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Spatial analysis of veteran access to healthcare in Los Angeles County
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Spatial analysis of veteran access to healthcare in Los Angeles County
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Content
SPATIAL ANALYSIS OF VETERAN ACCESS TO HEALTHCARE IN LOS ANGELES COUNTY
by
Patrick McCullen
A Thesis Presented to the
FACULTY OF THE USC DORNSIFE COLLEGE OF LETTERS, ARTS AND SCIENCES
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOGRAPHIC INFORMATION SCIENCE AND TECHNOLGY)
December 2020
Copyright 2020
Patrick McCullen
To a special person, you know who you are.
i ii
Acknowledgements
These acknowledgements are a testament to everyone who has supported and inspired me
in this process. My mother Jean for never judging and teaching me what a good person is. My
Father George McCullen US Army, my brother, for protecting me, and showing me what
leadership is. My Uncle Patrick, thank you for always being a great uncle. My cousin Patrick
thank you for all your help, thanks little Lulu for helping me and showing me how to run quicker
when there is no sun. Also my Aunt Jeanne, you’re a good person, the McCullen clan would
never have survived without a person like you. I would also like to say thank you to my
cousin Patrick’s wife Jennifer (Professor McCullen), soon to be Dr. McCullen, I admire your
intelligence and being genuine and helping me with this process.
I would also like to thank Jimmy R. Sandoval MSG (Ret) US Army, Richard Riley US
Army, and Robert O’ Neill USN (Ret). Glad I know you and get to see and talk to you every
week and go down the rabbit hole. Also Zach Nickens, CDR Kyle (Dream) Weaver USN (Ret),
you were our cat herder, team old guys, thank you for all your help, we were up way too late for
old guys on Catalina island working on the best idea ever.
My first GIS professor, Warren Roberts, you were the best professor I ever witnessed,
you have a gift. My Thesis Committee, Dr. Oda, Dr. Wu. Dr. Vos, thank you for all your
valuable insight and being a good person I am glad I got to meet you and see the light turn on
when talking about anything spatial. Dr. Loyola, awesome job being the leader on a piece of rock
surrounded by water, your leadership helped us all succeed. Cousin Tony US Army (Ret) and his
Uncle, the most charismatic and all-around good person I have ever known, who helped me in so
many ways, Michael Peak Sr (The Dude). Also his son Michael, thanks little dude, you’re a good
iv
person. Got a thank my dog named Cool, glad you found me in your Sr years, wish I knew you
when you were puppy.
Also, Robert Wayne, I searched, there are no fiddle sounds in the software, and it needs
a bowed string option for sure, so we can turn off and then hear what great geniuses can do with
that instrument. George Winston (pianist), glad I was able to hear such beautiful notes from a
piano during the writing of this thesis. Carl Sagan, out amongst the stars.
v
Table of Contents
List of Figures ............................................................................................................................... vii
List of Tables ................................................................................................................................. ix
Acknowledgments ......................................................................................................................... iii
List of Abbreviations ................................................................................................................... ... x
Abstract .......................................................................................................................................... xi
Chapter 1 Introduction .................................................................................................................... 1
1.1. Motivation for Study ...........................................................................................................2
1.2. Study Area...........................................................................................................................3
1.3. Sociodemographic Data ......................................................................................................6
1.4. Future Research Applicability ............................................................................................6
1.5. Structure of this Thesis .......................................................................................................7
Chapter 2 Related Works ................................................................................................................ 8
2.1. American Community Survey ............................................................................................8
2.1.1. American Community Survey Data: Uncertainty ......................................................9
2.1.2. American Community Survey: Margin of Error (MOE) ...........................................9
2.1.3. Coefficient of Variation (CV) ..................................................................................10
2.2. Spatial Accessibility..........................................................................................................10
2.2.1. Provider-to-Population Ratio ...................................................................................11
2.3. Gravity Model Assessment ...............................................................................................12
2.3.1. Gravity Model Limitations ......................................................................................13
2.4. Two-Step Floating Catchment Area Method ....................................................................13
2.5. Enhanced Two-Step Floating Catchment Area Method (E2SFCA) .................................15
2.6. Gaussian Function .............................................................................................................17
Chapter 3 Methodology ................................................................................................................ 19
3.1. Data Sources .....................................................................................................................19
3.2. Demand Volume ...............................................................................................................21
3.3. VA Hospital and Primary Care Outpatient Facilities .......................................................22
vi
3.3.1. Latitude and Longitude ............................................................................................23
3.3.2. Supply Volume ........................................................................................................24
3.4. Road Network Creation ....................................................................................................26
3.5. Origins-Destinations (OD) and Closest Facilities.............................................................27
3.6. Enhanced Two-Step Floating Catchment Area Tool (USWFCA2) ..................................31
3.6.1. USWFCA2 Addin Tool Settings .............................................................................32
Chapter 4 Results .......................................................................................................................... 37
4.1. Analysis Overview ............................................................................................................38
4.1.1. Decay Bandwidth Symbology Comparison .............................................................42
4.1.2. Decay Bandwidth 20 Testing ...................................................................................42
4.1.3. Decay Bandwidth 50 Core Model ............................................................................43
4.1.4. Drive Time Analysis and Spatial Accessibility Scores ............................................44
4.2. Source of Error ..................................................................................................................46
4.3. Uncertainty Analysis .........................................................................................................47
4.4. Supply Volume Increase – San Gabriel Valley VA Clinic ...............................................52
4.5. Review of Additional Accessibility Location ...................................................................56
4.6. Overall Summary of Results .............................................................................................60
Chapter 5 Discussions and Conclusions ....................................................................................... 61
5.1. Review of The Methods ....................................................................................................61
5.2. Limitations ........................................................................................................................62
5.2.1. Modifiable Areal Unit Problem (MAUP) and ACS Data and Uncertainty .............63
5.2.2. 15-Minute Catchment Threshold Assessment .........................................................64
5.2.3. Closest Facility.........................................................................................................66
5.2.4. Precision of Travel Times on Routes .......................................................................66
5.2.5. Census Tract Centroids ............................................................................................67
5.3. Conclusions .......................................................................................................................68
References ..................................................................................................................................... 70
vii
List of Figures
Figure 1 Study Area ........................................................................................................................ 5
Figure 2 Workflow Showing Demand Centroid Creation ............................................................ 21
Figure 3 Census Tract Centroid Example ..................................................................................... 22
Figure 4 Workflow Diagram Showing Supply Point and Volume Creation ................................ 23
Figure 5 VA Locations and Supply Volume ................................................................................. 25
Figure 6 Network Dataset Streets and Network Junctions ........................................................... 27
Figure 7 Origins and Destination Map .......................................................................................... 29
Figure 8 Closest Facilities Results ................................................................................................ 30
Figure 9 Origins and Destination Line with Closest Facility Route. ............................................ 31
Figure 10 USWFCA2 Addin Tool Workflow Diagram ................................................................ 32
Figure 11 Catchment Areas .......................................................................................................... 34
Figure 12 Distribution Using Decay Bandwidth 20 ..................................................................... 39
Figure 13 Distribution Using Decay Bandwidth 50 ..................................................................... 39
Figure 14 Decay Bandwidth Value 50 .......................................................................................... 40
Figure 15 Decay Bandwidth Value 20 .......................................................................................... 41
Figure 16 Decay Bandwidth 20 .................................................................................................... 42
Figure 17 Decay Bandwidth 50 with Same Intervals ................................................................... 42
Figure 18 Coefficient of Variation Map ....................................................................................... 49
Figure 19 Lower Boundary Interval Map ..................................................................................... 51
Figure 20 Upper Boundary Interval Map. ..................................................................................... 52
Figure 21 San Gabriel Valley VA Clinics with Increased Supply Volume .................................. 56
Figure 22 Additional Outpatient Facility Location ....................................................................... 59
Figure 23 Antelope Valley Catchment ......................................................................................... 64
Figure 24 Antelope Valley Veteran Estimations Values .............................................................. 65
viii
Figure 25 Total Drive Time Routes .............................................................................................. 67
Figure 26 Demand Centroid Limitations ...................................................................................... 68
ix
List of Tables
Table 1 Data Sources .................................................................................................................... 20
Table 2 Veterans Administration Names and Locations with Supply Volume ............................ 24
Table 4 Database File Output Source: Mitch Langford, December 2015..................................... 33
Table 4 Nearest Supply Catchment Data ...................................................................................... 35
Table 5 Decay Bandwidth 20 Coverage ....................................................................................... 43
Table 6 Decay Bandwidth 50 Coverage ....................................................................................... 44
Table 7 Decay Bandwidth 20 and 50 Spatial Accessibility Scores with Drive Time ................... 45
Table 8 Confidence Interval Equation. ......................................................................................... 47
Table 9 San Gabriel Valley VA Clinic Drive Time Analysis using Decay Bandwidth 50 .......... 53
x
List of Abbreviations
2SFCA Two-Step Floating Catchment Area
ACS American Community Survey
CV Coefficient of Variation
E2SFCA Enhanced Two-Step Floating Catchment Area
FCA Floating Catchment Area
FC Feature Class
GIS Geographical Information Systems
MOE Margin of Error
MUAP Modifiable Areal Unit Problem
OD Origins and Destinations
USWFCA2 University Southern Wales Floating Catchment Area 2
UCLA University of California Los Angeles
VA Veterans Administration
xi
Abstract
This study was undertaken to determine if gaps in health care accessibility existed in Los
Angeles County. A primary consideration of this study was the veteran population in Los
Angeles County and their accessibility to healthcare. Accessibility is defined by the Veteran
Administration (VA) as the acceptable travel time to the nearest VA healthcare center for a
veteran to receive desired care. As part of the MISSION (Maintaining Internal Systems and
Strengthening Integrated Outside Networks) Act of 2018, veterans may receive primary care
outside the VA system if the average drive time to a VA facility is thirty minutes or more. This
thesis examines the spatial accessibility for veterans to travel to VA facilities instead of
accessing care outside of the VA system. At this time, there are three VA medical centers and
seven primary care facilities located throughout Los Angeles County. This study analyzed the
areas around the three medical centers and seven primary care facilities and identified gaps in
accessing health care based on drive time using the enhanced two-step floating catchment area
(E2SFCA) method. It identified where gaps in spatial accessibility exist using veteran
estimations at the census tract level extent. The study found that gaps in coverage exist in the
eastern area of Los Angeles County. The methodology and detailed analysis can serve to
determine differences in drive time distance decay for veterans to access primary medical care in
other locations throughout the country.
1
Chapter 1 Introduction
Many veterans in Los Angeles County, California, have complex health care needs as a result of
their service while engaged in conflicts around the world. In exchange for veterans’ active duty
in any of the armed forces, each veteran may be eligible to receive health care through the
Veterans Administration (VA). Veterans who desire to have their health care needs met through
the VA must meet eligibility requirements that include active duty service with an honorable
discharge (VA Benefits and Healthcare 2019).
