Fig.
Fig.
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Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.

Fig.

Fig.
Fig.

Fig.

LIST OF FIGURES

1. Map of study area ..................................................................................................... 4
2. Dead bird distribution by county ............................................................................ 17
3. Human population by block group ......................................................................... l9
4. Human population density by block group ............................................................. 20
5. Estimation of Ripley’s K ........................................................................................ 23
6. Estimating the weights for Ripley’s K ................................................................... 23
7. 100 by 100 cell grid processing steps ..................................................................... 36
8. 10 by 10 cell grid processing steps ......................................................................... 36
Ripley’s K Maps
9. Ripley’s K graph legend ......................................................................................... 43
10. All Record Results ................................................................................................ 44
11. May Results .......................................................................................................... 44
12. June Results .......................................................................................................... 45
13. July Results ........................................................................................................... 45
14. August Results ...................................................................................................... 46
15. September Results ................................................................................................ 46
16. October Results ..................................................................................................... 47
Anselin’s Local Indicator of Spatial Autocorrelation Maps
17. All Record Results ................................................................................................ 52
18. April & May Results ............................................................................................. 53
19. June Results .......................................................................................................... 54

viii

Fig.
Fig.
Fig.
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June 1-15 Results .................................................................................................. 55

June 16-30 Results ................................................................................................ 56
July Results ........................................................................................................... 57
July 1-10 Results .................................................................................................. 58
July 11-20 Results ................................................................................................ 59
July 21-31 Results ................................................................................................ 60
August Results ...................................................................................................... 61
August 1-10 Results ......................................................................... . .................... 62
August 11-20 Results ............................................................................................ 63
August 21-31 Results ............................................................................................ 64
September Results ................................................................................................ 65
October Results ..................................................................................................... 66

Kulldorff Scan Method Maps

All Record Results ................................................................................................ 69
April & May Results ............................................................................................. 69
June Results .......................................................................................................... 69
June 1-15 Results .................................................................................................. 69
June 16-30 Results ................................................................................................ 70
July Results ........................................................................................................... 70
July 1-10 Results .................................................................................................. 70
July 11-20 Results ................................................................................................ 70
July 21-31 Results ................................................................................................ 71

ix

Fig. 41. August Results ...................................................................................................... 71

Fig.
Fig.
Fig.
Fig.

Fig.

Fig.
Fig.
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August 1-10 Results .............................................................................................. 71
August 11-20 Results ............................................................................................ 71
August 21-31 Results ............................................................................................ 72
September Results ................................................................................................ 72
October Results ..................................................................................................... 72

Geographic Analysis Machine Maps

All Record Results (99%) ..................................................................................... 74
All Record Results (99.999%) .............................................................................. 74
All Record Results (99.99999999%) .................................................................... 74
April & May Results (99.9%) ............................................................................... 75
June Results (99%) ............................................................................................... 76
June Results (99.999%) ........................................................................................ 76
June Results (99.99999%) .................................................................................... 76
July Results (99%) ................................................................................................ 77
July Results (99.999%) ......................................................................................... 77
July Results (99.99999999%) ............................................................................... 77
July 1-10 Results (99%) ....................................................................................... 78
July 1-10 Results (99.9%) .................................................................................... 78
July 11-20 Results (99%) ..................................................................................... 78
July 11-20 Results (99.999%) .............................................................................. 78
July 21-31 Results (99%) ..................................................................................... 79

Fig.
Fig.
Fig.
Fig.
Fig.
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July 21-31 Results (99.999%) .............................................................................. 79

July 21-31 Results (99.99999999%) .................................................................... 79
August Results (99%) ........................................................................................... 80
August Results (99.999%) .................................................................................... 80
August Results (99.99999999%) .......................................................................... 80
August 1-10 Results (99%) ................................................................................... 81
August 1-10 Results (99.999%) ............................................................................ 81
August 1-10 Results (99.99999999%) .................................................................. 81
August 11-20 Results (99%) ................................................................................. 82
August 11-20 Results (99.999%) .......................................................................... 82
August 11-20 Results (99.99999999%) ................................................................ 82
August 21-31 Results (99%) ................................................................................. 83
August 21-31 Results (99.999%) .......................................................................... 83
August 21-31 Results (99.99999999%) ................................................................ 83
September Results (99%) ..................................................................................... 84
September Results (99.999%) .............................................................................. 84
September Results (99.99999%) .......................................................................... 84
October Results (99%) .......................................................................................... 85
October Results (99.9%) ....................................................................................... 85
October Results (99.99%) ..................................................................................... 85

Images in this document presented in color.

xi

1 Introduction

1.1 Introduction

This research was designed to examine the geographic extent that disease data
collected from the public can be used in spatial and temporal cluster analyses. The term
“geographic” refers to the Earth’s surface and near-surface, and defines the subject matter
of this thesis; however other terms have similar meaning. The term “spatial” is used
frequently throughout this document, almost always with the same meaning as
“geographic” (Longley, Goodchild et a1. 2001). The underlying structure patters of the
disease data will be analyzed using spatial statistics. The statistical models progress from
global models that identify general spatial structure, to local models that locate disease
clusters. The introductory chapter provides an overview of medical geography, West Nile
Virus, and spatial statistics. This section followed by a literature review focusing on the
history, virology, and pathology of West Nile Virus. The literature review also discusses
the spatial statistical models used in the research.

Understanding the factors that allow, or more importantly, cause a disease to spread,
greatly affects the manner in which the public health officials respond. By examining the
spatial locations of disease cases, as well as the environmental and social milieu, patterns
and commonalities may emerge among the individual events. These patterns often reflect
underlying environmental influences. Medical geography attempts to identify the
relationship between diseases and their spatial context.

Medical geography uses the concepts and techniques of the discipline of geography to

investigate health—related topics (Meade and Earickson 2000). The ability to combine

Geographic Information Systems (GIS) with medical diagnoses allows for the novel
assessment of a disease over a geographic region. By using location as a factor in disease
research, spatial statistics enable researchers to examine the quantitative and qualitative
patterns associated with the disease. Many disease characteristics, for example risk and
extent, can be identified using these types of geospatial analyses. Further, clusters and
point sources may be located. Also, the direction and intensity of a spreading virus
epidemic can be estimated. Knowing how a virus interacts with the environment is
critical in controlling the spread of the disease.

Spatial statistics encompass a collection of tools that are used to analyze patterns and
trends in data across a map. These spatial techniques are used to find or describe the
extent of clustering or autocorrelation across a given area. For the purpose of this study,
structure or autocorrelation describes any deviation from complete spatial randomness,
such as regularity, clustering, or a first order trend. Global models only examine if
structure is present and not if the data points are clustered. Local models explore the
spatial dependence of deviations in attribute values from their mean; that is, the second
order properties (Bailey and Gatrell 1995). If a second order trend is found to be present,
then the point pattern is referred to as being clustered. These methods can be traced back
to the famous case of John Snow’s evaluation of the 1854 cholera epidemic in London,
where the pattern of disease cases was observed and analyzed to determine if the pattern
was of a global or local nature. Techniques such as cluster detection have grown in
demand with the increasing availability of high accuracy spatial datasets. Identifying the

locations of data points is often done for individual cases by geocoding (process of

assigning geographic identifiers to data records, such as street addresses) the address of
the event (Lawson and Kleinman 2005), and is used for the dataset in this research.

West Nile Virus became endemic (a disease native to a particular people or specific
region) to the Western Hemisphere in 1999. It surfaced in New York City causing 67
human cases and seven deaths (Craven and Roehrig 2001). During the next few years the
disease spread across the United States through a bird-mosquito-bird cycle. The birds act
as the reservoir for the virus and mosquitoes spread the virus throughout susceptible
populations. In the beginning of the 2000 transmission cycle it was confirmed that at least
12 species of mosquito could spread the disease (Craven and Roehrig 2001). Currently 43
species of mosquito have tested positive for West Nile Virus (WNV) (Marra, Griffing et
al. 2004). The Culax species of mosquito is the most common bridge vector transferring
the virus from birds to humans. Since 1999, the disease had infected at least 400,000
humans, and killed countless birds, mammals, and reptiles (Dodd 2003; Marra, Griffing
et al. 2004).

The counties presented in this thesis are, by design, limited to urban or populated
areas. The Greater Detroit Area is representative of urban areas in Michigan. Wayne,
Oakland, and Macomb counties of the Greater Metropolitan Detroit Area were selected
for this research (Fig. 1), because they contained the most dead bird records and the
greatest at risk population. With a fairly consistent population density and widespread
urbanization the Metro Detroit Area provides the largest uniform study area available
where many events were reported. This region of the state manages its own assets
through the South East Michigan Commission of Governments (SEMCOG). The road

fi‘amework data used to georeference the WNV bird data are some of the most accurate in

the state. Dense population, high number of dead bird records, highly urban landcover,
and accurate GIS information combine to make the Greater Detroit Area the overall best

site for this research in the state of Michigan.

Macomb
Oakland

Wayne

Map of study area, urban areas shown in gray.
Fig. 1

The primary objectives of this research are to explore geographic epidemiology of
West Nile Virus in the Detroit Metropolitan Area in 2002, though the analysis of the
spatial point patterns developed from the citizen reported dead bird data, and to compare
and contrast repeatable methods that permit the identification of disease clusters.

The exploration of this dataset is designed to provide information about the
distribution of WNV. The three global models will demonstrate that WNV in the Detroit
area presents global spatial autocorrelation across the study area. The progression of the
global models will attempt to identify spatial structure within only the dead bird
locations; first by examining the dead bird data as individual level data (Ripley’s K) and
then as grouped data (Moran’s I). The final global test will examine if autocorrelation is
still present when the human population is included (Oden’s I(pop)). The local spatial
models will be used to identify areas of intense WNV activity (hotspots). The first two
local models will examine if clusters can be identified when the dataset is aggregated to
grid cells. The first method examines the relationship of only the neighboring cells
(LISA) and the second incorporates a circular moving window that increases until a
cluster is found (Kulldorff’s Spatial Scan). The last local method will examine the same
dataset but as individual points using a circular moving window at various scales
(Geographic Analysis Machine). This research also explores the temporal distribution of
the virus through the infection season. The diffusion of the virus can be mapped in
direction and intensity using the point locations along with the date the birds were found.

Given the process used to report these data, certain assumptions needed to be
addressed before statistical modeling was possible. The first assumption was that the

dataset contains 100% of the dead birds. This was necessary because the statistical

methods operate under the assumption that the dataset is comprised of an entire
population. By assuming that the dataset contains 100% of the dead birds, it must also be
assumed that all of the dead birds in the dataset were WNV positive. The infectivity of
the birds must be assumed due to the limitations used in testing the birds. After the first
positive test, the subsequent birds found in the county were considered positive. These
assumptions introduced some error into the dataset. However, the extent of the error
cannot be quantified due to the collection process and insufficient data on the entire crow
population.

The remainder of this thesis examines a methodology for preparing and modeling a
spatial dataset. The results of the global and local models are then examined for spatial
trends and disease hotspots. In closing, final conclusions and recommendations for

fiirther research are discussed.

1.2 Literature Review

To understand the geographic aspects of West Nile Virus there are three main topics
that need to be examined. The first section reviews the origins of the disease and how it
spread to the United States. This is required to track the path of the virus and examine
possible ways to stop its spread. The second section is on the disease itself. It discusses
medical descriptions of the virus, disease rates, human symptoms, and treatment. The
final section examines the transmission of the disease, the mosquito (vector), and the

crow (reservoir).

West Nile Virus (WNV) was first identified in 1937 in the West Nile region of
Uganda (Petersen and Marfin 2002). Since the discovery of the virus, there have been
sporadic outbreaks across Europe, Africa, and Asia. The first large-scale outbreak
occurred in Israel from 1950 to 1957. Hundreds of clinical cases were reported. In 1974,
an epidemic of WNV spread across South Africa producing tens of thousands of
infections. With the exception of a few cases in France in 1962, the Middle East and
Africa were the known extent of the virus.

It was not until 1996 when a large-scale outbreak occurred in Europe that the
disease moved out of Africa. The mid-August outbreak, around Bucharest in
Southeastern Romania, saw 835 patients admitted to hospitals showing signs of central-
nervous-system infections. Of these cases, 767 met the clinical definition of WNV, and
441 of those had the proper blood and cerebrospinal fluid samples necessary for
confirmation of the virus. From this sample, there were 352 confirmed cases, but there
were also 41 patients who did not show symptoms who had positive tests.

The World Health Organization confirmed 393 infections. Among the clinical cases,
the diagnoses were meningitis (40%), meningoencephalitis (44%), and encephalitis
(16%) (Tsai, Popovici et al. 1998). The illness progressed to coma in 13% of cases, and
there were 17 fatalities out of all patients over 50 years of age. Age is the main
contributing factor in the fatality rate associated with WNV (Tsai, Popovici et al. 1998).
From birth to age 50 the case fatality rate during the Romania outbreak was zero, 3.4%
for persons age 50 —— 59, 4.3% for ages 60 — 69, and 14.7% in those over 70 years. The

disease attack rate in Bucharest was reported to be 12.4 per 100,000 people.