Veterans who are eligible and wish to have their healthcare needs provided by the VA
include those from World War II, Korea, Vietnam, the Cold War, and more recent wars in
Afghanistan and Iraq. The health care needs include those related to the conflict when the
veteran served, and many are combat-related traumatic injuries with extensive rehabilitation
requirements. There are also illnesses and conditions related to the era served that include
environmental exposure associated with the service location, combat-related chemical exposures,
intense noise exposure, infectious disease exposure, substance abuse issues, and mental health
concerns. Some of the diseases and health conditions that occurred during a veteran’s military
service may lead to chronic diseases including respiratory, heart, kidney diseases, mental health
illnesses, sensory problems, and development of various cancers (VA Benefits and Healthcare
2019). Primary care is the entry point for many veterans to access their VA healthcare benefits.
Primary care is patient-centered, comprehensive, and continuous since it intends to
coordinate various types of specialized care and reduce fragmented care delivery (Lin et al.
2018). Primary care is usually provided by physician generalists alone or in combination with
nurse practitioners and at designated primary care facilities sites. The focus of care is long-term
with a holistic approach. The purpose of primary care is to assist the veteran patient with greater
2
access to available services that leads to better management of health care problems. It also
includes modalities for disease prevention and health management education to create less need
for specialty care and hospitalization (Lin et al. 2018). The provision of primary care is a critical
component for each veteran’s overall health management within the VA system.
1.1. Motivation for Study
This study analyzes health care coverage gaps for veterans living in Los Angeles County.
Coverage gaps exist if maximum drive times exceed VA mandates or areas in Los Angeles
County where no health care facilities exist. This writer became aware of this issue because of
family and friends who wanted their care provided by the VA. However, they needed to drive
more than 30 minutes to obtain primary care services. Veterans, many of whom have complex
health care treatment and care needs, have chosen to have their care provided by VA health care
practitioners who have expertise providing care to injured and ill veterans. Many veterans who
live in Los Angeles County can be ill-equipped to re-enter non-veteran communities after being
discharged from the military. Physical and psychological needs after military discharge may not
have been addressed while in the service. This can exacerbate the reasons for their difficulty in
transitioning to civilian life. The ease of access to obtain care and services is paramount in both
the urban and rural areas of Los Angeles County for veterans. Accessibility, ambiance, and
convenience of the distance to travel to receive care is also an incentive for veterans to obtain
and follow up with primary care needs (Chatterjee and Mukherjee 2013).
The Veterans Access, Choice, and Accountability Act of 2014 and its amendments
mandated specific maximum drive times to access facilities for primary care (Becker 2016). The
Maintaining Internal Systems and Strengthening Integrated Outside Networks Act (MISSION)
Act of 2018 included the drive time of not more than thirty minutes to access primary care. The
3
issue of VA healthcare access prompted the exploration of research methods that used spatial
accessibility in healthcare to understand this potential problem’s complexity better. As discussed
in more detail in Chapter 2, the past research findings motivated the author of this thesis to study
if the current distribution of VA healthcare locations in Los Angeles County ensures veterans can
easily access health care after serving their country. The VA states its concern on veterans’
physical access to primary care. The Veterans Access, Choice, and Accountability Act of 2014
and its amendments mandated specific maximum drive times to access facilities for primary care
(Becker 2016). The MISSION Act of 2018 included the drive time of not more than 30 minutes
to access primary care.
This research aimed to assess if gaps in coverage exist from veteran demand locations to
VA hospitals and primary care facilities. Adhering to the guidelines provided by the VA in the
mandate, MISSION Act of 2018. s stated, veteran healthcare provided by VA healthcare
practitioners may provide a better experience for veterans as opposed to healthcare provided by
non-VA practitioners. VA leaders and other stakeholders will have a greater understanding of
where drive time thresholds exceed mandated requirements. This study’s results and suggestions
can enhance the body of knowledge to assist planners in the decision process of relocating,
opening, closing, or modifying existing primary care facilities.
1.2. Study Area
As discussed above, this study’s focus was accessibility for veterans to seek primary
medical care in a location not more than 30-minute travel time from their location within Los
Angeles County. The county of Los Angeles is the eleventh largest in California with more than
4,000 square miles (County of Los Angeles n.d.) and is the most populous county in the United
4
States (DPH 2015). The large, broad geographic area and the often congested freeway network
of Los Angeles County may cause impedance in accessing health care.
The Los Angeles County network of veteran care (Figure 1) includes three
comprehensive medical centers in West Los Angeles, North Hills, and Long Beach. All three
medical centers provide primary and specialty care such as mental health, women’s health,
audiology, cardiology, ophthalmology, optometry, orthopedics, urology, and dental services (US
Department of Veteran Affairs 2019). Also, there are seven community-based outpatient care
centers within the county. They are in Arcadia, Santa Fe Springs, Commerce, Long Beach,
Lancaster, Gardena, and the Ambulatory Care Center in North Hills. The staffing in these PCF
centers ranges from one physician as a solo practitioner to additional NPs, and physician’s
assistants.
The driving distance from the Greater Los Angeles County VA facility to the Long Beach
VA facility is 33 miles, which takes approximately 1.5 hours to drive and 2.5 hours via mass
transit (Los Angeles Public Transit 2015). The drive distance to North Hills from the Greater LA
VA facility is approximately 1 hour and 1.5 hours. This thesis examines the spatial relationship
of the PCFs and the veteran estimations per census tracts with access to care within a 15-minute
drive catchment.
Meeting the primary health care needs of Los Angeles County veterans requires the
geospatial analysis of the maximum drive time standard from a veteran’s home to the nearest VA
health care facility providing primary care services. This analysis raises the question if the
current PCF locations are serving the needs of the veterans or if there are gaps in coverage due to
driving time delays to access primary health care. It also adds information and analysis of the
presence of locations that are closer than 30 minutes from a veteran’s home. Figure 1 below
5
shows the study area with each supply having a unique color symbolized with a square. The
major freeways shown were to provide a reference for the reader and their proximity to the
hospital and PCF locations. The large, broad geographic area and the often congested freeway
network of LAC may cause travel impedance in accessing health care.
Figure 1. Study Area
6
1.3. Sociodemographic Data
Los Angeles County has the largest number of veterans in California (LAO Report 2017).
There are approximately 264,635 veterans (Los Angeles Almanac 2017) living in Los Angeles
County and about 12,000 veterans moving to the county each year (Castro, Kintzle, and Hassan
2014). The most significant percentage of veterans is 65 years old and above, representing 53.2%
of the veterans (Los Angeles Almanac n.d.). The second-largest age group is 35-54 years old,
which represents 21.8% of the veterans. The third-largest is 55-64 years old, which represents
15.3%. The smallest group comprises veterans 18-34 years old that represent 9.7% of the total
veterans (Los Angeles Almanac n.d.).
1.4. Future Research Applicability
This thesis examined spatial access to primary care for veterans in Los Angeles County.
A core model was used as a baseline for further analysis. The core model was developed from a
third party add-in tool called the USWFCA2, which stands of the University of South Wales
Floating Catchment Area 2. The add-in tool accelerated the laborious process when manually
applying the E2SFCA statistical equation in a GIS. The 30-minute mandate enacted by VA was
considered for a catchment boundary in this analysis. However, due to traffic congestion, urban
sprawl, and street network data attributes a 15-minute drive time, catchment provided a more
realistic threshold boundary. The applicability of the core model provided results that can be
used in future research.
This study indicated if travel time gaps in coverage exist and provided data to assess
spatial accessibility regarding veteran healthcare. The thesis examined existing locations and
spatially exhibited which veteran census tracts meet the drive time threshold to access care. It
also spatially displayed veterans who are inside of drive time distances to access multiple
7
primary care facility locations. The examination of supply and demand volume and the
application of the E2SFCA method may assist VA planners, veteran stakeholders, and county
administrators in more accurately understanding if gaps in spatial accessibility exist. Other
scientists have not conducted such research to this author’s knowledge, particularly in the
context of Los Angeles County.
1.5. Structure of this Thesis
There are five chapters in this thesis. Chapter 2 provides a review of past spatial studies
related to healthcare access, consisting of simple gravity models to advanced spatial analysis
using the E2SFCA method. An in-depth analysis of the methodology was highlighted throughout
Chapter 3 using an open-source addin tool to expedite the lengthy procedural application of the
E2SFCA method in a GIS. Chapter 4 reports the results of the spatial analysis. From the results
of the spatial analysis, Chapter 4 also includes a general discussion of potential site parameters to
review and one additional location within Los Angeles County is identified. In Chapter 5, there
is a discussion about the analysis of the methods and final results. There is also a limitation
section in Chapter 5 that provides the reader with insight into how improvements could be made.
Also, this chapter offers implications for further research on accessibility to healthcare facilities.
8
Chapter 2 Related Works
This chapter provides the reader with the background knowledge that qualifies the methods
described in Chapter 3. Moreover, this chapter discusses past research in spatial accessibility and
a comprehensive assessment of why the E2SFCA method was chosen.
Spatial accessibility models depend on three components: population data in census
tracts, the method to aggregate the data, and the defined measure of accessibility (Apparicio et al.
2017). Research on spatial accessibility is essential to promote veteran equitable access to health
care facilities. Equity through accessibility leads to patient satisfaction, improved health
outcomes, decreased hospitalizations, and reduced cost. These indicators of effectiveness in
healthcare are associated with travel time to access care (Saxon and Snow 2016).
2.1. American Community Survey
The American Community Survey (ACS) is sent out by the United States Census Bureau
monthly and aggregated yearly, which collects socio-demographics on US residents. The
ongoing survey is sent out to more than three million residents and is considered a sample of the
population (Berkeley 2017). Moreover, different samples are taken and yield different estimates
of the actual population value. The ACS offers one-year, three-year, and five-year estimates
where five-year estimates are based on five-times as many samples and provide increased
statistical reliability. Depending on the analysis undertaken, the US Census Bureau has general
guidelines to best estimate the most warranted dataset. Also, when analyzing a small subset of a
population such as veterans, five-year estimates are preferred.
9
2.1.1. American Community Survey Data: Uncertainty
Uncertainty in the ACS data is the result of the process of how the survey data is
collected. Since the ACS conducts sample surveys of a segment of the population, as discussed
in Section 2.1 at one year, three-year, and five-year intervals. The data does not reflect the exact
characteristics of the entire population. The word uncertainty in this instance can also be
considered a sampling error. The sampling error described by the ACS is the difference between
a sample survey and if the entire population was surveyed. The sampling error size is expressed
as the margin of error (MOE) and is published with each ACS report (US Census Bureau n.d.).