The Tsai study (1998) identified the Culex pipiens as the vector responsible for
bridging the disease from birds. However they suggested that infected birds from Africa
or the Middle East migrated into the area, and then the Culex modestus species of
mosquito transmitted the virus throughout the birds in the area. As the virus spread
through the bird population by Culex modestus, the Culex pipens acted as the bridge
vector spreading the virus from the birds to the human population (Tsai, Popovici et al.
1998)

Until 1999 the virus was still limited to Africa, the Middle East, Western and Central
Asia, India, Europe and Australia (where the virus is known as Kunjin virus) (Anderson,
Vossbrinck et al. 2001). The disease emerged in the United States in 1999, in New York
City. These were the first recognized cases in the Western Hemisphere. There were 59
patients from New York (almost entirely from Queens) diagnosed with advanced clinical
symptoms of the disease. After the initial outbreak, the virus quickly spread across the
United States through the South and Midwest. It was spread through the bird migrations
across the country establishing endemism in humans, mosquitoes, mammals (horses) and
birds. As of 2002, there were positive reports of the virus in all states except Arizona,
Utah, Nevada, Oregon, Alaska, and Hawaii (Huhn, Sejvar et al. 2003). Currently (2006),
there have been confirmed cases of WNV in all 48 contiguous states, and since 1999 it
has become an endemic disease to North America. The spread of this virus caused the
largest human arboviral encephalitis epidemic in United States history (Huhn, Sejvar et
al. 2003). From June 10 to December 31, 2002, 4,156 cases of WNV infection (including
284 deaths) were reported across 39 states and the District of Columbia (Huhn, Sejvar et

al. 2003). This huge increase in positive infections was probably due to the expanded

knowledge of the virus among those in the medical community, and to public recognition
that symptoms required medical attention (Huhn, Sejvar et al. 2003).

The geographic diffusion of WNV across the United States in 2002 was similar to a
large (2,131 cases) epidemic of St. Louis encephalitis in 1975. Both viruses concentrated
in the Ohio and Mississippi river valleys. It was recognized that there was a geographic
distribution of the time of infection for human cases for WNV (Huhn, Sejvar et al. 2003).
In the southern states, infection occurred from the summer months until December, which
is beyond the characteristic arboviral disease-transmission season of June to October
(Huhn, Sejvar et al. 2003). In the northern states, the infections started later in the
summer and ended earlier in the fall. The South had a longer season with a lower
transmission peak, where as the North had a slightly shorter transmission season but the
intensity of the peak weeks was two to five times higher. This was most likely due to the
seasonally cooler weather, causing a shorter but more intense breeding season for the
mosquitoes. (Huhn, Sejvar et al. 2003).

WNV is a vector-borne RNA flavivirus that affects mainly birds, horses, and humans
(Anderson, Vossbrinck et al. 2001). However, all mammals and some reptiles are at risk.
The virus is maintained in the United States in an enzootic, mosquito-bird-mosquito
cycle. The most common mosquito vector known to spread the virus is the Culex species,
however it has been isolated or detected in greater than 20 species of mosquitoes in the
eastern United States (Anderson, Vossbrinck et a1. 2001). These mosquitoes develop in
the early spring from aquatic stages and begin to infect birds. The birds (mainly corvids)
then become the reservoir for the disease; subsequent mosquito blood meals complete the

cycle (Craven and Roehrig 2001).

Risk associated with this virus is difficult to assess, as there are many risk factors
such as, age, previous illnesses, and viral dosage. Since most of the cases never develop
recognizable symptoms, those sub-clinical cases go unreported. Thus, the overall risk to
the population cannot be accurately calculated. However the risks to those patients who
seek medical attention, or are hospitalized can be calculated. From patients hospitalized
with this disease the case fatality rate ranged from 4% in Romania (1996) to 12% in New
York (1999), and 14% in Israel (2000) (Petersen and Marfin 2002). The New York case
fatality rate remained constant throughout the United States in 2000 and 2001. Age is the
dominant risk factor associated with the disease. In New York, persons 75 and older were
nine times more likely to die than younger persons (Petersen and Marfin 2002). Not
much is known about the long-term morbidity associated with post-hospitalization for
WNV infection but may be quite substantial (Petersen and Marfin 2002). Of the people
who were hospitalized in New York and New Jersey in 2000 half did not fully recover by
the time of discharge. Follow-ups on the patients from the 1999 outbreak found persistent
symptoms such as fatigue (67%), memory loss (50%), muscle weakness (44%), and
depression (38%) (Petersen and Marfin 2002).

Only about one in 150 infected humans will develop recognizable symptoms. The
symptomatic illness has an incubation period of two to 15 days. A study of the 59
hospitalized patients from the New York City outbreak found the most common
symptoms were fever (90%), weakness (56%), nausea and vomiting (51-53%), headache
(47%), and changes in mental state. Advanced cases may develop into meningitis,

encephalitis, flaccid paralysis, coma, and death (Huhn, Sejvar et al. 2003).

10

The treatment for WNV is supportive, and there are currently no licensed medications
for the prevention of the disease. In order to prevent infection of WNV on a personal
level, the recommended measure is protective clothing during the high-risk season (April
to October). The state and local level prevention plan most often suggested in the
literature was to identify the vector species breeding sites and use aggressive surveillance
to determine the risk posed by the vector (Enserink 2000; Huhn, Sejvar et a1. 2003).

Mosquitoes may live up to several weeks, and the females are capable of laying
multiple batches of eggs in their short lifespan. The females of some mosquito species
require vertebrate blood to produce each batch of eggs; however this is not always a
necessity, blood from any animal would provide the proper proteins. Many mosquitoes
have a specific preference (e.g., birds, mammals, or reptiles) for their blood meal. The
time between the blood meal from an infectious host and when the mosquito is able to
transmit the virus varies by species and environment. It is possible for the cycle to occur
in as little as four to five days (at high ambient temperature around 26-30°C) and the
testing showed mosquitoes were still able to transmit the disease at 32 days (Dohm,
O'Guinn et al. 2002).

Mosquito species also vary in their ability to transmit WNV. Among laboratory-tested
species, it was found that different “doses” of WNV were required to cause infection with
different mosquito species. It was also found that WNV does not reach the salivary gland
in all mosquito species, so not all infected mosquitoes are capable of spreading the virus
through blood feedings (Marra, Griffing et al. 2004).

The main vector that is associated with the avian spread of WNV is the Culex pipiens

species of mosquitoes. This species breeds in standing water, urban drains and catch

11

basins (Allen and Shellito 2004). Normally, the Culex species will breed from April to
October in wet, richly organic areas such as swamps, fresh water rivers, and on poorly
drained agricultural land (Allen and Shellito 2004). These areas, as opposed to urban
microenvironments (e. g. old tires), allow for the greatest breeding potential of the vector.

Culex pipiens species transmit WNV through a bird-mosquito-bird cycle. There are many
bird species susceptible to WNV and act as hosts for the virus. The best recognized host
for this cycle is the American Crow (Corvus branchyrhynchus). This species has a high
case fatality rate, and is recognized as the main reservoir of the virus (Komar 2000;
Eidson, Kramer et al. 2001). The crow presents a high rate of infection and morbidity
from this disease with death occurring four to eight days after infection, following
exposure (McLean, Ubico et al. 2001; Komar, Langevin et al. 2003). During the outbreak
in New York City in 1999 nearly 89% of the dead birds that were collected and had
laboratory confirmed WNV infections were American crows (Komar 2000).

In order to examine the dataset of dead birds for structure, spatial point pattern
analysis will be used. Spatial point pattern analysis became common in geography in the
late 19505 and early 19603. At that time, the desire to examine spatial relationships in
datasets was at the forefront of the discipline. The techniques were adapted from the
literature relating to plant ecology. These methods of analyses were slow to gain
popularity due to the absence of suitable software tools. The first programs published
generated textual and numerical output, but did not have graphing and map capabilities
(Gatrell, Bailey et al. 1996). The advances in geographic information systems provided
the proper tools for these type of data to be analyzed and displayed more efficiently

(Gatrell, Bailey et al. 1996).

12

There are many methods for examining spatial point patterns such as “nearest-
neighbor” and “quadrat” analyses. However these two methods look for structure within
a dataset of points and do not allow for the inclusion of underlying causes, such as
population. The exclusion of population data is a problem with the study of disease
epidemiology in that the pattern of most diseases is directly related to the density of a
population. As such, spatial variation in patterns of disease is often explored with
techniques of cluster detection analysis (Klassen, Kulldorff et al. 2005). Detecting
clusters in spatial data can be done many ways, for the purposes of this study three cluster
detection methods will be used, Global, Local, and Temporal.

Global cluster detection methods are used to search for spatial patterns across the
entire study area. Global methods determine whether structure exists within the dataset,
and if the structure is unlikely to have arisen from chance. The statistics modeled for this
method are, Ripley’s K, Moran’s I, and Oden’s I(pop). Local methods look for clusters in
a particular area. They examine the proximity of cases and determine if they are closer
than would be expected by chance. The models that were preformed for this method are
Anselin’s Local Moran, Kulldorfi’s Spatial Scan Test, and the Geographic Analysis
Machine (GAM). Temporal tests examine the data over time. Using the results from the
previous models and dividing the data into smaller divisions of time, variations in the

intensity of the virus may indicate peaks during the transmission season.

13

2 Methodology

2.1 Data

The Michigan Department of Community Health (MDCH) collected information on
dead bird sightings via a toll-free hotline and a web report system. The hotline was a
message service where citizens could leave information on the species of bird, the street
address of where the bird was observed, the date of the observation, whether the bird had
been collected, and a contact number if the person was willing to have the bird collected
for West Nile Virus testing. The original statewide dataset contains 8,249 dead bird
records. From the original database only the corvids (crows and blue jays) were selected
for geocoding. The dead bird sightings used for this research were collected from April

through December of 2002.

2.1.1 Dead Crow Data

The dead bird database used the address information of where the bird was found to
place the location on the map. Most records also included township and county data. This
assisted in confirming the proper location when address matching. Address matching is a
process that uses road addresses to append points to an estimated spatial location along a
road segment using a GIS road layer. This was done, using ESRI GIS software, for the
entire state. This produced a new database (shapefile format) that contained geocoded
points representing the locations where the dead birds were found.

Due to the nature of the data collection process, citizen reported and not

systematically constructed, there were fields in the dataset that contained no data or

14

improperly entered data. These points failed to meet location accuracy standards. In order
to reduce error to a minimum the dataset was first clipped to the spatial extent of the
study area (Oakland, Macomb, and Wayne counties). From the original 8,249 statewide
records the three county study area dataset contained 2,533 bird records. All records were
individually checked for a positive road match; also crossroad information was verified,
if present. The county field was left blank for some cases in the original database. If the
road information were correct, that point would be placed in the county to which it was
addressed. In addition, if the county name was entered and incorrect, the point was
removed.

With the dataset cleaned of unreliable records, 2,497 dead bird points remained,
coincidently, only crows. With the file “cleaned” the data points were attributed with
spatial boundary information. Using a tagging function, township, city, and block group
information was appended to each data point. The data preparation process was
completed using TransCAD (Caliper 2006). At this point, the data set was considered
complete, closed for modification, and suitable for statistical analyses. As Table 1
illustrates, most of dead birds were found in Wayne County, with Oakland and Macomb

Counties having comparable ratios of dead birds to people.

 

 

 

 

 

 

 

 

 

 

 

Records by County
Dead Bird . .
County Records Population Ratio
Oakland 887 1,194,156 .00074278
Macomb 502 787,625 .00063736
Wayne 1,108 2,061,162 .00053756
TOTAL 2,497 4,042,943 .0006] 762
Table l.

15

The data were then divided by month and within the month over the course of the

transmission season (Table 2).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Records by Month
Month Records
April 2
MaL 32
April & May 34
June 59
June l-15 34
June 16-30 25
July 396
July 1-10 20
July 1 1-20 108
JulL21-3l 268
Augu_st 1,826
August 1-10 875
August 11-20 461
August 21-31 490
September 166
October 16
TOTAL 2,497
Table 2.

The distribution of dead bird records can be seen in Figure 2.

l6

 

Dead bird distribution by county.
Fig. 2

2.1.2 Census Data

Given the method of collection, it was likely that the underlying human population
influenced the bird data simply due to opportunity and observation, the observation bias
attributed to population had to be accounted for in the models. By incorporating human
population, the models can examine the data objectively and compare the ratio of found
birds to the number of people who could have found them. Population data were obtained
from the 2000 United States Census. For the population data, census block group data
were selected, because it was the finest spatial resolution dataset available for the study
area.

The dataset downloaded from the US. Census web site was for the entire state of
Michigan. The raw data were in the ESRI Shape file format, as centroid points,
containing latitude and longitude spatial information, and attributed with the population
for each block group. Using TransCAD, only the points from the study area were selected
and edited to the proper extent. These data were used as the underlying population for all

statistical models.