2.1.2. American Community Survey: Margin of Error (MOE)
When using ACS data, there is a need to assess the MOE, which is present in sample size
estimates. Three factors contribute to the MOE, and these are the confidence level of the sample
size, the sample size itself, and the amount of variability in the population (Bell and Cai 2015).
The confidence level that corresponds to the MOE suggests the ACS sample estimate is within
the realm of the population estimate. The ACS estimates with corresponding MOEs have a 90%
confidence level attributed to them. From these published MOEs, 90% confidence intervals that
define a range calculated. This is the range that holds the real value of a population 90% of the
time.
10
One example of a calculated 90% confidence interval for an estimate was taken from the
data used in this thesis. One census tract that held a veteran estimation of 438 and had an MOE
of 103. Taking the MOE value of 103, then adding and subtracting from the veteran estimate of
438, resulted in a 90% confidence interval for that estimate (US Census Bureau n.d.). When
researchers look at ACS estimates and MOE, they must consider that smaller sample sizes will
have greater MOE, and some MOE will be larger than the estimate itself. Using larger geography
can reduce the MOE, and the smaller the MOE, the more accurate the data is to use (Berkley
2017).
2.1.3. Coefficient of Variation (CV)
The coefficients of variation (CV) calculated within the ACS veteran data are statistical
measures that show the amount of sampling error for each census tract. This calculation is used
to assess data reliability. The following indicates the reliability of the sampling data: CV < 15
indicates the data is reliable, CV >=15 and < 30 the data is moderately reliable, and CV>= 30 is
not reliable, and a coefficient of variation of 0 indicates no data (Census Data, Montgomery, MD
n.d.). According to Rural Data Portal (n.d.), and ArcGIS (2012), the measures of reliability are
not standardized and vary slightly by researchers to estimate reliability based on established CV
formulas. ArcGIS (2012) indicates that the following reliability: CV = < 12 indicates high
reliability, CV >12 to not more than 40 is medium reliability, and CV > 40 is low reliability.
2.2. Spatial Accessibility
The assessment of adequate health care accessibility for veterans in Los Angeles County
for this research is based on travel time to access a VA healthcare facility. Spatial accessibility is
measured in many different ways, such as distances to a health care facility or practitioner,
distance to travel in time estimates, and distance decay calculations (Ludivine et al. 2019).
11
Distance decay, in essence, is how far someone is willing to travel. If a supply location is far
away from a demand origin, the less inclined someone would be to use that location for services
(GISGeography 2020). The closer the demand is to the supply, the lower the time distance and
the lower the decay. As the supply gets further from the demand, the time increases or decays to
the point that it is too far in time to travel to access the supply point.
In one study, physicians were used as a supply-side, and population demographics were
designated as demand. Using physician as supply to population demand was considered an
essential criterion in assessing spatial accessibility in healthcare (Luo 2004). Spatial accessibility
in healthcare has been widely studied in the past. One study used four separate categories to
define the methods most used: provider-to-population ratios, distance to nearest provider, the
average distance to a set of providers, and gravitational models of provider influence. Each
spatial accessibility method produced its capabilities and shortfalls (Guagliardo 2004).
2.2.1. Provider-to-Population Ratio
The provider-to-population ratio is a measurement that is used the most. The reason for
its popularity is that data sets are easy to obtain and use and do not require advanced expertise in
GIS. The provider-to-population ratio is an indicator of supply availability and is calculated
inside a geographic area of extent. The extent of these areas can be as small as health service
areas or as large as counties and states. Doctors and nurse practitioners, location of primary care
clinics, or wait time are all considered health service capacity indicators and are used as the
numerator in the equation. Demographic data such as population size within a specified
geographical extent is assigned as the denominator. Contiguous areas or regions are evaluated for
similarities between provider-to-population ratio values concerning some form of healthcare
indicator (Guagliardo 2004). Using physician to the population as supply and demand are
12
𝑆𝑆
considered an essential criterion in the assessment of spatial accessibly in healthcare (Luo 2004).
The provider-to-population ratio does have limitations. One of the provider-to-population
limitations is that it does not measure distance or travel time.
2.3. Gravity Model Assessment
Gravity models in simplistic terms measure the attraction between two points, a supply
origin and a demand destination (Esri n.d.). Gravity models are thought to be reliable in
measuring spatial access since the model addresses the decreasing attraction of demand as it
moves further away from the supply sites (Crookes and Schuurman 2012). Gravity models, also
known as cumulative opportunity measures, are evaluation for accessibly. The cumulative
opportunity measures calculate how many opportunities (demand) that are within a specific
travel time or distance threshold. If more opportunities exist within a given travel time or
distance, accessibility increases (Higgs 2004). Gravity models are mathematical equations that
measure spatial accessibility concurrently, including the supply, the demand, and the ranges in
time or miles between the two (Pan et al. 2015). The basic gravity model formula is as follows:
𝐴𝐴 𝑖𝑖
= ∑
𝑗𝑗
𝑑𝑑 𝛽𝛽
𝑗𝑗 𝑖𝑖 𝑗𝑗
The equation of the basic gravity model is Ai becomes spatial accessibility from point i,
which is considered population. This population point can be a census tract centroid or any area
of interest such as a residence. The service capacity is considered Sj at j, which is the provider
location This measurement usually takes on a numerical capacity range. Travel impedance
(distance or travel time) is d between points i and j. The gravity decay coefficient is β (Beta). To
interpret the results, the summed supply capacity increases when the total travel impedance
declines. (Guagliardo 2004).
13
2.3.1. Gravity Model Limitations
Some basic limitations with the gravity model are that it only measures supply.
Moreover, it uses a statistical equation that nonprofessionals may have a hard time interpreting
(Guagliardo 2004). La Mondia, Blackmar, and Bhat (2010) completed a comparison study of
transit accessibility models, one of which was a gravity model. They identified three limitations
of the gravity model but also indicated the popularity of the model of gravity models to measure
accessibility. The first limitation they cited was the gravity model assumes the attractiveness of
each destination is equally attractive to all individuals. The second limitation they cited was the
model did not consider individual travel patterns, travel behavior, and did not include time
constraints to a destination. The third limitation which the authors considered to be a significant
limitation was the lack of defining the impedance or friction factor of locations at further
distances.
2.4. Two-Step Floating Catchment Area Method
In examining spatial accessibility for health care, the two-step floating catchment area
(2SFCA) method was reviewed. In healthcare, supply and demand variables vary; hospital
locations, number of doctors at a provider site, road network datasets, and travel to provider
locations are all dynamically connected (Luo et al. 2018). The 2SFCA is a unique gravity model
(Lou and Qi 2009). The 2SFCA uses spatial and non-spatial factors to measure spatial
accessibility based on travel impedance between demand and supply. Wang and Luo (2005)
researched to examine consumer access to primary healthcare using spatial and non-spatial
factors in Illinois. The spatial component illustrated how geographic locations could be
impediments between the provider and the consumer to access healthcare. The non-spatial
factors included demographic information obtained from census data. The physician data were
14
obtained from the American Medical Association. They utilized a 2SFCA method to measure
spatial accessibility based on travel time from the consumer to the healthcare location. They then
grouped the consumers into sociodemographic groups. The study’s outcome was combining the
spatial and non-spatial results to identify areas of poor access to healthcare. The challenge
indicated by Wang and Luo (2005) was integrating the spatial and non-spatial indicators into one
spatial analysis, which was accomplished using the 2SFCA method. Their research concluded
that integrating spatial and non-spatial factors in one system is essential when designing a
method to assess healthcare access. This study showed that GIS was useful to analyze spatial
relationships and complete computations related to spatial data.
The 2SFCA method building on the provider-to-patient relationship uses floating
catchment areas. They are a determination of travel impedance from supply to demand. Typical
travel impedances used in analyzing health care related to spatial accessibility are maximum
travel time or distance. Most healthcare studies using the 2SFCA regard a 30-minute drive-time
as maximum travel time for people to spend traveling to a primary care clinic (Luo and Qi 2009).
The 2SFCA measures the accessibility values from the demand point, which is the sum of the
provider-to-population ratio that falls within a catchment area (Shin and Lee 2018). Step one in
the 2SFCA method calculates a population that is within the catchment at each provider. In step
two, services are allocated to potential populations in the catchments (McGrail and Humphreys
2009). All populations (demand) within a specific floating catchment are considered equal and
share the same accessibility to that specific supply location. (McGrail 2012). Results from these
steps become the spatial accessibility index score for each demand point. The formulas and
procedures are shown below with an explanation of the equation.
15
𝑅𝑅
𝑆𝑆
𝑅𝑅
𝑆𝑆
𝑖𝑖
𝑖𝑖
The first step begins with using a physician location j, and searches locations k for all
populations that fall within a travel time threshold do from location j, to compute the physician-
to-population ratio Rj that fall in each catchment area. Pk represents the population of k and is in
the boundary catchment j (dkj ≤d0). Sj represents the number of physicians at location j; dkj is the
travel time between k and j.
=
𝑗𝑗
∑
𝑘𝑘 𝑘𝑘 {𝑑𝑑 𝑘𝑘 𝑗𝑗 ≤ 𝑑𝑑 0
}
𝑃𝑃 𝑘𝑘
In step two, the population location i, then search every physician location j, that is in the
threshold travel time d0 from location i (catchment area i), then sums up of the physician-to-
population ratio (originated from step 1), Rj at those locations. 𝐴𝐴 𝑓𝑓
is the accessibility of the
population at location i to physician. Rj is the physician-to-population ratio originating at
physician location j who center falls within the catchment centroid at population
location i. The dij is the travel time between i and j.
∑ = ∑
𝑗𝑗
𝑗𝑗
𝑗𝑗 𝑗𝑗 { 𝑑𝑑 ≤ 𝑑𝑑 }
𝑗𝑗 𝑗𝑗 { 𝑑𝑑 ≤ 𝑑𝑑 }
∑
𝑘𝑘 ∈ { 𝑑𝑑 ≤ 𝑑𝑑 }
𝑃𝑃 𝑘𝑘
𝑖𝑖 𝑗𝑗 0 𝑖𝑖 𝑗𝑗 0 𝑖𝑖 𝑗𝑗 0
When interpreting the results, larger values of 𝐴𝐴 𝑓𝑓 represent better access to supply at the
demand location. Ratios are assigned in the first step, and in the second step, the initial ratios are
summed up from overlapping service areas, where potential demand has access to multiple
supplies.
2.5. Enhanced Two-Step Floating Catchment Area Method (E2SFCA)
The E2SFCA is another type of gravity model that considers distance decay in the
modeling process. After careful review of the gravity models described earlier in this study.
McGrail (2012) discusses the use of E2SFCA by Luo and Qi (2009) with the addition of three
𝑗𝑗
16
𝑅𝑅
𝑆𝑆
𝑅𝑅
𝑆𝑆
distance decays. The E2SFCA uses different intervals of distance impendence, which provides a
more accurate spatial pattern regarding accessibility and shortage areas (Luo and Yi 2009). The
E2SFCA distance decay is a factor that can influence care location choices Guagliardo 2004).