18

  

 

Population

. O to 611 (431)
612 to 777 (625)

' 778 to 932 (625)
933 to 1129 (559
1130 to 1374(464
1375 to 1745(4001
1746 to 2479(282)
26480 t01k0000(11856>

 

 

Niles

 

Human population by block group.
Fig. 3

 

 

 

 
 

 

 

 

 

g” 1560 to
fini-2951 to
- 4335 to
- 5670 to
- -7122 to
- 8830 to

   

Pop_
4 0 to 1560 (457)

Den

2951 (510)
4335 (489)
5670 (480)
7122 (520)
8830 (480)

11450 (406)

 

 

- ‘11450 to 100000(251)

 

Population density by block group.
Fig. 4

20

2.2 Global Statistics

2.2.1 Ripley’s K

Ripley’s K-function was used to analyze the spatial pattern of point data by
considering its density within a set of distances, and to detect global spatial structures in
individual-level data by comparing the observed proximity of cases with the pattern
generated by a homogenous Poisson process. Ripley’s K-function describes the extent to
which there is spatial dependence in the arrangement of events. The K-fiinction is
estimated for the observed data, and then compared to an arrangement of events showing
complete spatial randomness (CSR). The CSR pattern used to model the dataset is created
by a homogenous Poisson process. It can also be compared using a Monte Carlo
randomization of the data (Bailey and Gatrell 1995).

The expected number of other events within a fixed distance (h) of one event is
KK (h), where 2. is the intensity, or mean number of events per unit area. The variable h is

the radius of a circle from each event used to examine the point pattern (Fig. 5).

K(h) or Khat can be estimated by the following formula (Bailey and Gatrell 1995)

. R " " Ihld.)
K h =— ——/—
l) 22 w.

(1)

Here R is the area of the region of interest, n is the total number of events in region R, dij

is the distance between the ith and fh events, and lh(d,'j) is the indicator function which is

21

1 if dif- Sh and 0 otherwise. The function sums the number of events within distance h of

each location in the dataset (each 1'). Typically Wij is the conditional probability that

points around event 1' will be in the study area. The Ripley’s K model calculates the
weight as a proportion of the circle’s area that falls within the study area. The weight for
a circle falling completely within the study area would be 1, and if half of the circle’s
area is outside of the study area the weight would be 0.5. The event count in that area is
essentially doubled to account for the missing half of the circle (Fig. 6). If Khat is
estimated for a number of distances, one can examine the spatial dependence of points
relative to distance. In addition, the estimate of Khat can be converted/normalized to a
test statistic Lhat that permits the significance of the deviation of an observed value of
Khat from its expected value (under the assumption of randomness according to a
Poisson distribution) to be tested (Fortin 1999); if Lhat is significantly different from zero

then the distribution of points is not random. The general form of Lhat is:

Lhath = (Khan/700'5 — h
(2)

Ripley’s K results are reported as Lhat in the graph outputs. The null hypothesis for
Ripley’s K is the distribution of events is a spatial Poisson point process (complete spatial
randomness). The alternative hypothesis is that the dataset shows structure at some

scales.

22

 

 

. 6eventswm'n
adistanoeh,
olfOunitsfrom
eventj

 
 
 
 

 

 

 

 

 

adistanoe,h.
0110me
eventi

 

 

 

 

Fig. 5 Estimation of Ripley’s K

 

 

M} = 1.0

 

 

 

 

 

 

Fig. 6 Estimating the weights for Ripley’s K

2.2.2 Moran’s I

Moran’s I is a weighted correlation coefficient used to detect departures from spatial

randomness (Moran 1950). Departures from randomness indicate patterns such as

23

clusters, but may also identify geographic trends. Moran’s 1 examines global spatial
autocorrelation in group-level data. Positive spatial autocorrelation means that nearby
areas have similar autocorrelation rates, this would indicate spatial structure within the
dataset. Nearby areas have similar autocorrelation rates when the populations and
exposures are alike. When rates are similar, Moran’s I will be large and positive. A
Moran’s I value close to 1 is indicative of positive autocorrelation or a clustered spatial
structure. When rates in nearby areas are dissimilar, Moran’s I will be negative. A
negative Moran’s I value indicates negative spatial autocorrelation, or regularity in the
point pattern.

Moran’s I (Moran 1950) is used to determine whether neighboring areas are more
similar than would be expected under the null hypothesis. The null hypothesis for
Moran’s I, is that the disease rates are spatially independent and that the observed rates
are assigned at random among locations. If I is close to 0 then the null hypothesis is
accepted. The alternative hypothesis is that the disease rates are not spatially independent.

The null hypothesis would be rejected if I were not 0.

Moran’s I is defined as:

I 1:111

_ =N
S022,2

l-l

 

N N
szmm.

(3)

24

Where, N equals the number of regions, wij is a weight representing the intensity of the
connection between areas i and j, z,- is the rate in zone i centered around the mean rate

(using z,- = x; — ave(x); x,- is the rate in zone i); and So is the sum of the weights.

N N
So =Zzwij,i¢j

i=1 j=l

(4)

The expectation of I under the null hypothesis is:

—1

E")=m

(5)
The expectation gets closer to 0 as N increases. The variance of I is determined under
two null hypotheses or assumptions: Normality (denoted N) or randomization (denoted
R). Under assumption N the rates are sampled from a mean-zero population whose
distribution is normal. Under the R assumption the rates are random samples from a
population whose distribution is assumed to not follow a normal distribution. Assumption
N is useful when the observations are thought to follow a normal distribution.
Assumption R is less restrictive and, since we often don’t know the theoretical
distribution, is appropriate for disease rates.

The variance under assumption N is:

1
V 1 = N25 —NS +352 —rv:12
ar/v() (N-lXN+l)S§( l 2 o) ()

 

(6)

25

The variance under the assumption R is:

N|(N2—3N+3)S— ——NS+3sg| b,|(N2— N)s -2NS2 +6sg|

VarR (I): (N 1)" 52
0

Where, a falling factorial is written 3”” = s(s-I)... (s-b+l),

and where

b2 =m4/m22

mle/N242: z,

mzzl/NZIi-Z 1 Z'
= 52:12:1(“41 + W}, )2

2

52 =2 (Wio +Woi)

—E(I)2

(3)

Significance for the Moran’s I model is evaluated under assumptions R and N, and by

Monte Carlo simulations. For assumptions R and N the model calculates two z-scores as:

1— EU)
N=\/VarN(I)

 

 

and

26

(9)

Z ___ I—E(I)
R J VarR (I ) (10)

 

 

These z-scores express the difference between the observed and expected value of I in
standard deviation units. The distribution of the z-scores is approximately normal with a
mean of 0 and a variance of 1.0. The Moran’s I model reports a two-tailed P-value
because spatial pattern is of interest both when Moran's I is positive (rates in connected

areas are similar) or negative (rates in connected areas are dissimilar).

2.2.3 Oden’s I(pop)

One major issue with Moran’s I, is that it does not take into account underlying
variation in a collinear variable population, which for the purposes of this study is
important due to the nature of the data collection process. This problem was corrected
with Oden’s I(pop) (Oden 1995). Oden adapted Moran’s I to examine population data to
detect departures from spatial randomness. When population data are not used, large
differences in population hinder Moran’s I to accurately detect spatial autocorrelation and
spatial randomness. Like Moran’s I, Oden’s I(pop) is a global level model for grouped
data.

This model was adapted from Moran’s I (Moran 1950) to take population data into
account for computing the departure from randomness for spatial pattern data. The
datasets for the population and disease events need to be in numeric totals for each

unique polygon. When there is autocorrelation within a region or in adjacent regions the

27

I(pop) statistic will increase. Large values of Oden’s I(pop) indicate positive spatial
autocorrelation or similar rates in connected areas; small values indicate negative spatial
autocorrelation or dissimilar rates in connected areas. The range of Oden’s I(pop)
depends on population size.

The statistic I(pop) is as follows:

Nziiwfie, —d,.)(ej —dj)—N(l—2b)zm:w,je, —Nb—iwfidi

i=1 j=l l=1 i=1

3013(1—5)

 

1170.0 =

(11)

where:
e,- = ni/N and d,- = xi/X

(12)
Here m represents the number of cells in the grid, and N is the total number of cases
in all of the areas. For a given region, ni is the total number of cases in area i, and e,- is the
proportion of cases in area i (e,- = ni/N). For the population counts, X is the total size of
the risk population in all areas; xi is the size of the risk population in area i, and d,- is the
proportion of the population in area i, d; = xi/X. Also, e,- - d,- is the difference between the
proportion of cases in area i and the number of cases expected given the area’s population
size; and b is the average prevalence, b = N/X, b2 = I/b(l-b) -3. Finally, wil- is a weight
denoting the strength of connection between areas i and j, developed from neighbor

information.

28

The equations for calculating S0 and SI are:

s0 = XZA — X8
(13)
S, = X’E—4X2F +4XD
(14)
For calculating these variables the following formulas are used:
2
m m m m
422444- E=zd z<w +w )
i=1 j=1 .j=1 =1
m m m
B=Zdiwfi F=Zdwn2dj(wij +wfi)

i=1 j=1 j=1

D=idiwif H: iiw..( (e. —d,.j)(e +d)

i=1 i=1 F1

(15)
Under the null hypothesis, which is that there is no autocorrelation, I(pop) approaches

zero when the population is large. This value E (Ipop) is represented as:

—l

E (11901?) = m

(16)

29

Oden’s I(pop) calculates the variance in two ways. First, it is based on a random
distribution, which is good for disease rates (Cliff and Ord 1981). Secondly, if the
distribution is assumed to be normal the variance is approximated.

This variance under the null hypothesis is:

X[(X2 -3X+3)s, -XS, +353J—b,[X‘2’S, —2XS, + 6S;J_

 

 

VarR (Ipop) = (X _ 1)( ”S2 E(IP0P)2
0

(17)

Approximation of variance (VarA):
C
2A2 + —2- — E
Var], (Ipop) = A 2X 2
(13)

For examining significance, Oden’s I(pop) uses three methods: z-scores and variance,
Monte Carlo randomization, and using multinomial randomization. These methods report
similar P-values. For the purpose of this research only the Monte Carlo randomization

assumption was used.

2.3 Local Statistics

2.3.1 Anselin’s Local Moran (LISA)

The local Moran model (Anselin 1995) detects local spatial autocorrelation in group-
level data. It is similar to Moran’s I (Moran 1950), a model for global spatial
autocorrelation, but the local Moran decomposes Moran’s I into contributions for each

location, termed LISAs, for Local Indicators of Spatial Association. These indicators

30

detect clusters of either similar or dissimilar disease frequency values around a given
observation. The sum of LISAs for all observations are proportional to Moran’s I, and are
also an indicator of global pattern. Therefore one can make two interpretations of LISA
statistics: as indicators of local spatial clusters and as a diagnostic for outliers in global
spatial patterns.

The range of the LISA statistic is not as readily interpretable as the global Moran’s 1
statistic, the values will depend on the number of observations in the dataset. Therefore
the statistic should be evaluated such that positive values indicate like areas surrounded
by like areas. Negative values indicate outliers in the dataset that do not constitute
clustering. Values near zero indicate either the local area under consideration or the

average of the immediate neighbors of the cell, or both, are near zero.

2.3.2 Kulldorff’s Spatial Scan Statistic

Kulldorff’s Scan method (Kulldorff and Nagarwalla 1995; Kulldorff 1997) can detect
local space or space-time clusters in group-level data. The scan statistic uses a circular
window to identify high concentrations of cases in space and time. The area is divided
into spatial zones and in each zone a circular window increases in size until it reaches a
set upper size limit. The Kulldorff scan statistic then compares a measure of whether the
observed number of cases is unlikely for a window of that size, using reference values
from throughout the study area. By searching for clusters without specifying their size or
location, the method provides a model with no pre-selection bias. Kulldorff developed
two models, a Poisson model and a Bernoulli model. For a small number of cases, the

two models are similar. The Bernoulli model is best when studying disease using a

31

population with the disease and a control group without the disease, while the Poisson
model better answers questions when using case and population-at-risk counts.

For the spatial scan, a circular window is moved systematically through the study
area. The scan window starts at each location in the dataset. The spatial scan model uses
the centroid of each polygon as the location for the window to start. The window expands
to include the nearest region centroids. The maximum size of each window will not
exceed 50% of the total population-at-risk size for the study period.

The hypotheses are evaluated with a maximum likelihood ratio test that examines
whether the null or alternative model better fits the data (Kulldorff 1999). The scan
statistic is the maximum likelihood ratio over all possible window sizes. Its P-value is
obtained through multinomial Monte Carlo randomizations. If the null hypothesis is
rejected, the spatial location and the extent of the cluster that caused the rejection were
reported.

The likelihood ratio is:

 

L(Z) 77(7) N-MZ)

Lo N N

 

 

(17)

ifnz > 11(2), I/Lo otherwise.

32

Where nz is the observed number of cases and ,u(Z) is the expected number of cases in

cylinder Z. The observed (N) and expected [/1 (A ) ] number of cases are calculated over the

entire study area.

2.3.3 Geographic Analysis Machine (GAM)

The Geographic Analysis Machine (GAM) was developed in 1987 by Stan Openshaw
at the Center for Computational Geographies at the University of Leeds (Openshaw,
Charlton et al. 1988; Openshaw 1995). Originally, it was designed to identify disease
clusters such as childhood leukemia (Openshaw, Charlton et al. 1988; Bailey and Gatrell
1995). The process is a computationally intensive approach to the automated
identification of clusters.