Luo et al. (2018) used the E2SFCA method to spatially explore the accessibility of medical
services for the elderly in Wuhan, China. The E2SFCA, like the 2SFCA, calculates an
accessibility index score and requires an additional step using distance decay.
The E2SFCA incorporates a Gaussian distance decay function into its formula, and this
thesis used drive time as the distance decay. Conversely, the 2SFCA has fixed distance
impedance and does not incorporate multiple distance decays. The use of distance decay
provides a more accurate depiction of where coverage gaps exist. The addition of distance decay
allows for an in-depth interpretation of the results (Luo and Qi 2009). The statistical equation
beginning with step one is shown below.
=
𝑗𝑗
𝑗𝑗
𝑘𝑘 𝑗𝑗 { 𝑑𝑑 𝑘𝑘 𝑗𝑗 𝑗𝑗𝜖𝜖 𝑟𝑟
}
𝑃𝑃 𝑘𝑘
𝑊𝑊 𝑟𝑟
=
𝑗𝑗
𝑗𝑗
𝑘𝑘 𝑗𝑗 { 𝑑𝑑 𝑘𝑘 𝑗𝑗
𝑗𝑗 𝜖𝜖 1 }
𝑃𝑃 𝑘𝑘 𝑊𝑊 1
+ ∑
𝑘𝑘 𝑗𝑗 { 𝑑𝑑 𝑘𝑘 𝑗𝑗 𝑗𝑗 𝜖𝜖 2 }
𝑃𝑃 𝑘𝑘 𝑊𝑊 2
+ ∑
𝑘𝑘 𝑗𝑗 { 𝑑𝑑 𝑘𝑘 𝑗𝑗 𝑗𝑗 𝜖𝜖 3 }
𝑃𝑃 𝑘𝑘 𝑊𝑊 3
The first catchment of supply location j is represented by thirty-minute drive time. Next,
the E2SFCA method calculates three travel time zones from within each catchment. The travel
time zones are set up with minute breaks of 0-10, 10-20, and 20-30. Population locations are
considered (k) in the equation. These population locations denoted by (k) are searched within a
travel time zone represented as (Dr) from provider location j. The following way computes the
∑
∑
17
weighted provider-to-population ratio (Rj) within the catchment area. Pk becomes the population
18
𝑅𝑅
𝑅𝑅 𝑅𝑅 𝑅𝑅
𝑖𝑖
𝑖𝑖
of k that falls within the catchment j. Then Sj becomes supply-side count at location j; dkj is the
travel time between k an j. In this equation, the Dr is the rth travel zones (i.e. travel time zones1-
3) from within each catchment. Wr represents the distance weight with regards to the rth travel
time zone. The Wr takes into account the Gaussian function, which captures the distance decay
of providers j access (Luo and Qi 2009).
In step two shown below, population location i searches every provider location j. This is
done within the 30-minute travel time zone starting at location i. The sum of the ratio, which is
the provider-to-population at those locations, is labeled as Rj. At those locations, 𝐴𝐴 𝑓𝑓 is the
accessibility of population at location i with regards to the providers. The travel time
between i and j is represented by dij. As with step one, the derived weights using the Gaussian
function are applied for representing distance decay in each travel time zone (Luo and Qi 2008).
The travel time between i and j is represented by dij.
𝐴𝐴 𝐹𝐹 = ∑ 𝑗𝑗 𝑊𝑊 𝑟𝑟
𝑗𝑗𝑗𝑗 { 𝑑𝑑 𝑖𝑖 𝑗𝑗 𝑗𝑗 𝜖𝜖 1}
= ∑ 𝑗𝑗 𝑊𝑊 1 + ∑ 𝑗𝑗 𝑊𝑊 2 + ∑ 𝑗𝑗 𝑊𝑊 3
𝑗𝑗𝑗𝑗 { 𝑑𝑑 𝑖𝑖 𝑗𝑗 𝑗𝑗𝜖𝜖 1} 𝑗𝑗𝑗𝑗 { 𝑑𝑑 𝑖𝑖 𝑗𝑗 𝑗𝑗𝜖𝜖 2} 𝑗𝑗𝑗𝑗 { 𝑑𝑑 𝑖𝑖 𝑗𝑗 𝑗𝑗 𝜖𝜖 3}
2.6. Gaussian Function
The Gaussian distribution was chosen as the functional form to consider distance decay
in this thesis. Its use was to show supply accessibility based on time limits to access primary
care. The Gaussian function used with the E2SFCA identified distance decay through weighted
values represented by the normal distribution curve. The literature suggests that the Gaussian
curve is an advantageous function to calculate travel impedance through a gravity model. (Luo
19
and Qi 2009, Lin et al. 2018, Chen and Fei 2019). The choice of the impedance coefficient is
essential when using the Gaussian distribution since it affects the outcome of accessibility
results.
Wang and Tormala (2014) conducted a study to measure access to primary care
physicians for an aboriginal people located in Canada. They utilized an E2SFCA method with
the Gaussian function to weight distance decay to determine accessibility to a physician. Their
weighting method was adopted from research completed by Luo and Qi (2015). Ma et al. (2018)
also used an E2SFCA with a Gaussian function to define and assess travel distance weights.
Each of these researchers used different beta coefficient weights that were chosen dependent on
the study of spatial and non-spatial factors. The populations studied in the research above-
identified and tested different travel times as distance decay from the physician location. The
weights chosen by researchers depend on the most suitable decay rate applied to the Gaussian
curve. The writer of this manuscript tested multiple weights to assess the rate of distance decay
for this project. Testing was performed using different coefficients that affected the rate of the
curve of the Gaussian model within the computational formulation. The impedance beta
coefficient used to show distance weighting was 0.5 with range values of 0-1.0. Testing with
other coefficients was also conducted, but the decline was too steep.
20
Chapter 3 Methodology
Chapter 3 is a description of the data and processes used in this project. The methods utilized
were based on the research discussed in Chapter 2. Building on prior work was the basis of this
thesis and the methods used to elicit the results presented in Chapter 4.
The first section describes the steps needed to obtain, combine, and calculate all dataset
utilized in this project. That data included hospital and primary care facilities with practitioner
volume, and veteran estimations per census tract. Subsequent sections within this chapter
illustrate the data integration into the methods chosen to achieve the outcome discussed in detail
in Chapter 4. The methods utilized within this study were the use of an add-in tool called the
Enhanced Two-Step Floating Catchment Areas Accessibility Tool. This was used to ease in the
analysis of multiple E2SFCA assessments. This tool also used a Gaussian decay function with
decay bandwidth values to mimic different drive times.
3.1. Data Sources
Datasets listed in Table 1 were used to determine if gaps in veteran coverage exist in
LAC. Table 1 reports what types of datasets were obtained and what source they came from,
including datasets, file type, and source. The demographic dataset used was ACS 5-year
estimates of veterans living in Los Angeles County from the years 2012 to 2017.
21
Table 1. Data Sources
Datasets File Type Source
Veteran Demographics Tabular
.CSV
United States Census Bureau
American Community
Survey
Los Angeles County
Census Tracts
Polygon
Feature Class
United States Census Bureau
TIGER/Line
Los Angeles Network
Data
Polyline UCLA Geo-Portal
VA Locations Point
Feature Class
Veteran Administration
The chosen road network dataset had a drive time attribute. The TIGER/Line street
datasets were not used because of connectivity errors in the line segments and no mile per hour
or drive attributes in the dataset. The Los Angeles road network provided by the University of
California, Los Angeles (UCLA) geoportal had drive-time attributes associated with the dataset
and was used for cost impedance in this manuscript. All four of the datasets were obtained
online, and the author of this thesis created the VA hospitals and primary care facility layer.
22
3.2. Demand Volume
The total veteran estimation used in this study was 280,014 dispersed throughout the
2,341 census tracts of Los Angeles County. Each census tract represents an areal unit of a
demand-side layer, which was used for further spatial analysis. This thesis used veteran ACS
estimates joined with census tracts as the first set of data to be geo-processed. Figure 2 shows the
workflow of the data processing to develop demand-side point data, which also records the
veteran estimation. The census tract polygons were transformed into points representing their
centroids (Figure 3) through the Feature to Point tool of ArcGIS. Of those 2,341 census tracts
there were 47 that had no veteran estimates associated with them. These census tracts were
occupied by parks, airports, and industrial parcels.
Figure 2. Workflow Diagram Showing
Demand Centroids Creation.
For ease in the visualization of what the feature to point tool did, Figure 3 shows a part of
the study area, where polygons were turned into census tract centroids. Graduated symbology
with Jenks natural breaks represents veteran estimation. The dark grey census tracks below show
which areas have no veterans in the ACS data.
23
Figure 3. Census Tract Centroid Example.
3.3. VA Hospital and Primary Care Outpatient Facilities
This thesis used VA hospital and primary care facilities as the supply side and volume
attribute used in this spatial analysis. To obtain the supply volume attribute, the author of this
study called individual VA locations and obtained doctor and nurse practitioner counts.
Moreover, the author collected the VA facilities’ phones numbers and addresses from their
websites.
Figure 4 shows the workflow of developing point data representing the locations of the
supply locations and the counts. The first step was to obtain VA addresses, these were converted
to latitude and longitude. Next, the data was imported to ArcMap and transformed to a point
feature class. This was then exported to a new feature class where the supply volume attributes
were appended. This data processing resulted in a supply-side input layer usable for further
analysis.
24
Figure 4. Workflow Diagram Showing Supply Point and Volume Creation.
3.3.1. Latitude and Longitude
To obtain the latitude and longitude for each VA location, an online address converter
was used. The program, which was called LatLong.net, converted street addresses to latitude and
longitude based on World Geodetic System 1984. This transformed the addresses to XY
coordinates that ArcMap was able to read. A list of all VA hospitals and outpatient facilities by
name in alphabetical order (Table 2) was used in this analysis. The three locations with the high
supply volume were the VA hospitals in Long Beach, West LA, and the Sepulveda medical
center. Phone numbers were added to the table so that any updates in the future with regards to
volume could easily be ascertained.
25
Table 2. Veterans Administration Names and Locations with Supply Volume.
Veterans
Administration
Facility Name
Latitude
Longitude
Phone Number
Doctor &
Nurse
Practitioner
Count
Antelope Valley VA
Clinic
34.703353 -118.124274 661-729-8655 3
Cabrillo VA Clinic 33.79222 -118.22213 562-826-8414 1
East Los Angles VA
Clinic
34.014927 -118.154192 323-725-7372 1
Gardena VA Clinic 33.85884 -118.296517 310-851-4705 2
Los Angeles VA Clinic 34.052559 -118.238586 213-253-5000 4
San Gabriel Valley VA
Clinic
34.151328 -118.032492 818-672-2800 2
Sepulveda VA Medical
Center
34.246545 -118.482171 818-891-7711 23
VA Long Beach
Healthcare System
33.778217 -118.119196 562-826-8000 64
West Los Angeles VA
Healthcare System
34.05239 -118.4584 310-478-3711 68
Whittier/Santa Fe
Springs VA Clinic
33.94238 -118.08182 562-347-2200 4
3.3.2. Supply Volume
Doctor and nurse practitioners’ counts were used as supply volume, which contributed to
the accuracy of spatial accessibility scores. Each of the three main hospitals has a higher number
of counts than the seven VA clinics. Figure 5 shows the study area of VA locations, names, and
supply volume. The total supply volume is 172 doctors and nurse practitioners
26
Figure 5. VA Locations and Supply Volume.
27
3.4. Road Network Creation
The Los Angeles County area is 4,751 square miles, plagued with urban sprawl and
traffic congestion, all factors for using drive time as travel impedance in this study. Drive time as
impendence provided more accuracy than straight-line Euclidean distance, which is more
intuitive to understand since Euclidean distance is a straight line distance between two points and
does not follow a road network. Moving around Los Angeles almost always requires the use of a
vehicle. The quickest route in conjunction with drive time on road segments provided a more
accurate depiction of real-world impendence.
A street dataset was downloaded from the University of California, Los Angeles
geoportal. To ensure the dataset was applicable, a new network dataset was created using the
road network provided by the source. When the network dataset was created, the travel mode
was set with drive time and used as impedance in this study. The resulting network elements
after a network dataset was run were road network edges and network dataset junctions used for
calculating locations and later used in the E2SFCA analysis tool process. Figure 6 shows a
neighborhood where the VA clinic is located in the Antelope Valley area. The green dots
represent nodes connecting individual line segments in the network dataset.
28
Figure 6. Network Dataset Streets and Network Junctions.
3.5. Origins-Destinations (OD) and Closest Facilities
The USWFCA2 analysis tool produced an origins and destinations (OD) cost matrix layer
and closest facility layer. The OD cost matrix and the closest facility solver tools were ancillary
outputs produced by the add-in tool. The OD cost matrix detects and measures a least-cost-path
from multiple origins along a network and only solves in one direction from origins to
destinations. Conversely, the closest facility tool measures the cost between two points called
facilities and incidents. It is used to find the path of two points which are closest to each other
and it can solve find routes in either direction. The results of those outputs are shown and
discussed later in this section. In this analysis, the incidents became demand points, and facilities
were the supply points. The cost impendence was drive time in minutes, and all closest incidents
to facilities routes that were found had a drive time attribute associated with each route.
29
Both the OD cost matrix and the closest facility tools found the least cost path and
produced six feature layers automatically updated into the table of contents in ArcMap. Within
the OD cost matrix output layer, there were six feature layers that represented multiple outputs.
The first feature layer was origins, and this represented all of the supply points located during the
analysis. The origins layer also had three categorical sublayers consisting of located, unlocated,
and if there was an error found. The destinations feature layer found all the census tract centroids
that held veteran estimations that were within the 15-minute catchment. Located, unlocated or
errors that were found were all subcategories and were inside the destination feature layer. There
was a third feature layer called lines representing all of the OD lines found in the analysis.
The study area in Figure 7 shows the output of the OD cost matrix analysis centered
around the Antelope Valley VA Clinic. Census tracts (destinations) outside the 15-minute
catchment were not found or analyzed during the OD cost matrix analysis. The map shows that
all census tracts within 15-minutes of drive time from the supply location to census tract
centroids were calculated in the network analysis. The red circle symbol shows the Antelope
valley VA clinic’s location with black origin-destination lines emanating from that location. The
small blue circles represent all thirty-five destinations found during this analysis. All census
tracts that fell outside the catchment area were shaded light blue and considered areas lacking
accessibility.
30
Figure 7. Origins and Destination Map
The areal extent in Figure 8 below is the same as that in Figure 7. The 15-minute
catchment boundary represented the spatial extent that was used during the add-in tool
processing phase. The fastest routes are on a street network, and no routes extended past 15-
minutes. The blue circle symbology is the demand point destinations in which thirty-five points
were located. The area outside the catchment boundary shown in light blue were areas that did
not receive a score and was considered areas that lack accessibility.
31
Figure 8. Closest Facilities Results.
An example of the difference between an OD cost matrix line and the fastest facility
route can be seen in Figure 9. The study area showed the Antelope Valley VA clinic and the
surrounding census tracts. The OD cost matrix line in light blue color is straight and connects an
origin to a destination. the fastest route in dark blue follows the local streets and the total drive
time in minutes on that route is 14.7 minutes.
32
Figure 9. Origins and Destination Line with Closest Facility Route
3.6. Enhanced Two-Step Floating Catchment Area Tool (USWFCA2)
The USWFCA2 analysis tool requires installation on ArcMap10.1 or greater. The
analysis also required a supply-side and a demand-side layer as inputs. The supply-side point
layer represented the locations of hospitals and outpatient facilities. This layer also held the
supply volume of doctors and nurse practitioners at each location. The demand layer was a
centroids shapefile that also included veteran estimates per census tract. Figure 10 below shows
the inputs in light blue and outputs in light green for the add-in tools operation.
33
Figure 10. USWFCA2 Addin Tool Workflow Diagram.
The outputs were an origins-destination cost (OD) matrix layer, a closest-facility layer,
and a database file, which contained spatial accessibility scores, drive distances from supplies to
demands, and the nearest supply points. The analysis tool also required a catchment area to be
set, where a 15-minute threshold was used as the spatial extent.
3.6.1. USWFCA2 Addin Tool Settings
The initial setup of the USWFCA2 add-in tool required all processed data to be in a
geodatabase. It included a network dataset, which was used to obtain the OD cost matrix and
closest facility layer to be discussed later in this chapter. The add-in tool uses a graphic interface
where users of the tool input parameters. They are catchment size of the study, a scale multiplier,
travel impedance, supply and demand layers, and decay bandwidth values.
The add-in tool produced an output database file, which was joined with the LAC census
tracts layer to assess spatial accessibility scores, drive time to visualize the results. Table 3 shows
the newly created fields calculated by the add-in tool. The fields that were discussed in the
34
results chapter were m1_SupID, m1_Dist, and m1_fca. The floating catchment area (FCA)
accessibility score is what this thesis called spatial accessibility scores. The OID of its nearest
supply point was used to assess how many estimated veteran census tracts were closest to which
supply location. The FCA accessibility scores were the results used in sensitivity analyses that
were described in Chapter 4.
Table 3 Database File Output
LSOAcentro the field we elect to copy from the demand points layer
DemandID OID of each demand point in the analysis
m1_SupID OID of its nearest supply point
m1_Dist distance/time to the nearest supply point
m1_Choice number of supply points within the FCA threshold set
m1_ChoiceW total supply volume within the FCA threshold set
m1_AveD average distance/time to these supply points
m1_AveDW weighted average distance/time to these supply points
m1_fca FCA accessibility score
Source: Mitch Langford, December 2015.
Census tracts were given an identification value (m1_SupID), which represented which
specific hospital or outpatient facility they were closest to. Those results were calculated when
the closest facility network analysis was run. Figure 11, a catchment area map, shows which
census tracts were closet to which individual supply point. A green circle symbol represents each
hospital and clinic location.
35
Figure 11. Catchment Areas.
The catchment numbers listed in Table 4 correspond with supply points denoted by
numbers shown in Figure 11. There is also a column showing the ratios between veterans’
estimations per census tracts and the doctor and nurse practitioner count per catchment area.
36
Table 4. Nearest Supply Catchment Data.
Catchment
Number
Nearest
Supply Point
Veteran
Estimation
Total
Closest
Facility
Catchment
Doctor
Nurse
Practitioner
Count
Ratio
Between
Veteran
Estimates
and Doctor
& Nurse
Practitioner
Census
Tracts
Total Per
Catchment
1 Antelope
Valley VA
Clinic
19,254 3 1:6418 83
7 Cabrillo VA
Clinic
9,960 1 1:9960 87
2 East Los
Angles VA
Clinic
7,706 1 1:7706 127
3 Gardena VA
Clinic
43,668 2 1:21834 299
10 Los Angeles
VA Clinic
41,975 4 1:10494 567
4 San Gabriel
Valley VA
Clinic
38,938 2 1:19469 271
5 Sepulveda
VA Medical
Center
43,729 23 1:1901 371
9 VA Long
Beach
Healthcare
System
11,125 64 1:174 60
8 West Los
Angeles VA
Healthcare
System
32,882 68 1:484 255
6 Whittier/Santa
Fe Springs
VA Clinic
30,920 4 1:7730 221
37
The methods described above were used to identify gaps in spatial accessibility for
veterans in Los Angeles County. The implemented methodology can be duplicated or further
expanded upon by the readers of this manuscript.
38
Chapter 4 Results
This chapter examined the gaps in veteran access to VA primary care clinics in Los Angeles
County using the E2SFCA method and taking into account uncertainty in the ACS data. It was
noted that although veterans had access to facilities situated throughout the county, there were
some areas with no access at given drive times and other areas that had more accessibility than
others. This variation was produced by drive time distances and by differing ratios of access to
healthcare practitioners relative to the number of veterans. The E2SFCA method was used to
examine the relationship between the veteran locations and access to primary care clinics and to
assess the spatial accessibility score results.
The core model used represented a decay bandwidth of 50. Then sensitivity analyses
were performed which produced results from different decay bandwidths values. The highest
decay bandwidth is then taken as a core model, which serves as the baseline to test both
uncertainty in the ACS counts of veterans and various scenarios that could increase or smooth
variations in coverage across Los Angeles County.
One notable finding is that in the eastern portion of Los Angeles County there was a lack
access for veterans to VA primary care. Therefore, one scenario tested was to increase the supply
volume to a clinic somewhat isolated in the eastern part of the county. This was done by
increasing the supply volume at the San Gabriel Valley VA clinic. Analyzing scores from three
different supply volumes revealed that there was an increase in spatial accessibility scores that
spatially extended further out from the San Gabriel outpatient facility. Related to this, a second
sensitivity analysis was performed by suggesting and modeling for a new location for VA
primary care, using an existing medical building that could work in partnership or provide
options for leasing.