GAM is a cluster location tool used to analyze spatial point distributions. Its purpose
is to find evidence of localized geographical clustering. It incorporates a technique that
compares the intensity of events within circles of varying radius; the circles are centered
on a fine grid imposed over the area of interest. The levels of intensity are compared to a
constant that represents the expected intensity. The circles identify areas of significant
differences from the constant. The technique involves a Poisson model for the statistical
distribution. Once the condition of statistical significance and the intensity rate is met the
circle is drawn on the map over the area. This process is continued across the study area
(Openshaw, Charlton et al. 1988).

This process only looks for the clusters and does not seek to explain the underlying

cause of the cluster. Also by looking at the entire study area it does not require the

33

specification of a spatial scale at which we expect clusters to occur. Therefore this
process makes few assumptions about the dataset and is considered an exploratory

method (Bailey and Gatrell 1995).

2.4 Data Preparation/ Methods for Statistical modeling

After researching the appropriate spatial analytic tests, ClusterSeerTM, a commercial
software package, was selected because it provided a comprehensive suite of models for
spatial data. ClusterSeerTM was specifically designed to analyze disease clusters in both
spatial and temporal data. This program also was able to run all desired statistics except
the Geographic Analysis Machine. The following sections are the methods for preparing

the data for use with ClusterSeerTM, and the processes involved in performing the models.

2.4.1 Ripley’s K

Data preparation for running the Ripley’s K model began with the entire dead bird
point file. Selections were made for each month from the dataset using the Caliper GIS
software TransCAD (Caliper 2006). These files were exported as shape files and used in
ClusterSeerTM for processing. The ClusterSeerTM interface required a point file for this
model with spatial location information and a unique ID field. The data were imported
with a geographic projection (latitude and longitude), and kilometer was selected as the
unit for distance. Selecting the proper projection information is important; Ripley’s K
reports an interpoint distance that allows for an interpretation of approximate cluster
scale. If the wrong projection information were selected the units of the results may not

be correct. Interpoint distance refers to the measurement between data points. Next,

34

parameters for the distance step limits were set for the model to run. The distance step
limit was set to 10 steps in each model. The distance used for each step was set as
default; the software estimated an approximate minimum interpoint distance. It is
required for determining the autocorrelation between points. Finally, the number of
Monte Carlo Randomizations was set to 100. This model produced the output as the
maximum deviation from identity (one-to-one line). It also produced a graph of the

simulation envelope and Lhat line (Fig. 10-16).

2.4.2 Moran’s I and Local Moran (LISA)

For the Global and Local Moran’s I models the same 100 by 100 and 10 by 10 grid
cell files were used. These models required a uniquely identified polygon file. The only
attribute that was required for the models was a count of the disease records for each
polygon; dead birds were used as the disease frequency. The polygon file had to be clean,
with no double lines or overlapping segments, the background files that were available
did not meet these requirements. For the purposes of being uniform and unbiased, the
data were converted to a grid. To create the attributed grid the Caliper GIS product,
TransCAD was used.

The data files that were used included the dead bird records, as points, clipped to the
study area, and the geographic outline of the study area. TransCAD allows the import of
ESRI shapefiles into the Caliper native format of the Standard Geographic File. Both files
were imported into this GIS. The function used to make the grid was Create Vector Grid.
This function allows for the creation of area grids with a specified number of cells or
cells at a set distance. This allowed the entire map window to be covered with a set

number of cells without specifying a size for the individual cells (Figs. 7 and 8). The

35

grids cover the entire map window going beyond the borders of the study area. This was
corrected by using the Clip by Area function, leaving a grid the exact dimensions of the
study area (Figs. 7 and 8). Two grid size resolutions were used for these models, 100 by
100 and 10 by 10. The 100 by 100 grid cells measure approximately 900 meters square,
and the 10 by 10 grid cells measure approximately 9000 meters square. After the clipping
process the numbers of cells for each resolution were, 6,019 and 79 respectively (Figs. 7

and 8).

     
 

  

WW.- H
AWM
,.

r

W.“
WM“ 42..

  
 

 

      
 

’ '11!" 4 11!.”

l
:33? it!

i..- ,
3132::
E
2151 ‘

100 by 100 grid processing steps. Fig. 7

 

 

 

 

 

 

 

 

 

 

10 by 10 grid processing steps. Fig. 8

36

The next step involved with the data preparation was attributing the grid with counts
of the dead birds within each cell. A new field was added to the grid database. The field
was filled using an aggregate function that counted the specified contents of the given
cell. This worked extremely well. There was an issue of points being counted in more
than one polygon using this function with other background files. This multiple counting
did not occur with the grid base files. Summing the count column, then comparing to the
total dead bird count, verified this. This was done for all of the bird records and for each
of the time frames mentioned in (Table 2). The grids were then exported as shapefiles for
use with ClusterSeerW.

For the Moran’s I model the ID field and the disease frequency count field were
selected. A geographic coordinate system was used again. A queen’s relationship of eight
cells adjacent to the center cell was selected for the polygon contiguity. The other
parameter that was used for this model was the level of significance, which was set at
0.05 using 100 Monte Carlo randomizations. The output contained the numeric Moran’s I
results, a graph of the Monte Carlo distribution, and a plot of the p-values against the
Monte Carlo runs. No map was produced from this model.

For Anselin’s Local Moran model, the same files were used at the 100 and 10 cell
grid sizes. This model also required the polygons to be clean, and the dead bird data in
numeric count form. The same fields were selected and the significance was set at 0.05
with 100 Monte Carlo randomizations. The queen’s relationship was used. Products from
the LISA model were the same as with the Moran’s I model, with the exception of a map

attributed with the local Moran statistic. There were some problems with exporting some

37

of the shapefile maps from ClusterSeerm. The program had a tendency to freeze and shut

down. However exporting the session logs presented no problems for any model.

2.4.3 Oden’s I(pop) and Kulldorff’s Scan Method

Data preparation for these models was very similar to the previous models. The
additional information required for these statistics was the population information.
Population was calculated for each cell in the grid. Some of the cells did not contain 3
Census block group point. ClusterSeerTM required a number greater than zero for all cells,
to perform the models. For these blank cells a value of one was entered as the population
count. Only four cells required this adjustment, and all four cells had a zero bird count.
Therefore, the results were modestly affected. However, due to the non-zero requirement
these models were not run using the 100 by 100 grid.

The last global model was Oden’s I(pop). Oden’s I(pop) required the unique ID field,
a count field for the records in each grid cell, and a record for the aggregate population
for each cell. With these fields selected, the projection was set. For this model the
queen’s relationship was selected. The significance threshold was set to an alpha of 0.05
and 100 Monte Carlo simulations were used. This model produced results for I(pop) and
the significance level.

The final model was the Kulldorff Spatial Scan method. The Kulldorff Spatial Scan is
a local cluster indicator, and has the option to look for clusters in space or space and time.
The same three fields and projection information was entered. Also the queen’s
relationship was used for this model. The only other parameter for Kulldorff was the

number of Monte Carlo randomizations, which was set at 100. Kulldorff also calculated

38

an average disease frequency based on the dead bird counts and population data. The
advantage of this model is that it produces three classes of likely clusters and also
provides a map showing the locations of each class. It also calculates average disease

frequency, the log likelihood ratio and the upper-tail P-value for each class.

2.4.4 Geographic Analysis Machine

The Geographic Analysis Machine (GAM) was the only model that could not be
completed using the ClusterSeerTM software program. The GAM model was programmed
using the ‘R’ Statistical package. This programming language and analysis environment
is used for statistical computation and graphics applications (Team 2006). The ‘R’
language is very similar to the ‘S’ language that was developed at Bell Laboratories
(Chambers et al 2006).

The environment for executing the program requires libraries or packages for
processing the various functions within the code. There were four libraries required for
completion. The first was the splancs 2.01-17 package (Rowlingson and Diggle 2006).
This library provided the spatial and space-time point pattern analysis functions. Next,
the gstat 0.9-31 package was used for geostatistical modeling, prediction and simulation
(Pebesma 2006). The third library was fields 2.3 (Nychka 2005), required for calculating
the distance functions within the program. The last package, maptools 0.5-12 (Lewin-
Koh and Bivand 2006), was required for reading in the boundary file, which was in
“shapefile” format.

The study area boundary and population centroids were projected to UTM Zone 17

using the WGS 1984 datum. The dead bird point files that were used previously were re-

39

projected using TransCAD and exported as comma delimited text format. Also, the
Census population centroids were converted to comma delimited text format. The
boundary file was used as a convex hull for the data and in the final maps for this model.
After data import, the program first calculated a background rate for use in the model.
The background rate was calculated by dividing the length of the dead bird point column
and the sum of the population centroids. This value changed for every model because
each time period had a different number of birds. Also required for the model was a grid
of points overlaying the study area; the grid acts as the locations at which regional counts
will be aggregated. Therefore, a finer resolution of grid points would make for a
smoother final map. The finer resolution would also exponentially increase computation
time. For all time periods a grid spacing of 1609.344 meters (1 mile) was used. Then the
boundary file was used to remove the grid points outside the study area. GAM required a
function to calculate the distance between the grid points and the bird points and the
population centroids. The function used the Euclidian distances between the points for
calculations. A four-column array was created to hold the results from the GAM
calculations. The first column contained the number of birds within each calculated
distance of each grid point. The second column contained the sum of the population
centroids within the specified distance of each grid point, which only needed to be large
enough to contain a bird and a population centroid. A distance of 10,000 meters was
used. The third column was filled with the ratio of birds to people, and the fourth column
contained the expected bird count, based on the population and background rate. With the
array completed the confidence interval needed to be set. This method is known for

requiring extremely high confidence intervals to see meaningfirl results. All models were

40

compared using the Poisson distribution starting at an alpha of .01 and increasing from
there. The confidence interval was increased until there were only a few clusters present.
The model produced a map of the study area showing areas of potential clustering for

each time period.

41

3 Results & Analyses

3.1 Results from Global Methods

3.1.1 Ripley’s K

The Ripley’s K function models the nearest neighbor limited to the smallest possible
scales, as though there is no first order effect within the dataset. In order to more easily
interpret the results from the Ripley’s K model as a straight line, the Khat statistic is
converted to Lhat. This allowed for comparisons to a straight line. As the Lhat differs
from the straight line (randomness) the point pattern can be interpreted as having spatial
structure.

Examination of the graphs produced by the model showed a noticeable pattern
associated with the amount of dead bird locations from each model. As the number of
points increased the graph showed increasing spatial structure. This could be seen when
comparing the graph for all results (Fig. 10) and the graphs for July and August (Fig. 13
and 14). These graphs showed a smooth arc for the data points far above the simulation
envelope, denoting structure within the point pattern. The model for April showed no
results due to insufficient points (two records). When reviewing the results for May (Fig.
11) the model showed complete spatial randomness. As the spatial relationships between
the points change throughout the transmission season greater structure is present. This
can be seen in the June data (Fig. 12); as the points began to show signs of positive
structure Lhat is above the simulation envelope. The positive structure continued to

intensify through the peak of the transmission season in August (Fig. 14). The data began

42

to lose cluster associations at the end of the season. The graph for September (Fig. 15)
showed the model just outside of the prediction envelope. At the end of the season in
October (Fig. 16) the model falls completely within the prediction envelope showing a
return to randomness in the data. For this model and all subsequent models randomness
describes a spatial pattern in which all records have the same probability of occurrence at
any location. Also, a cluster is defined as a statistically significant subset within a
population.

For a better understanding of the graphs a legend has been included (Fig. 9). The
legend shows the identity function as the red line; this represents the one-to-one line
signifying complete spatial randomness for the model. The gray lines represent the
simulations run by the model; the combined extents of the simulations are shown as the
envelope in blue; the average for the simulations is depicted in green. Together these
lines show the extents of the model for randomness. The black line shows the fit of the

data to the model. Interpoint distance is measured in kilometers.

Legend

— Identity function
Llh] :i-dalion:

— Average simulation vahre:
— Llh] inflation envelope
0 L-points

— Llh]

Fig. 9

43

All Records

 

 

 

 

 

38.9—
E
A
q
.C l
.0 29.2
Interpoint Distance
Fig. 10
May
16.5—
E
o-‘l
t
.G I
.2) 17.3
Interpoint Distance
Fig. 11

June

 

 

 

 

 

E
r-‘l
.C 1
.0 22,5
Interpoint Distance
Fig. 12
July
34.9-
/
2 /
g
i
.G 41
.3 26.9
Interpoint Distance
Fig. 13

45

August

 

 

 

 

38.9—
A
5
o-‘l
1
.G 1
.1: 28.9
Interpoint Distance
Fig. 14
September
32.5—
2 it
5
o-‘l
4
.c 1
.3 28.3
Interpoint Distance
Fig. 15

October

AA

4'J.3—

L(h)

 

 

 

Interpoint Distance

Fig. 16

3.1.2 Moran’s l

Moran’s I is a weighted correlation coefficient used to detect departures in spatial
randomness in global level data. The statistic indicates spatial patterns such as clusters or
geographic spatial trends across the area of interest. The values of Moran’s I range from
—1 to 1. Positive values represent positive spatial autocorrelation meaning that the
neighboring areas contain similar rates. This relationship indicates spatial structuring
within the point distribution. When Moran’s I is negative the model indicates that the
nearby areas are dissimilar, usually indicating an increase to a regular pattern.