39
4.1. Analysis Overview
The USWFCA2 addin tool mimicked the E2SFCA statistical equation and produced
results which used a Gaussian function and a decay bandwidth option. This author contacted the
addin tools creators and it was determined that a decay bandwidth in the ranges from 20 to 50
were generally considered the best values (Langford and Higgs 2019). The addin tool creator
suggested that it can be used to control the specific shape or rate of decline of the Gaussian decay
style function. It is a number that refers to the actual floating catchment area threshold distance
set, which in this analysis is a 15-minute drive time. Then it is applied in the calculation of the
rate of decay. This ranges from 1.0 at the supply location point, that is where the first catchment
is created to a theoretical minimum of 0.0 at the catchment outer limits. In short, higher decay
values produce a slower rate of decay so that large portions of populations at longer distances are
included in a catchment than with lower decay values. The addin tool creator also suggested
there really is no right answer and decay bandwidth values requires one to assess the best fit for
each type of study that is proposed. Analyzing those two values, showed that the value of 50
produced a more gradual rate of decay while the value of 20 had a rate of decay that was sharper
and did not spatially extend to the fifteen-minute catchment. In Figure 12 and 13 are histograms
showing the distribution of result from the decay bandwidth value 20 and 50. The total census
tract count is on the Y-Axis, and the spatial accessibility scores are on the X-axis. There are
mean and standard deviation vertical line demarcated in both figures with mean on the left and
the standard deviation on the right.
40
Figure 12. Distribution Using Decay Bandwidth Value 20
Figure 13. Distribution Using Decay Bandwidth Value 50
Figures 14 below shows the decay bandwidth value of 50 and the amount of coverage
area it encompassed. The decay bandwidth value of 50 was chosen over a decay band width
value of 20 from results through sensitivity analyses and became the core model. The decay
bandwidth value of the 50 map is a visual observation of how much more coverage was utilized
using a higher value as opposed lower bandwidth value of 20.
41
Figure 14. Decay Bandwidth Value 50.
Figure 15 below, the Decay Bandwidth Value 20 map showed coverage that does not
spatially extend past a 10-minute drive time catchment, which suggested a sharp rate of decay at
or around 10-minute drive time interval. Both maps use Jenks natural breaks and are shown with
no spatial accessibility scores represented by the light grey color. A darker grey showed a lower
bound interval with zero and negative veteran estimation, and the darkest grey showed census
tracts with no veteran estimation. They are visual representations to assess how much of the 15-
minute drive time catchment each decay bandwidth value covered.
42
Figure 15 Decay Bandwidth Value 20.
As discussed in Chapter 2, the choice of the decay bandwidth was important when using
the Gaussian distribution model as it will affect the outcome of the spatial accessibility results.
The Gaussian distribution model, which as the literature suggested and cited within this study, is
part of a gravity model used to identify accessibility for healthcare demand and supply in an
identified location. Testing was undertaken using a decay bandwidth of 20 and 50. The decay
bandwidths and sensitivity analysis results are discussed later in this chapter. Drive time in
minutes was used as the travel impedance. The decay bandwidth of 50 produced results that
reached a threshold boundary of 15-minutes. The threshold boundary was the spatial extent that
was set during the addin tool process and used within the core model.
43
4.1.1. Decay Bandwidth Symbology Comparison
For purposes of direct comparison, the interval classification from the decay bandwidth
20 was imported into the decay bandwidth 50 map. This is shown in In Figures 16 and 17 when
both maps are compared.
Figure 16. Decay Bandwidth 20 Figure 17. Decay Bandwidth
50 with Same Intervals
4.1.2. Decay Bandwidth 20 Testing
The decay bandwidth value of 20 used the same parameters from decay bandwidth 50
test. The only change that was made was the reduction in decay bandwidth to a value of 20. The
value of 20 produced results that did not reach the outer 15-minute catchment. Total census tracts
that were given scores in this analysis were 1,412 with a total veteran estimate of 151,356. As
discussed earlier in this chapter the decay bandwidth value of 20 produced a sharper rate of
decay then that of the decay bandwidth value of 50. The rapid decay in distance created more
census tracts with zero SA scores. The rapid decay started at approximately the ten-minute drive
time catchment. There were 929 census tracts that did not receive a spatial accessibility score.
44
From those 929 census tracts there were an estimated 128,656 veterans who lack accessibility.
As seen in Table 5 below, the percentage of veterans that received no spatial accessibility scores
was 46%. The decay bandwidth value of 20 had 54.1% veteran estimates with spatial
accessibility scores.
Table 5. Decay Bandwidth 20 Coverage.
Decay Bandwidth 20
Census Tract Total
Veteran Estimation Total
Convenient Accessibility 1,412 151,356
(54.1%)
Lack of Accessibility 929 128,656
(46%)
Total 2341 280,012
4.1.3. Decay Bandwidth 50 Core Model
The decay bandwidth value of 50 used a threshold size of 15-minute drive time
impedance. This 15-minute floating catchment became the spatial extent for this, and other
analyses discussed later in this chapter. Any census tracts that fell outside of the catchment area
of fifteen minutes were not assigned a score. Table 6 below, and Figure 15 above showed the
results when the decay bandwidth value of 50 was used. The total demand volume inside the
15-minute catchment was 222,370 estimated veterans. The total demand volume for veterans
outside a 15-minute catchment was 57,642. This showed that out of the 280,012 estimated
veterans inside the county boundary 79.4% were assigned a score and dispersed through 1,969
census tracts. The decay bandwidth value of 50 and its total of 79.4% created a difference in
coverage of 25.3%. Meaning, the value of 20 testing resulted in coverage for 25.3% fewer
veterans in the county than the decay bandwidth of 50.
45
Table 6. Decay Bandwidth 50 Coverage.
Decay Bandwidth 50
Census Tract Total
Veteran Estimation Total
Convenient Accessibility 1969 222,370
79.4%
Lack of Accessibility 372 57,642
20.6%
Total 2341 280,012
4.1.4. Drive Time Analysis and Spatial Accessibility Scores
To better assess differences between a decay bandwidth value of 20 versus 50, a table
was created from results of both analyses. The results were partitioned into drive times of 0-5, 5-
10, and 10-15- minutes. Each increment of drive time had low and high spatial accessibility
scores assigned to a cell. Census tract totals with and without scores were shown to establish
where the lack of coverage existed. The decay bandwidth of 20 produced more census tracts with
zero SA scores.
46
In Table 7 below is an evaluation and comparison of drive time the decay bandwidth 50
showed high and low spatial accessibility scores in each drive time catchment window, where
high scores represent better spatial accessibility. The 0-5-minute drive time from supply points
resulted in a low score of 0.0008 and a high score of 0.083. The total census tracts that were
found in a 5-minute catchment was 345. The 5-10 minutes low score was 0.0002 and the high
score 0.052 which was made up of 1039 total census tracts. At the drive time of 10-15 minutes
the low score was 0.00002 and high Score 0.014, covering a total of 585 census tracts. The best
scores were centered around the three main hospitals and were inside a 0-5-minute drive time.
The Long Beach VA Medical Center, West Los Angeles VA, and Sepulveda VA medical center.
Table 7. Decay Bandwidth 20 and 50 Spatial Accessibility Scores with Drive Time.
Decay Bandwidth 20
Drive Time
Minutes
Low High Total number
of census
tracts per
Drive Time
Catchment
With SA
Scores
Total
Veteran
Estimation
Census Tract
Count with
No
Accessibility
0 – 5 0.000794 0.553412 345 35,207 0
5 – 10 0 -0.000001 0.030275 1039 112,477 32
10 – 15 0 - 0.000001 0.000006 585 74,686 525
Total 1969 222,370 557
Decay Bandwidth 50
Drive Time
Minutes
Low High Total Census
Tracts per
Drive Time
Catchment
with SA
Score
Total
Veteran
Estimation
Census Tract
Count with
No
Accessibility
0 – 5 0.000824 0.083927 345 35,207 0
5 – 10 0.000207 0.052985 1039 112,477 0
10 – 15 0.000023 0.014952 585 74,686 0
Total 1969 222,370 0
47
The decay bandwidth value of 20 had a sharp decline in distance at the ten-minute
catchment boundary. Almost all spatial accessibility scores beyond ten-minutes from their
respective supply point were given a score of zero. This analysis showed that a decay bandwidth
value of 20 would not produce accurate spatial accessibility scores inside a fifteen-minute
catchment area. As seen in Table 7 above the census tracts started to receive zero spatial
accessibility scores at the 5-10- minute drive time, and of those 32 tracts in that drive time
received a zero spatial accessibility score. There was a steep rise in tracts with no scores at the
10-15-minute interval.
4.2. Source of Error
A scale multiplier that was built in the addin tool was used in this thesis to assess the
spatial accessibility scores. SA scores are inherently small with many zeros to the right of
decimal which can be cumbersome when assessing scores from many iterations. Spatial
accessibility scores that the addin tool produced used a scale multiplier of 10. The scale
multipliers function was to decrease the number of zeros to the right of decimal to ease in the
analysis of different scores, plotting of maps, and to preserve precision.
One example and results from the core model (decay bandwidth 50) with the SA scores
and scale multiplier set to ten. The highest spatial accessibility score was a 0.083 and was a
census tract that the VA hospital in Long Beach occupies. The Long Beach VA had a supply
volume 64, and the census tract centroid had a 0.1755 drive time in minutes from the nearest
supply point. That census tract also had a demand volume (veteran estimation) of 56.
Conversely, the lowest non-zero spatial accessibility score was a census tract in the San Pedro
area at 0.00002 with a drive time distance from supply at 14.956 minutes. The total veteran
estimation for that census tract was 239, with the closest supply point at the Gardena VA
48
Clinic.
49
In this study the highest (best) scores emanated around the three main hospitals that had high
supply volumes. There were census tracts in this study that did not receive spatial accessibility
scores, because they were tracts with zero estimations or had lower bound scores that were zero.
4.3. Uncertainty Analysis
The upper and lower boundary maps shown later in this section represented ACS data
with upper and lower confidence intervals for each tract. The upper and lower estimates for
veteran population at the 90% confidence level, as provided in the ACS data, were tested on the
core model to show how much and where results would change if the upper or lower scenarios
were true across the study area. The analysis used ACS data with corresponding MOE in each
census tract. The MOE value in each tract represented a confidence level of 90% that the MOE
was accurate using the standard error calculation of 1.645. This indicated the veteran estimate in
the lower intervals was the census tract population minus the MOE. The upper intervals
published for each census tract included the census tract population plus the reported MOE for
the tract.
The values in the Table 8 below represented a census tract in Los Angeles County within
this study with the highest estimation of veterans and the corresponding plus or minus, upper and
lower MOE. It represented the equation to find the upper and lower bound intervals.
Table 8 Confidence Interval Equation.