The 100 by 100 cell grid was modeled first. For all dead bird records the model
indicated a Moran’s I value of 0.32 showing positive autocorrelation in the point
distribution. From all the other time periods modeled, August indicated the greatest

Moran’s I value of 0.29. July was the only other month to show any significant positive

47

autocorrelation with a Moran’s I value of 0.14. Values from outside the peak season
were all very close to zero for other time periods. The significance values for these
models only met the alpha value for the all records, July and August. Full results for this
model can be found in Appendix 1.

When the data were aggregated to the coarser 10 by 10 grid there were many more
models that showed spatial autocorrelation. The model for all records increased to 0.63
showing positive spatial autocorrelation. Early in the season the Moran’s I value showed
a small peak in May rising to 0.27. There is a brief drop-off during June, with a sharp
increase toward the later half of the month. The Moran’s I value increases through July
showing increased autocorrelation with the season peak in the first part of August with a
value of 0.64. The model for August showed the greatest positive autocorrelation Full

results for this model can be found in Appendix 1.

3.1.3 Oden’s Ipop

Oden’s Ipop is an adaptation of Moran’s I that has been adjusted for population. This
model reports three different significance values using z-scores and variance, Monte
Carlo randomization, and using multinomial randomization. A multinomial distribution
describes the outcomes of independent trials with two or more possible but mutually
exclusive outcomes. This approach is used for redistributing cases of disease among
spatially referenced sub—groups. The cases are distributed among the sub-groups at
random where the probability of a case being placed in a particular group is proportional
to the population at risk for that group. The first two methods for significance are

designed for data which is normally distributed, because the data are not assumed to be

48

normally distributed the Monte Carlo significance values will be used for analysis. The
statistic also calculates the I(pop) value which is used to see if the data present spatial
structure. The I(pop) statistic will get large when there is clustering within a cell or
between cells. The null hypothesis for this model is that there is no clustering in the data,
this hypothesis is excepted as the I(pop) statistic approaches zero. The range for this
statistic is dependent on the size of the population. For this model population is large,
This will cause the range of I(pop) to be very small. This model showed significance in
months that contained large bird counts (all records, and July through October) (Table 3),
and with I(pop) values close to zero for all models, structure is said to be present if the

model was found to be significant. The full results for this test can be found in Appendix

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.
Ipop Ipop' E[I] Test. Upper Tail
Statrstrc

All Records 8.80E-05 0. 142425 -2.47E-07 0.142425 0.0099
April-May 6.56E-07 0.077993 -2.47E-07 0.077993 0.18812
June 7.40E-06 0.507 3 l l —2.47E—07 0.50731 1 0.0099
June 1-15 8.38E-06 0.997917 -2.47E-07 0.997917 0.44554
June 16-30 -2.98E-07 -0.0482642 -2.47E-07 -0.0482642 0.44554
July 2.60E-05 0.265002 -2.47E-07 0.265002 0.0099
July 1-10 4.81 E-07 0.0971934 -2.47E-07 0.0971934 0.16832
July 1 1-20 4.46E-06 0.166938 -2.47E-07 0.166938 0.0099
July 21-30 2.35E-06 0.354976 -2.47E-07 0.354976 0.0099
August 8.33E-05 0.184354 -2.47E-07 0.184354 0.0099
August 1-10 6.72E-05 0.310556 -2.47E-07 0.310556 0.0099
August 11-20 2.58E-05 0.226085 -2.47E-07 0.226085 0.0099
August 21-31 4.06E-05 0.334904 -2.47E-07 0.334904 0.0099
September 2.01 E-05 0.490066 -2.47E-07 0.490066 0.0099
October 8.69E-06 2. 19463 -2.47E-07 2. 1 9463 0.0099

 

Oden’s I(pop) Monte Carlo assumption results. An alpha of 0.05 and 100 Monte Carlo

Simulations were used for all time periods

Table 3.

49

 

3.2 Local Models

3.2.1 Anselin’s Local Indicator of Spatial Autocorrelation

Anselin’s Local Indicator of Spatial Autocorrelation is a Moran’s test identifying
local clusters in group-level data. Consistent patterns in the data started to develop after
the first couple months of the year. Clustering was focused near the center of the study
area (Birmingham/ Royal Oak areas) and along the coast (Grosse Pointes areas).

The All Records map (Fig. 17) showed this in a dark green band across the middle of
the study area. Moving away from these areas the intensity of the clustering tends to
diffuse. The records for April had no valid results; therefore they were included with the
records from May for modeling (Fig. 18). This model showed signs of clustering in areas
with greater human population. The transmission season began to intensify during June
(Fig. 19), and there was a shift in the areas of clustering. The focus changed to the
Livonia] Westland area due to a large number of records in the last two weeks of June
(Fig. 20). This cluster is offset by the randomness shown in the first half of June (Fig.
19). The July map (Fig. 21) demonstrated a cluster pattern that surrounded the city of
Detroit. The densely populated suburban cities around Detroit showed mild clustering
with moderate intensity in the cities of Royal Oak and Warren. This pattern varies little
during the month of July (Fig. 22). The August maps showed the peak of the season, as
well as, the majority of the records. Throughout the month of August the cluster intensity
shifts from the immediate areas around the city (Fig. 26), to areas farther away. The map
for the first part of August (Fig. 27) showed the most intense clustering between the
Redford/Southfield areas, with moderate clustering in Birmingham. For the next map for

August (Fig. 28) the most intense areas migrate north to Birmingham and Southfield and

50

east to the Grosse Pointe communities. The final map for August (Fig. 29) showed this
trend continuing as the clusters present over the Farmington and Bloomfield Hills areas.
This map also showed the first instance of clustering advancing as far north as Rochester/
Rochester Hills areas, and as far west as Novi. Although the intensity of the clusters
slightly drops off, the clusters are more widespread and occur in more areas. September
(Fig. 30) showed very mild clustering throughout the middle of the study area. The map

for October (Fig. 31) presented some clustering in the east side of Oakland County.

51

All Records

 

umm_1o_ond_usa
Local Moran

as to -1.5(1)

(WE-1.5 to 41.5 (1)

--o.5 to 0.5 (32)

-as in 1.5 (e)

-1.5 In 2.5 (4)

-zs to 3.5 (3)

-3.5 no 4.5 (2)

   

Fig. 17

52

April and May

 

Fig. 18

53

June

 

Juno_10_6rid_LlSA
Local Moran

m-m 1o -o.5 (1)

-o.5 to 0.5 (74)

-os 1o 1.5 (3)

-1 5 to 2.5 (1)

   

Fig. 19

54

June 1-15

    

m_1_15_10_6fid_u5A
Local Moran
-o.5 to 05 (791

Fig. 20

55

June 16-30

 

   

m_15_5o_1o.o:u_r.lu
Moran

45.1.4.5")
4*“ 41.1.5» up)
”(00.5”
-ubum
-1.5ou(n
menu)
-3.51uo(1)

Fig. 21

56

July

 

July_10_Grid_LlSA
Local Moran

1.31: 4.5 to as (1)
--0.5 to 0.5 (55)
-c5 1o 15 (5)
-1.5 to 2.5 (2)
-25 1o 15 (3)
-3.5 to 4.5 (2)

   

Fig. 22

57

July 1-10

    

Juty_1_10_10_6rld_LlSA
Local Moran

m-u to -0.5 (2)

; -0.5 to 0.5 in)

(w -0.5 to 1.5 (5)

Fig. 23

58

July 11-20

    

m_11_a_10_oiu_m -
Local loan

-1.5|o-0.5|1)
--051o0.5(u)
-0.5101.5('n
-1.5u2.5(3)
Inna-5131
-ubulll
mini-5m

Fig. 24

59

July 21-31

    

Juiy_21_51_10_oud_usA
Local Iona

,15 to 4.5 (1)
--0.5 to 0.5 (00)
-0.5 b 1.5 (4)
-1.5 b 2.5 (a)
-2.5 to 5.5 (3)
-3.5 to 4.5 (1)
-4.5 in 5.0 (1)

Fig. 25

60

August

ii .
' l
. 4
=-—1
. J T
,5.
..i.
(.1
.1.
~+-~~ ,

. amidst-.. .r..._.j _, _' a.

 

A-ubum

Fig. 26

61

August 1-10

   

SID-0.512)

m_1_10_10_om.i.ru
Local Heron

-.ng
Leash"

Fig. 27

62

August 11-20

 

August_11_20_10_Grld_LlSA
Local Moran

-3.5 in -2.5 (1)

as to -1.5 (0)

wig-1.5 in .115 (0)

--0.5 in 0.5 (05)

-115 to 1.5 (7)

-1.5 in 2.5 (3)

-2.5 to as (2)

-1510 4.5 (1)

   

Fig. 28

63

August 21-31

      

AM21_31_10_Grld_USA
Local Moran
4.5 to -2.5 (1)
. .25» -1.5 (0)
M45 to -0.5 (2)
11., --0.5 to 0.5 (00)
/' -o.5 to 1.5 (0)
‘ -1.5 to 2.5 (2)
-2.5 to 3.5 (2)

    

Fig. 29

September

    
 
 

Septunbor_10_Grld_LlSA
Local Moran
as to -2.5 (1)
~25 to .1 .5 (0)
1M4. 5 to -0.5 (4)
1"“ --0. 5 1o 0. 5 (51)
-0. 5 to 1 .5 (7)

Fig. 30

65

October

     

3 --0.5.1o05(72)
1 -o.5101. 5(3)
1" -1.51025(1)

Fig. 31

66

3.2.2 Kulldorff

Kulldorff’s scan method calculates three separate clusters ranked by likelihood for
each time frame. “Likelihood” in this case refers to the chance of something actually
being a cluster. The Kulldorff model identifies the three clusters based on the value of the
test statistic, and whether the clusters overlap. The clusters are labeled as the first,
second, and third most likely locations where a cluster may be present. By rule the
second most likely cluster will not overlap the first, and the third will not overlap the
second or the first. In the series of maps (Figs. 32-46), the first most likely cluster are
represented in purple, the second most likely are shown in green, and the third most
likely cluster are shown in yellow. The areas in blue showed no signs of clustering. When
looking at the All Records map (Fig. 32) it showed that purple cluster for the dataset were
in the center of the study area centered over the Binningham/ Royal Oak/ Southfield
areas. The green cluster was over the Grosse Pointe area, and the yellow cluster appeared
just north of the purple cluster over Rochester. The rest of the plots showed results
separated by month and the results widely varied across the study area. For the months of
April and May the records were combined, due to insufficient data in April. The map for
April and May (Fig. 33) showed the purple cluster to the north of the study area near
Pontiac, with the green cluster located south near Lincoln Park and Allen Park. The
yellow cluster was over Sterling Heights and Warren townships. During the month of
June (Fig. 34) the clusters get much more focused. The purple cluster for June was near
the Westland area, and the green cluster was just to the north over Livonia and
Farmington Hills Township. The yellow cluster was a cell containing a single point

separated from the rest of the points in the time period. Disregarding the one outlying

67

record, the map for the first half of June (Fig. 35) showed a pattern similar to the results
for the whole month of June. The clusters focused around Westland, Farmington Hills,
and Highland Park. The second half of June (Fig. 36) presented a large area on the west
side of the study area as the purple cluster, with the single outlying point as the green
cluster, and a small cluster around the Grosse Pointes, shown as yellow. For July (Fig.
37), the dead bird cases began to increase in density. The purple cluster for July was a
large area covering much of the northeast part of the study area from Southfield to Shelby
Township. The green cluster was located near the same area as the green cluster for the
month of June (Livonia and Farmington Hills), and the yellow cluster covers Redford and
Dearbom. The data records from the first part of July (Fig. 38) showed the purple cluster
located over Independence Township in the northwest comer of the study area. The green
cluster was over Taylor Township, and the yellow cluster was a large area reaching from
St. Clair to Royal Oak and as far north as Shelby Township. For the middle of July (Fig.
37), the clusters continued to be located in similar areas as previously modeled time
frames, showing clusters over Sterling Heights, Rochester, and Livonia. Toward the end
of July (Fig. 40) the pattern began to reflect similarities to the All Records map (Fig. 32),
showing a large cluster over the center of the study area with smaller clusters near St.
Clair Shores. Throughout August the pattern of clustering more closely resembles large
singular cluster shown in the All Records map. All maps for August (Fig. 41-44)
maintain one strong, centralized cluster with a smaller, less significant cluster over the
Grosse Pointe communities. During September (Fig. 45) the point pattern was less dense
and caused a large dominating cluster over the northwest region of the study area.

However, there are still signs of clustering over the Grosse Pointe communities. For the

68

October records (Fig. 46) there are signs of strong clustering over the northwest region of

the study area, and along the coastline north of Harrison Township.