Veteran Estimation MOE
861 - 201 = 660 Lower Bound of the Interval
861 + 201 = 1062 Upper Bound of the Interval
50
The process for finding the coefficient of the variation (CV) started by finding the
standard error which was found by dividing the MOE by 1.645. The 1.645 value is what the US
Census Bureau referenced as 90% data confidence. The CV was another way to measure
uncertainty in the data. The CV is the standard error divided by each veteran estimate. This
author calculated the CV values in an excel table from conversion equations provided by the
census bureau. The highest scores from CV results were census tracts with low estimates and
relatively high MOEs. Most veteran estimations per census tract that received a high CV score
and had MOE values that were half of or above the estimate. The highest score was from a
census tract with a CV of 182.37 and a veteran estimation value of one and an MOE of three. An
example of a census tract that was considered moderately reliable was one which had a CV score
of 20.26 with an MOE of 143 and a veteran estimation of 429. The lowest score and most
reliable had a CV value of 13.3, with a veteran estimation of 388 and MOE of 85.
One way to visualize the values of the CV was to group them into three classes. As
discussed in Chapter 2 and seen in Figure 18, CV values that were 15 or less were considered
reliable. Values that were between 15 and 30 were considered moderately reliable and anything
above 30 were considered not reliable. There were 11 reliable census tracts, 846 moderately
reliable, and 1437 were not reliable.
51
Figure 18. Coefficient of Variation Map.
The upper and lower bound interval maps shown in Figures 19 and Figure 20 below were
processed using the core model parameters. The color scheme and graduated symbology was
matched, yet the values could not be. This was because the highest spatial accessibility score
from the lower bound was larger than the highest score from the upper bound results. This
created 265 census tracts with negative veteran estimation and thirty-one census tracts with zero
estimates. The census tracts with negative and zero lower bound interval estimates were
52
dispersed throughout the county. There is also symbology using shades of grey to represent
census tracts with no veterans, tracts with no veterans due to the lower bound assessment, and
tracts that received no spatial accessibility scores. The confidence interval equation using the
lower boundary resulted in census tracts with negative values. Because the E2SFCA statistical
equation is complex, the author of this thesis manually converted all census tracts with negative
values to test if results from zeros or negatives would alter results. The results of converting
census tracts with negative values to zeros did not produce different results.
53
Figure 19. Lower Boundary Interval Map.
54
Figure 20. Upper Boundary Interval Map
4.4. Supply Volume Increase – San Gabriel Valley VA Clinic
One of the objectives of this study was to help VA administrators understand how the
E2SFCA model could be used to assess changes in service levels or if expanded locations for VA
primary care in Los Angeles County is warranted. The San Gabriel Valley VA clinic located in
the city of Arcadia became part of the focus for assessing the lack of accessibility in the eastern
portion of the county because it is an existing location with a relatively low service capacity
55
equivalent to two physicians or nurse practitioners. There were an estimated 24,845 veterans that
were dispersed throughout 182 census tracts that made up a catchment of 15-minutes of drive
time closest to the San Gabriel Valley Clinic. In the analysis of increased volume at that location,
two iterations using the core model parameters were undertaken which used volume as a variable
which increased with each test. The results were analyzed, and SA scores were partitioned into
drive time increments.
Table 9. San Gabriel Valley VA Clinic Drive Time Analysis using Decay Bandwidth 50
Drive
Time in
Minutes
&
Census
Tract
Count
Core Model
Supply Volume 2
Spatial Accessibility
Scores
Supply Volume 3
Spatial Accessibility
Scores
Supply Volume 5
Spatial Accessibility
Scores
Veteran
Estimation
Low High Low High Low High
0 - 5
22
0.00183 0.002642 0.002754 0.003963 0.004575 0.00660 3,009
5 - 1 0
71
0.00050 0.00180 0.00075 0.00270 0.00125 0.00451 9,170
10 - 15
89
0.00005 0.00086 0.00008 0.00109 0.00016 0.00154 12,666
In Table 8 above, drive time intervals of 0-5, 5-10, and 10-15 minutes of drive time from
supply were assessed. SA scores from low to high along with veteran estimations and census
tract totals were compared. The building footprint at the San Gabriel Valley VA appeared unable
to accommodate more than five practitioners due to size, therefore testing was not done with a
supply volume higher than five. The 0-5-minute high SA score was 0.002 and was improved to a
higher SA score of .006 when the volume of 5 was added. The 5-10-minute drive time interval
had a high score of 0.001. When the supply volume was increased to five physicians or nurse
practitioner at that location, the high score improved to a value of 0.00451. By adding more
supply volume, the access became better to the estimated 9170 veterans in the drive time interval
56
of 5-10 minutes. The 12,666 veteran estimate occupying the 10-15-minute drive time interval
had a high score 0.00086 for a supply volume of two. An increased volume to five in that same
drive interval increased the SA score to 0.00154.
The volume of three was also chosen to test as it is the average number of practitioners
(volume) of the identified primary care facilities in Los Angeles County. The total outpatient
supply volume of twenty was divided by the total amount of primary care facility which equaled
2.8 practitioners per primary care facility. This value was rounded up to three to make a simple
modeling estimate. In Figure 21 below, the map shows increased supply volume at the San
Gabriel Valley VA Clinic. All three maps used the same parameters from the core model
analysis. The only variable changed was increasing the supply volume between iterations. The
bottom right square shows the legend and symbology that all three maps share which were seven
classes using graduated colors, natural breaks (Jenks).
57
There is a 15-minute catchment boundary represented by the time it took to reach a
demand centroid from the San Gabriel Valley VA supply point. They grey census tracts that
extend past the catchment boundary were tracts that did not receive a SA score. In the map on
the top left, VA location name is shown for visual reference. The top left map (A) uses seven
classes with Jenks classification. It showed that there were nine census tracts greater than a value
of 0.002 and less than a value of 0.006. When the supply volume was increased to three, shown
on the map on the top right (B), there were 39 census tracts that had values less than 0.006 and
greater than 0.002. Increasing the supply volume to five (C) showed there was a total of 64
census tracts had SA scores that ranged from 0.002 and 0.006488. The census tract the San
Gabriel Valley VA occupies had a score that now ranged from 0.006 to 0.013. The score for that
census tract using a supply volume of two was 0.002. When the volume was raised to three, the
score improved to a 0.003. The increase in supply using a volume of 5 showed that the census
tract with the VA clinic was raised to 0.006 SA score.
58
Figure 21. San Gabriel Valley VA Clinics with Increased Supply Volume.
4.5. Review of Additional Accessibility Location
As the result indicated above at the San Gabriel Valley VA Clinic, changing supply
volume can increase accessibility. Adding additional locations in the south eastern portion of Los
Angeles County can also be used to test improving veteran accessibility. This author also
reviewed VA medical center locations and primary care facility locations outside of the Los
Angeles County borders. This was accomplished by assessing the distance of the cities nearest
the Los Angeles County borders to the next closest primary care facility location within a
bordering but different county. The findings are driving distances in miles using Google Maps.
B
59
Reviewing the nearest VA location in Ventura County that borders the west side of Los
Angeles County is a VA primary care facility in Oxnard which is 25-28 miles to the western
portion of Los Angeles County border. The closest VA primary care facilities on the northern
portion of Los Angeles County is in Bakersfield which is in Kern County. The distance to that
facility is 89 miles from Lancaster and 48 miles from Gorman, two rural cities in the Antelope
Valley of Los Angeles County. Orange County borders Los Angeles County on the southeast
section of the county. The VA primary care facility closest to that border is in Anaheim. From
the various cities along Los Angeles County border with Orange County, the distance is 5-21
miles. The closest location outside of Los Angeles County where the coverage gap was identified
in this project is located on the eastern side of the county and borders San Bernardino County. It
is the VA primary care facility PCF in Rancho Cucamonga which is 12-21 miles from the cities
located in the east portion of Los Angeles County.
A short discussion of an additional site to consider improving veteran access to primary
health care based on the outcome of this research project is worth reviewing within this thesis.
Site selection involves identifying criteria and analyzing suitable sites within Los Angeles
County. Mishra et al. (2019) identified five criteria to evaluate a potential suitable site for
healthcare purposes. They included distance to the nearest facility, accessibility to existing
healthcare locations, the ratio of the supply to the demand population, the actual population of
the area to be served, the ease of access using road transportation and the health needs of the
population to be served. Parvin et al. (2020) completed a study of accessibility and site
suitability in a location in India with the objective of using GIS with spatial and non-spatial data.
They indicated that analyzing accessibility is the first consideration to evaluate a potential new
site for a healthcare facility. As written in the thesis, although not as a site suitability study, the
60
use of spatial models and non-spatial dimensions took into consideration accessibility along with
availability of existing primary care services and distance decay from supply to demand. Other
considerations not discussed in this project to analyze site suitability are zoning regulations for
the proposed site, and the size of the land parcel under consideration (Sarain 2019). Also, if
proposing to use an existing physical location, does the site have capacity to accommodate
practitioners, and demand volume. The ease of use to either public transportation or road access
is another consideration.
An existing potential site location that the VA could explore for additional veteran
primary care can be viewed in Figure 22. The map is a broad overview of Los Angeles County
that showed how county wide SA scores would look when visualized with a new location added
in the city of Diamond Bar. The study area below used the same symbology as the core model
with a decay bandwidth of 50. Although this study did not have a full site suitability analysis,
some suitable exiting locations for expanded veteran primary were analyzed. The most suitable
existing locations that have medical offices and offer other outpatient services, including a
pharmacy, was the Kaiser Permanente location in Diamond Bar. Three practitioners were the
average from the total supply volume of all the outpatient VA clinics and this number was used
when assessing the potential Diamond Bar location. The lower bound interval assessment
illustrated there was 265 tracts with negative lower bound scores and thirty-one zero scores.
From those scores only five census tracts with negative lower bound intervals ended up in a 15-
minute drive time catchment centered around the Kaiser location. In comparison to 79.41% of
coverage from the core model the new location using the core model parameters lifted coverage
to 85.02%, with 123 census tracts that now routed to a supply point within a newly created
floating catchment of 15-minutes around that Diamond bar location.
61
The analysis from the core model proved useful as baseline results. Moreover, it was
useful to compare scores from the results of the sensitivity analyses to determine what bandwidth
values was appropriate. Increasing the supply volume at the San Gabriel Valley VA clinic
showed that scores did improve when supply volume was raised. Adding a location in the eastern
portion of the county proved that adding a supply point improved accessibility.
Figure 22. Additional Outpatient Facility Location.
62
4.6. Overall Summary of Results
In summary, the results of the E2SFCA showed supply to demand accessibility gaps for
veterans in the eastern portion of Los Angeles County. Based on the E2SFCA methodology
using drive time decay of 15-minutes to access primary care in Los Angeles County, gaps were
identified. Accessibility scores were not only the result of the distance to a supply location but
also the supply number compared to the veteran estimates in the closest and nearby census tracts.
The addition of testing increasing supply volume in one location had improved accessibility. The
potential addition of another site also changed veterans' accessibility scores in census tracts
surrounding a new location within the 15-minute catchment.