All Records April and May

   

Fig. 32 Fig. 33

June June 1-15

   

Fig. 34 Fig. 35

69

June 16-30 July

 

Fig. 36 Fig. 37

July 1-10 July 11-20

   

Fig. 38 Fig. 39

70

July 21—31 August

   

Fig. 40 Fig. 41

August 1-10 August 11-20

   

Fig. 42 Fig. 43

71

August 21-31 September

   

Fig. 44 Fig. 45

October

 

Fig. 46

3.2.3 GAM

The outputs from the GAM model required setting the confidence interval extremely
high to begin to focus the areas of greatest cluster intensity. The models were all initially
completed with a 99% confidence interval; however this caused large areas to be
identified as significant. Therefore, higher confidence intervals were used to narrow the

clusters to more focused areas. Due to the number and locational variability of the data

72

records in each time period and the underlying population in these locations, different
confidence intervals were required to achieve the greatest focus of the cluster detection.
The All Records file (Figs. 46-49) for this model showed a very similar pattern to the
previous models. It presented a large central cluster over the Birmingham/ Royal Oak/
Southfield areas, with a smaller and separate cluster over the Grosse Pointes. The
decision to combine the April and May records for this model came from the results of
the previous models. The combination of these records from early in the year showed two
small clusters. The larger of the two clusters was centered over Pontiac Township and the
smaller cluster was located over the Grosse Pointe communities (Fig. 50). The maps for
June initially showed one large cluster over the southern part of the study area. However
after increasing the confidence interval, most of the intensity was over the Westland area,
with a thin band to the north reaching into Livonia (Figs. 51-53). For the month of July,
the model identified a large cluster stretching from Birmingham to St. Clair Shores, and
another large cluster reaching from Livonia to Westland (Figs. 54-63). The results for
August show similar patterns to the All Records maps. Two distinct clusters for the
month of August were identified. The larger more intense cluster centralized over the
Birmingham area, and the second cluster covered the Grosse Pointes (Figs. 64-75). For
September clustering was identified over the north half of the study area. Initially the
clustering was widespread; however after increasing the confidence interval the clusters
could be focused to two locations near Independence and Washington townships (Figs.
76-78). With few data points in October, the clusters moved even further into the rural
areas of the study area. The main cluster was located over Highland Township (Fig 79-

81); this is consistent with the results from the LISA and the Kulldorff models.

73

Potential GAM Clusters for All Records

99% Confidence Interval 99.999% Confidence Interval

 

Fig. 47 Fig. 48

99.99999999% Confidence Interval

 

Fig. 49

74

Potential GAM Clusters for April and May

99.9% Confidence Interval

 

Fig. 50

75

Potential GAM Clusters for June

99% Confidence Interval 99.999% Confidence Interval

   

Fig. 51 Fig. 52

99.99999% Confidence Interval

 

Fig. 53

76

Potential GAM Clusters for July

99% Confidence Interval 99.999% Confidence Interval

 

Fig. 54 Fig. 55

99.99999999% Confidence Interval

 

Fig. 56

77

Potential GAM Clusters for July 1-10

99% Confidence Interval 99.9% Confidence Interval

Fig. 57 Fig. 58
Potential GAM Clusters for July 11-20

99% Confidence Interval 99.999% Confidence Interval

Fig. 59 Fig. 60

78

Potential GAM Clusters for July 21-31

99% Confidence Interval 99.999% Confidence Interval

   

Fig. 61 Fig. 62

99.99999999% Confidence Interval

 

Fig. 63

79

Potential GAM Clusters for August

99% Confidence Interval 99.999% Confidence Interval

   

Fig. 64 Fig. 65

99.99999999% Confidence Interval

 

Fig. 66

80

Potential GAM Clusters for August 1-10

99% Confidence Interval 99.999% Confidence Interval

   

Fig. 67 Fig. 68

99.99999999% Confidence Interval

 

Fig. 69

81

Potential GAM Clusters for August 11-20

99% Confidence Interval 99.999% Confidence Interval

   

Fig. 70 Fig. 71

99.99999999% Confidence Interval

 

Fig. 72

82

Potential GAM Clusters for August 21-31

99% Confidence Interval 99.999% Confidence Interval

   

Fig. 73 Fig. 74

99.99999999% Confidence Interval

I

 

Fig. 75

83

Potential GAM Clusters for September

99% Confidence Interval 99.999% Confidence Interval

   

Fig. 76 Fig. 77

99.99999% Confidence Interval

 

Fig. 78

84

Potential GAM Clusters for October

99% Confidence Interval 99.9% Confidence Interval

 

Fig. 79 Fig. 80

99.99% Confidence Interval

 

Fig. 81

85

4 Discussion and Conclusions

4.1 Overview

West Nile Virus is a disease that affects many species of animals; however the
highest case fatality rates are in the avian population. Since the virus was first identified
in the western hemisphere in 1999, all 48 contiguous states have reported both human
and avian cases of the disease. In 2001, West Nile Virus was first reported in Michigan.
In clinical human cases, symptoms exhibited are fever, weakness, nausea, headache, and
changes in mental state, with advanced cases developing meningitis, encephalitis, flaccid
paralysis, or coma, and occasionally death. The most common host for the disease is the
American Crow (Corvus branchyrhynchus). The Michigan Department of Community
Health (MDCH) collected the spatial locations of over 8000 dead birds during 2002.
Initially the birds were tested for WNV; however once the disease was identified in a
county all birds reported from that county were assumed to be WNV positive. With the
disease becoming endemic, efforts toward minimizing the human impact have increased,
with applications of insecticides to eliminate the mosquito vector the most widely used
method. Effective insecticide application requires the identification of spatial and
temporal hotspots for the optional insecticide dispersal locations. The ability to accurately
locate hotspots remains difficult because the data were voluntarily reported. This
produced a dataset with a direct correlation between the numbers and locations of the
dead birds and population density. This research used a subset of the data that were

collected in 2002 in the Detroit Metropolitan area.

86

The dead bird data were collected through an information hotline which the public
would call and leave their home address and the type of bird that was found. Due to the
large number of dead birds reported, testing on each bird could not be completed, which
leaves the possibility that some reported birds may have died of factors other than WNV.
However with over 8000 reports statewide, and the mass deaths in the bird population,
any errors in the data attributed to reported bird deaths of other causes are thought to be
negligible. The spatial locations were identified for the dead bird records in the database
using address matching via the Michigan Geographic Framework from the Michigan
Center for Geographic Information (CGI). This data layer has a reported spatial accuracy
of +/- 20 feet. The attribute used identifies a range of addresses found on each segment
of street; for example if the segment range is 1000-2000, and the reported address is
1500, then the point will be placed at the mid-point on the segment. This decreases
spatial accuracy in the points by not taking parcel size and density into account; for
example rural points could possibly be off by a mile or more. Road naming conventions
are also an issue. Errors in the spelling of road names either from the bird reports or
within the road framework create the possibility of placing points on the wrong street,
county, or not placing them at all. The process of attributing spatial data to a GIS model
propagates any error already in the data with the error in the associated data layers.
Ideally, spatial location data would be collected using a Global Positioning System to
accurately place these locations using real world coordinates without projecting,
transforming, or matching the locations before analysis.

In this study, better correlations were obtained when the data were aggregated to a

larger cell size. However, one should be aware that this may be related to problems

87

related to the modifiable areal unit problem (MAUP;(Qi and Wu 1996)). When working
with spatial data, if one does not use the same size of spatial unit in two different
analyses, either the window size, or polygons of the same size, results may not be directly
comparable. Because of the MAUP, generally as the window size increases, correlations
between two variables are expected to improve. In this study, larger cell size produced
stronger correlations as expected to the MAUP, and when the finer grid cell size was used
weaker correlations were produced as was expected relative to the MAUP. It would be
ideal to be able to determine the magnitude of the MAUP effect in this study. Although a
number of researchers have suggested ways to analyze the MAUP effect, the process
generally employs stochastic simulation to generate a number of different window
sizes/aggregation schemes to evaluate the range of correlations (Openshaw 1984; Jelinski
and Wu 1996), these researchers also note that the magnitude of MAUP is unique to the
phenomenon being studied and can not be removed. Therefore, conclusions of any

studies that employ areal sample units must be constrained to the spatial units employed

(Plante, Lowell et a1. 2004)

4.2 Discussion of Results

4.2.1 Global Tests

Three separate models were employed to examine global spatial trends. Global trends
examine patterns over an entire study area. Each model was run with the ClusterSeerTM
software program using the dead bird data. These models were designed to show if the
data presented an overall trend. These methods do not identify the locations of clusters,

but rather only whether spatial structure is present.

88

Ripley’s K model reported results with a graph (Figs. 10-16), which showed an
envelope of Monte Carlo simulations representing spatial randomness, and the
relationship of the envelope to the empirically calculated statistic. The Ripley’s K model
determines if structure is present in the point pattern, and approximates an interpoint
distance. When the line representing the model is above the simulation envelope
structuring is present, and when the model is below the simulation envelope the result is
interpreted as regularity. The results can be interpreted across a range of scales. For the
purposes of this model, the data were first modeled in its entirety then divided by month.
There was a direct relationship between the deviation from randomness and the number
of bird points. As the number of birds in each month increased, the model showed greater
amounts of structure. The results for the Ripley’s K model showed spatial structure,
however from the graphs one cannot interpret the pattern as being clustered. Because
Lhat is above the simulation envelope across all scales the results are interpreted as a first
order trend and invalidate the model. Ripley’s K is a good indicator of spatial structure in
point level data, but the model does not specify whether there are many clusters, or one
large cluster.

Moran’s I was modeled at two different grid sizes, 100 by 100 and 10 by 10. The data
points were aggregated to the grid cells as numeric counts. The results from the 100 by
100 cell grid models were significantly lower than the 10 by 10 cell models. By using
more grid cells the data were dispersed, and each cell contained few, but similar, dead
bird counts. Thus Moran’s I showed no signs of spatial structure. By increasing the grid
cell size, from 100 by 100 to 10 by 10, larger groups of points could be modeled for

spatial structure. The larger grid cell models showed the same patterns throughout the

89

transmission season with an overall increase in Moran’s I value. The increased cell size
identified positive spatial structure during July and August where the dead bird counts
were the highest. Both the Moran’s I and Ripley’s K models work well for identifying
possible spatial patterns that may contain clusters. However these models only take into
account the relationship between the points and not the cause or spatial distribution of the
patterns.

To attempt to identify a cluster pattern with the underlying population information,
Oden’s I(pop) model was used. Oden’s I(pop) is designed to determine if the Moran’s I
patterns are still present when population is incorporated. Oden’s I(pop) was of specific
interest due to the population-based collection method. Months with large bird counts
were found to be significant; however the I(pop) statistic was extremely low for all
months. The low values of this statistic are attributed to the extremely large human
population count used in this model. Because of the low values, the I(pop) statistic may
be precisely interpretable. However assumptions can be made on the relationship between
the values. Since the population stays constant through the models and the dead bird
count changes, the increase in I(pop) values can be interpreted as structure.

All of the global models presented results showing the dead bird dataset had signs of
spatial structure. Cluster locations cannot be identified with global models. Global
models also do not describe the size or if there is more than one cluster present in the
data. However, the modeling process proved helpful. Ripley’s K was run first to
determine any significant trending in the dataset. Then Moran’s I identified that global
structure was present. Finally, Oden’s I(pop) was modeled to determine positive spatial

structure would be found significant by accounting for the human population. With these

90

initial models confirming that there was possible clustering in the dataset, the focus
turned to identifying the locations of the clusters. For this information, local cluster

models were employed.

4.2.2 Local Models

Three separate models were used to examine local clustering. Anselin’s Local
Indicator of Spatial Autocorrelation and the Kulldorff’s Spatial Scan models were run
using the ClusterSeerTM software program. The geographic analysis machine was
programmed using the ‘R’ statistical program. These models were designed to identify if
any local clusters were present, and to locate areas with a high likelihood of having
hotspots.

The local Moran’s model examined local clustering in group-level data, and produced
results that indicated clustering in very similar parts of the study area over time. From
late June through September (Figs. 21-30), cluster patterns were most intense over
Birmingham, Grosse Pointe and Dearborn Heights communities. The overall results (Fig.
17) for this model show the highest degree of clustering in the Birmingham/Southfield
and Grosse Pointe bedroom communities. These areas are some of the most affluent in
the study area. The communities with higher incomes and improved access to community
information, as well as homeowners working in there own yards could attribute to greater
reporting of dead birds from a more informed population. The advertising methods used
to inform the public of this reporting program are unknown; however, they would also

have a direct effect on the patterns seen in these data. People who were not informed of

91

the program would not have reported dead birds. This may be why there are no clusters
seen within the Detroit City limits, and lower income communities.

Kulldorff’s Spatial Scan modeled the dataset for adjacent regions (using the queen’s
pattern) with strong autocorrelation, to indicate clustering. Kulldorff uses an increasing
circular window to identify areas of clustering. The window has an upper extent of 50%
of the size of the study area, creating the possibility of the cluster potentially being nearly
as large as the study area. Kulldorff locates and ranks the three most likely clusters. The
clusters for this model appeared to be much larger than the Local Moran test; however
they were located in very similar locations. The larger clusters hold very similar shapes
over the underlying grid. The circular window that this model uses can be seen in areas
with large bird counts; therefore irregular clusters would be hard to identify. This circular
pattern shows late into the transmission season covering large, more rural, parts of the
study area. Because of the low bird counts and low populations in these areas, the shift of
these large clusters to the more rural areas makes identifying fine scale local hotspots
difficult. It almost appears as though the model attempts to include all possible points in
the three most likely clusters. The grid cells in the outlying areas contain such few points
and have similar population counts, that the model measures similar rates of people to
birds. It then identifies these large areas as clusters, even though they may be the only
dead bird points for that time period. Overall this model showed clustering in similar
locations to the local Moran’s I model with larger clusters.

The Geographic Analysis Machine allowed for local analysis on individual records
and the inclusion of the population data. This was the only model run on the dataset to

include population data and examine the dead bird locations as individual events. Oden’s

92

I(pop), LISA, and Kulldorff aggregated the population data to the grid cells. GAM was
first parameterized using a 99% confidence interval. This identified large areas as
significant. By further increasing the confidence interval to 99.99999999% (Fig. 49),
smaller areas were then identified. This focused the model on those areas with the highest
degree of clustering. Although the clusters were not small enough to pinpoint something
as small as a neighborhood, it did highlight community-sized hotspots such as Grosse
Pointe. This test demonstrated that hotspots could be identified to the community scale of
accuracy. The hotspots reoccurred in the same areas found in both the local Moran’s I
and Kulldorff models, confirming these locations of having the greatest dead bird to
population ratio in the study area. Although Kulldorff and GAM identified similar cluster
locations, the size and shape of the clusters varied. Kulldorff seemed to have a tendency
to attempt to include all data points in three clusters; the GAM model ignored these
outliers. The Kulldorff and GAM models used similar methods to scan the dataset
(circular window over grid intersections), the difference between the models occurred in
how the two models reported results. Kulldorff examined adjacent regions for
similarities; if the regions were similar then a cluster may be present. The three areas with
the most similarities were ranked as clusters. The reported cluster’s shape was an artifact
of the grid used; using a different grid cell size, or different shape polygons may have
provided very different results. The GAM compiled circular regions of various sizes that
had higher than expected dead bird-to-person ratios, these results were then smoothed for
representation on the map. There was no limit to the number or the size of clusters that

GAM produced. However, the shape of the clusters tended to have “half-moon” sections

93

removed as the confidence interval increases (Fig. 51-53). This pattern was due to the
circular window no longer finding the cluster significant.

The methods used in this research were designed to test the utility of datasets that are
reported by private citizens. By allowing the public to report information, many data
problems that already exist in well thought out data collection efforts are exacerbated.
Errors in data collection and data entry are always present, however when the data is
collected by phone call and web-based form, the quality control is highly speculative.
The data collector not only has to get the information provided correct, they also have to
trust that the source has credible information. The ability to monitor and maintain an
accurate database becomes suspect, as well as the accuracy of the information and spatial
locations provided. This combined with the dataset being biased to areas where people
lived and were informed of the program created a difficult data problem. In an attempt to
examine how these issues affected local clustering in spatial datasets two standardized
tests were run from a commercially available software program and one model was
programmed using a statistical package. Despite the challenges presented in this dataset,
similar results were found using each of the models. All local models identified clusters
in similar areas. However, these areas also support large human populations, and high
numbers of reported dead birds. The local models run on the complete datasets showed
nearly the same overall pattern. One large cluster was present in all three of the local
models for the complete dataset, showing that overall there is a single dominating cluster
for this dataset. Only when these data are separated into small units of time is local

clustering visible. The similarity of the cluster patterns show that the models did identify

94

hotspots within the dataset and further testing is needed to determine the dynamics of

these patterns.

4.3 Future Research

Further research on this topic could follow two different tracks. First from the
clustering perspective, alternative models and methods to identify spatial and temporal
clustering in the dead bird data would be useful, such as Besag & Newell’s method or
Grimson’s method. The second would examine the collection methods, environmental,
and biological aspects related to the spread of WNV.

Advancing the cluster analyses of this research would require additional years of data
collection. One additional year of data would allow for analyses on the reoccurrence of
the spatial patterns found in this study, and provide the ability to examine the temporal
clustering of the dead birds. Another year of data would allow for comparisons between
seasons to determine any relationships in the overall peak and smaller peaks within the
transmission season. One year of additional data would be the minimum required to
examine if these patterns are consistent. Many more years of data would allow for studies
on the movement of the disease, examining if the clusters tend to shift or change in size.
The combination of additional data would allow for the patterns identified in each season
to be jointly analyzed by randomly removing 20% (or the Case Fatality Rate) of the data
points and examining if the patterns still show consistent clustering. The development of
a control dataset with separate clusters containing disease rates similar to that of the dead
bird dataset and testing the model against other statistical methods would allow for

evaluation of the models used in this research.

95

Because the results for each model could not be directly compared from the statistical
results, it was difficult to make any overall conclusions in the performance of each
model. However one can compare the geographical results of the models by calculating
the areal extents of each models identified clusters and overlaying the results. From the
extent to which the clusters from each model overlay, calculations could be made to
quantify the prevalence of the identified clusters between models. This research only
employed a few of the many cluster detecting models and only one Individual Level
model; additional models may act to support or discredit these findings and should be
attempted.

There are many facets to disease cluster analysis that go beyond the information
found at the case-location level. Aspects of the environment such as land cover and land
use need to be looked at. Mosquito breeding micro-environments need to be identified to
determine points where the vector is initially located. Also, the availability of birds and
humans from these locations should be known. Examining the breeding cycle of the
vector would help in identifying possible blooms in mosquito activity. In addition
knowing the flying range of the vector would identify areas where humans and birds
would be at risk. This research did not examine the roosting patterns of the bird
population; this information would identify the range of the host, and combined with the
mosquito information would identify the host population at risk. Research into the case
fatality rate of WNV on the bird population, as well as the effects of the virus on the
movement, and the length of time before mortality would also assist in the temporal
study. One of the large drawbacks to the integrity of the dead bird data was that there was

not 100% testing of the reported birds; complete testing of the birds would remove any

96

 

false positive errors in the sample. Also obtaining a GPS (Global Positioning System)
location of the dead bird would remove the location error associated with address
matching and the error in the base GIS layers. Examining the methods used to inform the
public of the collection program could be used to see if the clusters were in areas where
there was more advertising or greater access to available resources for reporting.

There are many ways this problem could be further examined. However, inaccuracies
in the spatial location of the data points needs to be known when using this or similar
data. By obtaining additional information about the collection program, the vector and the
host, and advancing the cluster detection methods, the spatial and temporal locations of

WNV hotspots can be more accurately identified and contained.

97

Appendix 1

Moran’s I: 100 X 100 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 100 All Records April May April-May
Results Moran's I 0.322736 -0.0003 52 0.001741 0.001238
E[I] -0.000166 000166 -0.000166 -0.000166
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.000043 0.000043 0.000043 0.000043
Assumptions
z-Score 49.40718 -0.028457 0.291864 0.214839
Significance 0 0.977297 0.77039 0.829893
Random Variance 0.000042 0.000021 0.000037 0.000038
Assumptions
z-score 49.555182 -0.040227 0.312904 0.229132
Significance 0 0.967912 0.754354 0.818767
50 46762 46762 46762 46762
51 93524 93524 93524 93524
52 1472408 1472408 1472408 1472408
b2 38.869679 3007.500332 784.596166 729.88598
Monte Carlo Test Statistic 0.322736 -0.000352 0.001741 0.001238
Simulations 100 100 100 100
Regions ID 6019 6019 6019 6019
Avg disease Freq 0.414853 0.000332281 0.0053165 0.00564878
P-Value 0.0198 0 0.41584 0.00980229
Grid 100 June June 1-15 June 16-30 July
Results Moran's 1 0.001531 0.001257 -0.004419 0.140594
E[l] -0.000|66 -0.000166 -0.000166 0.000166
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.000043 0.000043 0.000043 0.000043
Assumptions
z-Score 0.259644 0.217692 -0.650694 21 .53769
Significance 0.795138 0.827669 0.515244 0
Random Variance 0.000014 0.000008 0.000041 0.000042
Assumptions
z-score 0.459967 0.518998 -0.663835 21 .793 l 14
Significance 0.64554 0.603762 0.506796 0
50 46762 46762 46762 46762
51 93524 93524 93524 93524
s2 1472408 1472408 1472408 1472408
b2 4100.820] 4959.0931 15 238.764171 143.150902
Monte Carlo Test Statistic 0.001531 0.001257 -0.004419 0.140594
Simulations 100 100 100 100
Regions ID 6019 6019 6019 6019
Avg disease Freq 0.0098023 0.00564878 0.00415351 0.0657917
P-Value 0.21782 0.13861 0 0.0198

 

98

 

Moran’s I: 100 X 100 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 100 July l-10 July “-20 July 21-30 August
Results Moran's I 0.01857 0.04051 1 0.1 17664 0.298348
E[l] -0.000166 -0.000|66 0000166 0000166
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.000043 0.000043 0.000043 0.000043
AssumLtions
z-Score 2.86688 6.223976 18.029254 45.67561 1
Significance 0.004145 0 0 0
Random Variance 0.000039 0.000042 0.000041 0.000043
Assumptions
z-score 2.993201 6.301259 18.437971 45.789031
Significance 0.002761 0 0 0
$0 46762 46762 46762 46762
51 93524 93524 93524 93524
52 1472408 I 472408 1472408 1472408
b2 499.920214 149.620081 266.678957 32.75664
Monte Carlo Test Statistic 0.01857 0.04051 1 0.117664 0.298348
Simulations 100 100 100 l 00
Regions ID 6019 6019 6019 6019
Avg disease Freq 0.0033228] 0.0179432 0.0445257 0.303373
P-Value 0.1 1881 0.0198 0.0198 0.0198
Grid 100 Aug 1-10 Aug 1 l-20 Aug 21-31 September
Results Moran's 1 0.239675 0.135355 0.128081 0.030819
E[l] -0.000166 -0.000166 -0.000166 -0.000166
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.000043 0.000043 0.000043 0.000043
Assumptions
z-Score 36.698072 20.736123 19.623081 4.741091
Significance 0 0 0 0.000002
Random Variance 0.000042 0.000042 0.000042 0.000039
Assumptions
z-score 36.932174 20.84748 19.706321 4.973168
Significance 0 0 0 0.000001
50 46762 46762 46762 46762
51 93524 93524 93524 93524
52 1472408 1472408 1472408 1472408
b2 79.001848 67.077472 53.700051 551.217315
Monte Carlo Test Statistic 0.239675 0.135355 0.128081 0.030819
Simulations 100 100 100 100
Regions ID 6019 6019 6019 6019
Avg disease Freq 0.145373 0.0765908 0.0814089 0.0275793
P-Value 0.0198 0.0198 0.0198 0.0198

 

 

 

 

 

 

 

 

99

 

Moran’s I: 100 X 100 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 100 October
Results Moran's 1 -0.002824
E[I] -0.000166
Alpha Level 0.05
Normal Variance 0.000043
Assumptions
z-Score 0406642
Significance 0.684271
Random Variance 0.00004
Assumptions
z-score -0.4 l 9803
Significance 0.674629
80 46762
S] 93 524
52 1472408
b2 374.190165
Monte Carlo Test Statistic -0.002824
Simulations l 00
Regions ID 6019
Avg disease Freq 0.00265825
P-Value 0

 

 

 

 

 

100

 

Moran’s I: 10 X 10 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 10 All Records April May April-May
Results Moran's I 0.638524 -0.038401 0.277096 0.320102
E[I] -0.012821 -0.0l2821 -0.012821 -0.012821
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.003544 0.003544 0.003544 0.003544
Assumtions
z-Score 10.941305 -0.429699 4.870024 5.592438
Significance 0 0.667415 0.000001 0
Random Variance 0.003436 0.001915 0.003309 0.003331
Assumptions
z-score l 1.1 l 1575 -0.584623 5.039594 5.768703
Significance 0 0.558801 0 0
50 510 510 510 510
51 1020 I 020 1020 1020
$2 14272 14272 14272 14272
b2 5.213742 37.525974 7.904171 7.45371
Monte Carlo Test Statistic 0.638524 -0.038401 0.277096 0.320102
Simulations 100 100 100 100
Regions ID 79 79 79 79
Avg disease Freq 31.6076 0.0253165 0.405063 0.43038
P-Value 0.0198 0 0.01198 0.0198
Grid 10 June June 1-15 June 16-30 July
Results Moran's I 0.13602 0.0461 54 0.225586 0.527694
EU] -0.0 l 2821 -0.01 282 I -0.012821 -0.01 2821
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.003544 0.003544 0.003544 0.003544
AssumLtions
z-Score 2.500229 0.990652 4.004762 9.079569
Significance 0.01241 1 0.321856 0.000062 0
Random Variance 0.001272 0.000831 0.003261 0.003334
Assumptions
z-score 4.173752 2.045626 4.174575 9.360875
Significance 0.00003 0.040793 0.00003 0
50 510 510 510 510
51 1020 1020 1020 1020
$2 14272 14272 14272 14272
b2 51.176094 60.531952 8.92303 7.38014
Monte Carlo Test Statistic 0.13602 0.046154 0.225586 0.527694
Simulations 100 100 100 100
Regions ID 79 79 79 79
Avg disease Freq 0.746835 0.43038 0.316456 5.01266
P-Value 0.0198 0.1 1881 0.0198 0.0198

 

101

 

 