63
Chapter 5 Discussions and Conclusions
This thesis was designed to assess if gaps exist in veteran primary health care access in Los
Angeles County based on supply and demand of the services needed. The VA has mandated
drive time limits in order to provide veterans with healthcare in locations that are both accessible
and available. The E2SFCA method resulted in detailed spatial accessibility scores in the context
of underlying uncertainty of veteran estimates in the ACS data. The results were determined
through sensitivity analysis. The results indicated that the area around the San Gabriel Valley
VA had the least supply volume to meet the estimated veteran demand. Corresponding
neighborhoods to the east of the San Gabriel Valley VA clinic also had low SA scores. In
addition, the eastern part of Los Angeles County had the largest area with low accessibility
scores. Census tracts with high spatial accessibility scores were all centered around the three
main hospitals with high supply volume. In addition this project offered a location of an existing
healthcare facility that has potential for use by the VA decision makers to provide additional
primary care. This chapter discusses the methods used in this thesis with results discussed in
Chapter 4. The next section analyzed in detail the limitation of this project. The last section
discussed future research and reviewed conclusions.
5.1. Review of The Methods
The methodology, as stated above, that was used in this study was the E2SFCA gravity
model with the use of the Gaussian distribution function to simulate travel time distance decay.
This gravity model was chosen as it integrates the availability and accessibility as a measure of
healthcare service from a spatial level. The choice of the E2SFCA method incorporating a
Gaussian distance decay function and utilizing the USWFCA2 accessibility tool was the
methodology used to perform the testing. As discussed earlier in this thesis, the use of the
64
USWFCA2 accessibility tool and decay bandwidth settings allowed for classification of drive
time zones of 0-5, 5-10, and 10-15 minute distance decay from the demand to each supply point.
The Gaussian model was used to simulate the distance decay function. The primary purpose of
the USWFCA2 accessibility tool established the rate of decay using the Gaussian model and was
used to facilitate the computation of the E2SFCA measure of spatial accessibility. Langford
(2015) discussed the Gaussian model typical decay bandwidths and the use of the USWFCA2
accessibility tool to simulate distance decay. According to Langford (2015), 50 is the most
typical decay bandwidth used, but using values from 20-50 can also be acceptable depending on
the research. This researcher initially tested a bandwidth of 20 when assessing which value
would best simulate the distance decay parameters for this thesis. The result of the Gaussian
model 20 decay bandwidth tested produced a steep rate of decline in the middle, and there were
no veteran estimates beyond 10 minutes. Examining the decay bandwidth of 50 produced the
results that showed the best coverage. The creation of the VA hospitals and primary care
facilities layer was obtained from the most up to date data sources. The supply volume numbers
that included physicians and nurse practitioners were acquired from telephone calls to the
facilities. The demand volume was represented by the veteran estimates in each census tract in
the county. This thesis will give future researcher information to understand better the spatial
complexities of evaluating healthcare accessibility from many different viewpoints.
5.2. Limitations
The limitations identified in this thesis can provide information to future researchers
assessing and analyzing healthcare accessibility in different locations. The limitations discussed
below include the MAUP, ACS, and the uncertainty, 15-minute catchment threshold, closest
facility catchment, accuracy of travel time routes, and neighborhood centroids.
65
5.2.1. Modifiable Areal Unit Problem (MAUP) and ACS Data and Uncertainty
One limitation worth discussing is the issue of modifiable areal unit problem (MAUP).
MAUP is an issue identified in spatial and geographical studies and needs to be considered when
measuring accessibility. According to Tuson et al (2019), counts from census tracts and
boundaries of many areas can be affected by the scale of the data aggregated. MAUP can occur
when geographical units are changed, or if census tract boundaries are be redrawn when census
counts are undertaken. MAUP has two forms; the scale and the zone effects. The scale effect
occurs when the size of the aggregation of units is changed but the analysis is applied to the same
data. With larger units the variation of the data decreases which will affect the spatial
accessibility. The zone effect is when the scale of the analysis is fixed but the zone or shape of
the aggregation units are changed. The zone effect can be the analysis of the zone and not the
data. The focus is on the aggregation of results from the spatial accessibility as a result of the
zone changes. Since this is an ongoing issue in GIS, the results from spatial accessibility studies
should state the reasons for boundary change decisions. The researcher needs to be mindful of
the MAUP when quantifying the data. This study utilized census tract veteran estimate data and
did not change geographical units or existing census tract boundaries. The veteran data estimates
used was obtained from the ACS for a 5-year period from 2012-2017. Although it was the most
accurate, and up to date information to use when this study was written, there is the inherent
issue of the uncertainty of the MOE. The unit of veteran estimation was represented by each
census tract and therefore contained different veteran estimations and MOE for each tract. As
indicated in other limitations listed below tracts were not combined to reduce the MOE even
though combining census tracts into regions can reduce the ACS MOE uncertainty. But if tracts
are combined to reduce the MOE, the issue of MAUP must be considered by future researchers.
66
5.2.2. 15-Minute Catchment Threshold Assessment
Using a 15-minute catchment threshold excluded 57,642 veteran estimates in 372 census
tracts. The mean value of veterans per census tract was 119.6 and was determined by dividing
the total estimates of veterans which was 280,012 by the total number of census tracts value
2341. In Figure 23 below, the area around the Antelope Valley VA had veteran estimates that
were above the mean value of 119.6. The Antelope Valley VA had numerous census tracts with
above average veteran estimates that were not analyzed in this study since they were outside the
15-minute catchment. The 15-minute drive time threshold that was set during the addin tool
setup procedure excluded all tracts that were beyond the catchment boundary from being
assessed. For example, there were 82 census tracts that were assigned to the Antelope Valley VA
Clinic as the closest supply point. Of those 82 census tracts only 36 were counted during the
analysis using the core model parameters. There were 46 census tracts that were not included in
that areas. The excluded tracts were ones that fell outside the 15-minute threshold. In those 36
census tract that were inside the 15-minute threshold there were total veteran estimation of 9172.
The 46 tracts that fell outside the catchment had a veteran estimation total of 10,082.
Figure 23. Antelope Valley Catchment.
67
The map in Figure 24 showed numerous census tracts that were not included in the
analysis because of the 15-minute threshold, these were colored in light grey and considered less
access. The Antelope Valley VA in the northern part of LAC is somewhat isolated from the rest
of the county. This area became a reference guide to the limitation of a 15-minute catchment
results when analyzing limitations with the parameters that were set. The map below Figure 20,
shows a zoomed-in extent of the Antelope Valley VA Clinic. It serves as an example to show
how many census tracts with high veteran estimations. That fell just outside the 15-minute
catchment boundary and were not included in the analysis and thus lacked accessibility.
Figure 24. Antelope Valley Veteran Estimations Values.
68
5.2.3. Closest Facility
The closest facilities were found using drive time as impedance. The limitations of this
data produced results there were not as accurate as it could have been as it did not consider types
of transportation options. It did not consider traffic, stop signs, or red lights that occur when
traveling from an origin to a destination. This would undoubtedly add more travel time when
assessing quickest routes. Public transportation such as trains or bus routes were not assessed.
Los Angeles County has over 15,000 bus stops (Rideshare LA County 2017), and the Metrolink
has 62 train stations (Metrolink 2020). Using that data could have produced SA scores with
higher values in neighborhoods that are spatially located close to train pick up locations, or a bus
stops where a quicker route may have been utilized.
5.2.4. Precision of Travel Times on Routes
An example of a limitation on travel time routes is seen in Figure 25. The route in blue
represented a drive time from the Antelope Valley VA clinic to its corresponding demand
centroid with a total drive time of 15.2 minutes. The other route in red showed a drive time of
15.7 minutes to its demand centroid. Perhaps there is imprecision in the drive time data and both
census tracts just outside the 15-minute drive time threshold should have been counted in the
analysis. Considering the isolation of that area all census tracts with veteran estimates would
most likely use the Antelope Valley VA clinic.
69
Figure 25 Total Drive Time Routes.
5.2.5. Census Tract Centroids
When assessing limitations using census tract centroids one must consider that using the
center of a census tract does not accurately depict true drive time from supply to demand
locations because of urban sprawl in the area. One example in Figure 26 below showed that a
demand centroid was not centered around the population and the location was in the middle of a
forested recreation area. Figure 24 with a zoomed extent of the study area shows the supply
location at the San Gabriel Valley VA in the city of Arcadia. A census tract with 209 estimated
veterans was isolated and then symbolized with an Environmental Systems Research Institute
(ESRI) base map to show the center of that census tract. That census tract is 9.3 square miles
with a major portion occupying a forest and recreation area. The vast majority of the population
70
of that census tract is located in residential zones along the foothills. The green supply to demand
route has a total drive time of 8.4 minutes. That route time could be shortened if the demand
points were centered more around the population in the foothills.
Figure 26 Demand Centroid Limitations.
5.3. Conclusions
This thesis was undertaken to analyze if gaps in primary healthcare coverage for veterans
in Los Angeles County existed based on drive time impedance. The thesis provided an analysis
of veteran access to exiting primary care VA locations using census tract information. The major
finding of this study indicated gaps in accessibility based on drive time existed in the eastern
portion of the county. The study also resulted in an interesting finding that veteran estimate
concentrations have an impact on accessibility to existing supply sites. The results of this project
71
could facilitate the VA with the ability to monitor accessibility on a re-occurring schedule based
on changes in census data. The analysis also projected a theoretical additional site location in the
southeast portion of the county to increase accessibility. The analysis of the identified limitations
in this study may give future researchers tools to study to improve the spatial accessibility results
of the veterans’ access to primary care. Through the use of data and GIS technology, this thesis
identified the spatial relationships between the veterans and the primary care locations to give
VA planners a better understanding of reviewing where supply may not adequately serve the
veteran demand. Moreover, census tracts were the areal unit used in this analysis. In closing one
could surmise that using a smaller aggregation of data such as blocks groups would improve
accuracy and spatial accessibility.
72
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Asset Metadata
Creator
McCullen, Patrick George
(author)
Core Title
Spatial analysis of veteran access to healthcare in Los Angeles County
School
College of Letters, Arts and Sciences
Degree
Master of Science
Degree Program
Geographic Information Science and Technology
Publication Date
12/13/2020
Defense Date
08/21/2020
Publisher
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Tag
American Community Survey,Census Bureau,coefficient of variation,Enhanced Two-Step Floating Catchment Area Method,Los Angeles County,margin of error,OAI-PMH Harvest,University of South Wales Floating Catchment Area 2,veterans,Veterans Administration
Language
English
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Vos, Robert O. (
committee chair
), Oda, Katsuhiko (
committee member
), Wu, An-Min (
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)
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mccullen@usc.edu,patrickmw43@msn.com
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Tags
American Community Survey
Census Bureau
coefficient of variation
Enhanced Two-Step Floating Catchment Area Method
margin of error
University of South Wales Floating Catchment Area 2
veterans