Moran’s I: 10 X 10 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 10 July l-IO July ”-20 July 21-30 August
Results Moran's I 0.031894 0.503241 0.50607 0.616699
E[I] -0.01282l -0.0|2821 -0.0|282| -0.012821
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.003544 0.003544 0.003544 0.003544
Assumptions
z-Score 0.751 I 16 8.668813 8.7 I 6343 10.574689
Significance 0.452583 0 0 0
Random Variance 0.002959 0.003266 0.003306 0.00341 1
Assumptions
z-score 0.822005 9.030203 9.024867 10.77906
Significance 0.41 1074 0 0 0
$0 510 510 510 510
Si 1020 1020 1020 1020
$2 14272 14272 14272 14272
b2 15.345473 8.828025 7.982491 5.751674
Monte Carlo Test Statistic 0.031894 0.503241 0.50607 0.616699
Simulations 100 100 100 100
Regions ID 79 79 79 79
Avg disease Freq 0.253165 1.36709 3.39241 23.] I39
P-Value 0.33663 0.0198 0.0198 0.0198
Grid 10 Aug MD Aug 11-20 Aug 21-31 September
Results Moran's 1 0.640958 0.456352 0.38235 0.148966
E[I] -0.012821 -0.012821 -0.012821 -0.012821
Alpha Level 0.05 0.05 0.05 0.05
Normal Variance 0.003544 0.003544 0.003544 0.003544
Assumptions
z~Score 10.982188 7.881 169 6.63 8089 2.717691
Significance 0 0 0 0.006574
Random Variance 0.003421 0.003181 0.003374 0.003254
Assumptions
z-score 1 1.177209 8.318739 6.803161 2.836359
Significance 0 0 0 0.004563
30 510 510 510 510
$1 I 020 1020 1020 1020
$2 14272 14272 14272 14272
b2 5.528253 10.633845 6.532733 9.090461
Monte Carlo Test Statistic 0.640958 0.456352 0.38235 0.148966
Simulations 100 100 100 100
Regions ID 79 79 79 79
Avg disease Freq 1 1.0759 5.83544 6.20253 2.10127
P-Value 0.0198 0.0198 0.0198 0.0198

 

102

 

Moran’s I: 10 X 10 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 10 October
Results Moran's I 0.039855
E[l] -0.01282|
Alpha Level 0.05
Normal Variance 0.003544
Assumptions
z-Score 0.884852
Significance 0.376236
Random Variance 0.003339
Assumptions
z-score 0.91 1544
Significance 0.362009
30 510
Si 1020
52 14272
b2 7.267707
Monte Carlo Test Statistic 0.039855
Simulations 100
Regions ID 79
Avg disease Freq 0.202532
P-Value 0.39604

 

 

 

 

103

Appendix 2

Oden’s I(pop): 10 X 10 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 10 All Records April May April-May
Results Ipop 8805-05 -7. 1 l E-07 6.05E-07 6.56E-07
Ipop' 0. 142425 I .43 784 0.0764277 0.077993
E[I] -2.47E-07 -2.47E-07 -2.47E-07 -2.47E-07
Alpha Level 0.05 0.05 0.05 0.05
% within 48.302394 147.504496 89.833083 87.297819
% among 51.697606 47.504496 10.166917 12.702181
Approximation Variance 1.18E-12 1.18E-12 1.18E-12 1.18E-12
z-score 81.3225 -0.427705 0.78571 1 0.832702
significance 0 0.668866 0.432037 0.405013
Randomization Variance 1.1513-12 5.79E-13 1.12E-12 1.12E-12
z-score 82.2297 -0.609419 0.806939 0.854395
significance 0 0.542247 0.419702 0.392886
Monte Carlo Test Statistic 0.142425 -1 .43784 0.0764277 0.077993
Simulations 100 100 100 100
Upper Tail 0.0099 0.9703 0.18812 0.18812
Grid 10 June June 1-15 June 16-30 July
Results Ipop 7.4OE-06 8.38E-06 -2.98E—07 2.60E-05
Ipop' 0.50731 1 0.9979 I 7 00482642 0.265002
E[I] -2.47E-07 -2.47E-07 -2.47E-07 -2.47E-07
Alpha Level 0.05 0.05 0.05 0.05
% within 90.900942 105.537876 94.374259 66.351 1 l
% among 9.099058 -5.537876 5.625741 33.64889
Approximation Variance 1.18E-12 1.18E-12 1.18E-12 1.18E—12
z-score 7.05319 7.95783 -0.0471 1 15 24.1575
significance 0 0 0.962424 0
Randomization Variance 1.13E-12 1.125-12 l.IIE-12 1.155-12
z-score 7.19124 8.16514 00486028 24.4528
significance 0 0 0.961236 0
Monte Carlo Test Statistic 0.507311 0.997017 00482642 0.265002
Simulations 100 100 100 100
Upper Tail 0.0099 0.0099 0.44554 0.0099

 

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Oden’s I(pop): 10 X 10 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 10 July 1-10 July 1 1-20 July 21-30 August
Results Ipop 4.81 E-07 4.46E-06 2.35E-05 8.33 E-05
Ipop' 0.0971934 0.166938 0.354976 0.184354
E[l] -2.47E-07 -2.47E-07 -2.47E-07 -2.47E-07
Alpha Level 0.05 0.05 0.05 0.05
% within 137.130233 73.822841 63.282] 1 45.809247
% among -37.l30233 26.177159 36.71789 54.190753
Approximation Variance 1.18E-12 1.185-12 1.18E-12 1.18E-12
z-score 0.671283 4.3392] 21.921 1 76.9889
significance 0.50204 0.000014 0 0
Randomization Variance 1.09E-12 1.14E-12 1.15E-12 1.155-12
z-score 0.696141 4.40705 22.2024 77.8534
significance 0.48634 0.00001 0 0
Monte Carlo Test Statistic 0.0971934 0.166938 0.354976 0.184354
Simulations 100 100 100 100
Upper Tail 0.16832 0.0099 0.0099 0.0099
Grid 10 Aug I-IO Aug ”-20 Aug 21-31 September
Results Ipop 6.72E-05 2.58E-05 4.06E-05 2.01E-05
Ipop' 0.310556 0.226085 0.334904 0.490066
E[I] -2.47E-07 -2.47E-07 -2.47E-07 -2.47E-07
Alpha Level 0.05 0.05 0.05 0.05
% within 45.532464 55.756862 55.326296 56.988446
% among 54.467536 44.243138 44.673704 43.01 1554
Approximation Variance 1.18E-12 1.1813-12 1.18E-12 1.18E-12
z-score 62.1914 23.9943 37.648 18.7783
significance 0 0 0 0
Randomization Variance 1.15E—12 1.155-12 1.15E-12 1.14E-12
z-score 62.9083 24.2833 38.099 19.041
significance 0 0 0 0
Monte Carlo Test Statistic 0.310556 0.226085 0.334904 0.490066
Simulations 100 100 100 100
Upper Tail 0.0099 0.0099 0.0099 0.0099

 

105

 

Oden’s I(pop): 10 X 10 Grid Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grid 10 October
Results Ipop 8.69E-06
Ipop' 2.19463
E[I] -2.47E-07
Alpha Level 0.05
% within 65.135795
% among 34.864205
Approximation Variance l . 18 E- I 2
z-score 8.235
significance 0
Randomization Variance l .08 E- I 2
z-score 8.59629
significance 0
Monte Carlo Test Statistic 2.19463
Simulations l 00
Upper Tail 0.0099

 

106

 

Works Cited

Allen, T. R. and B. Shellito (2004). "Spatial Interpolation and Prediction of Mosquito
Vectors for Surveillance of West Nile Virus." GeMto lntemational 19(2).

Anderson, J. F., C. R. Vossbrinck, et al. (2001). "A Phylogenetic Approach to Following

West Nile Virus in Connecticut." Proceedings of the National Academy of Sciences of
the United States of America 98(23): 12885-12889.

Anselin, L. (1995). "Local indicators of spatial association-LISA." Geogpaphical
Analysis 27: 93-115.

Bailey, T. C. and A. C. Gatrell (1995). Integctive Spatial Data Analysis, Longman.
Caliper (2006). TransCAD. Newton, MA.
Chambers, J. and e. al (2006). The S System, Bell Laboratories.

Cliff, A. D. and J. D. Ord (1981). Spatial Processes. Models and Applications, Pion,
London.

Craven, R. B. and J. T. Roehrig (2001). "West Nile Virus." Journpl of the America_n
Medical Associgtion 286(6): 651-653.

Dodd, R. Y. (2003). "Emerging Infections, Transfusion Safety, and Epidemiology." m
New England Joum_al of Medicine 349(13): 1205.

Dohm, D. J ., M. L. O'Guinn, et al. (2002). "Effect of environmental Temperature on the
Ability of Culex pipiens (Diptera: Culicidae) to Transmit West Nile Virus." Journal of
Medical Entomology 39(1): 221 -225.

Eidson, M., L. Kramer, et al. (2001). "Dead bird surveillance as an early warning system
for West Nile virus." Emerging Infectious Diseeiep 7: 631-635.

Enserink, M. (2000). "The Enigma of West Nile Virus." Science 290: 1482-1484.

 

Fortin, M.-J. (1999). Spatial statistics in landscape ecology. Landscape Ecological
Airlvsisz Issues grid Applications. New York, Springer: 253-279.

Gatrell, A. C., T. C. Bailey, et al. (1996). "Spatial Point Pattern Analysis and Its
Application in Geographical Epidemiology." Transaction_s of the In_stitute of British
Geoggphers 21(1): 256-274.

Huhn, G. D., J. J. Sejvar, et al. (2003). "West Nile Virus in the United States: An Update
on an Emerging Infectious Disease." American Familv thsicifiap 68(4): 653-660.

107

 

Jelinski, D. and J. Wu (1996). "The modifiable areal unit problem and implications for
landscape ecology." Landscape Ecology 11: 129-140.

Klassen, A. C., M. Kulldorff, et al. (2005). "Geographic clustering of prostate cancer
grade and stage at diagnosis, before and afier adjustments for risk factors." International
Journal of Health Geoggaphics 4(1).

Komar, N. (2000). "West Nile viral encephalitis." Revue Scientifigue et Technique 19:
166-176.

Komar, N., S. Langevin, et al. (2003). "Experimental infection of North American birds
with New York 1999 strain of West Nile viral." Emerging Infectious DISCM 9: 311-
322.

Kulldorff, M. (1997). "A Spatial scan statistic." Communications in Statistics 26: 1481-
1496.

Kulldorff, M. (1999). Spatial scan Stactistics: models. calculations, and applications, in
Scan Statistics and Applications. Boston, Birkhauser.

Kulldorff, M. and N. Nagarwalla (1995). "Spatial disease clusters: detection and
inference." .S_t_atisticgn Medicine 14: 799-810.

Lawson, A. B. and K. Kleinman (2005). Spatial & Syndromic Surveflmce for Public
Health, Wiley.

Lewin-Koh, N. J. and R. Bivand (2006). maptools: Tools for reading and handling spatial
objects.

Longley, P. A., M. F. Goodchild, et al. (2001). Geoggaphic Information Systems app
Science, John Wiley & Sons Ltd.

Marra, P. P., S. Griffing, et al. (2004). "West Nile Virus and Wildlife." BioScience 54(5):
393-402.

McLean, R., S. Ubico, et al. (2001). "West Nile virus transmission and ecology in birds."
Annals of the New Yfl Academy of Sciences 951: 54-57.

Meade, M. S. and R. J. Earickson (2000). Medical Geogmphy Second Edition, Guilford
Publications.

Moran, P. A. P. (1950). "Notes on continuous stochastic phenomena." Biometrika 37: 17-
23.

Nychka, D. (2005). fields: Tools for spatial data.

108

Oden, N. (1995). "Adjusting Moran's I for population density." Statistics in Medicine 14:
17-26.

Openshaw, S. (1984). The Modifiable Areal Unit Problem. Norwich, CATMOG: 38-41.

Openshaw, S. (1995). "Developing automated and smart spatial pattern exploration tools
for geographical information systems applications." the Statisticizfl 44(1): 3 - l6.

Openshaw, S., M. Charlton, et al. (1988). "Investigation of Leukaemia Clusters by use of
a Geographical Analysis Machine." The Lancet 331(8580): 272-273.

Pebesma, E. J. (2006). gstat: geostatistical modelling, predicting and simulation.

Petersen, L. R. and A. A. Marfrn (2002). "West Nile Virus: A Primer for the Clinician."
Annafls of Internal Medicine 137(3): 173-179.

Plante, M., K. Lowell, et al. (2004). "Studing deer habitat on Anticosti Island, Quebec:
relating animal occurrences and forest map information." Ecological Modelling 174: 387-
399.

Qi, Y. and J. Wu (1996). "Effects of changing spatial resolution on the results of
landscape pattern analysis using spatial autocorrelation indicies." L_andscape Ecolggy 11:

39-49.

Rowlingson, B. S. and P. J. Diggle (2006). splancs: Spatial and Space-Time Point Pattern
Analysis.

Team, R. D. C. (2006). R: A Language and Environment for Statistical Computing. R. F.
f. S. Computing. Vienna, Austria.

Tsai, T. F., F. Popovici, et al. (1998). "West Nile encephalitis epidemic in southeastern
Romania." The Lancet 352: 767-771.

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