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An enhanced two-step floating catchment area (E2SFCA) method
for measuring spatial accessibility to primary care physicians
Wei Luo
,YiQi
Department of Geography, Northern Illinois University, Davis Hall 120, DeKalb, IL 60115, USA
article info
Article history:
Received 23 December 2008
Received in revised form
29 May 2009
Accepted 2 June 2009
Keywords:
Two-step floating catchment area
Spatial accessibility
Primary care physician shortage
Gravity model
GIS
abstract
This paper presents an enhancement of the two-step floating catchment area (2SFCA) method for
measuring spatial accessibility, addressing the problem of uniform access within the catchment by
applying weights to different travel time zones to account for distance decay. The enhancement is
proved to be another special case of the gravity model. When applying this enhanced 2SFCA (E2SFCA) to
measure the spatial access to primary care physicians in a study area in northern Illinois, we find that it
reveals spatial accessibility pattern that is more consistent with intuition and delineates more spatially
explicit health professional shortage areas. It is easy to implement in GIS and straightforward to
interpret.
&2009 Elsevier Ltd. All rights reserved.
1. Introduction
Access to primary healthcare is recognized as an important
facilitator of overall population health (Guagliardo, 2004) because
primary care is the first line of defense for the population and
a critical part of preventive care. Good primary care can prevent
or reduce unnecessary expensive specialty care (Lee, 1995;Luo,
2004). To ensure adequate access to primary care, health service
planners and policy makers need accurate and reliable measures
of accessibility so that true physician shortage areas can be
accurately identified and resources allocated to those needy areas
to alleviate the problem.
Access to health care in a given location is influenced by many
factors, including the availability of health services in the area
(supply), the number of people living in that location (demand),
the population’s health status, the socio-economic and financial
resources available to the population, people’s knowledge about
health and the health care system, and geographical impedance
between population and health services (Aday and Andersen,
1974). Health care accessibility has been classified into two broad
categories: revealed accessibility and potential accessibility
(Joseph and Phillips, 1984;Phillips, 1990;Thouez et al., 1988),
with the former focusing on actual use of health care services and
the latter emphasizing the aggregate supply of medical care
resources available in an area. Based on spatial factors (e.g.,
geographic location, distance), non-spatial factors (e.g., social
class, income, age, sex, etc; Joseph and Phillips, 1984) and their
interactions (Meade et al., 1988) each of the broad categories can
be further divided into spatial accessibility and non-spatial
accessibility (i.e., the 2 2 matrix of Khan, 1992). This paper will
focus only on the methodology of measuring potential spatial
accessibility, because identifying where the truly underserved
populations are located is the essential first step toward any
meaningful and effective government intervention programs (Luo,
2004;Guagliardo, 2004). The integration of both spatial and non-
spatial factors has been discussed elsewhere (Wang and Luo,
2005) and the enhancement discussed here can be easily
incorporated into that framework.
1.1. Background on physician shortage designation in the US
Among the many factors that influence access to health care
services, two of them are critical: physician supply and population
demand. Both of these are spatially distributed, but it is rare that
their distributions perfectly match (Luo, 2004). Health care access
problems are especially pronounced, for example, in rural areas
and impoverished urban communities (COGME, 2000;Rosenblatt
and Lishner, 1991). The US federal government spends about
$1 billion a year on programs designed to alleviate health care
access problems, including providing incentives or awarding
financial assistance to providers serving designated shortage
areas through the National Health Service Corps Program, the
Medicare Incentive Program, and the J-1 visa waiver program,
among others (GAO, 1995).
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Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/healthplace
Health & Place
1353-8292/$- see front matter &2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.healthplace.2009.06.002
Corresponding author. Tel.: +1 815 753 6828; fax: +1 815753 6 872.
E-mail address: wluo@niu.edu (W. Luo).
Health & Place 15 (2009) 1100–1107
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These US federal programs, administrated by the Department
of Health and Human Services (DHHS; GAO, 1995;Lee, 1991),
depend on two main systems for identifying shortage areas. One
designates health professional shortage areas (HPSAs), the other
medically underserved areas or populations (MUAs/MUPs). A
summary of the historical development of the two systems can be
found in Ricketts et al. (2007). Briefly, the criteria for designating
HPSA are the following: (1) the geographic area involved is
rational for the delivery of health services, i.e., a rational service
area; (2) the ratio of population to full-time-equivalent (FTE)
physicians exceeds a specified shortage criterion within the area;
and (3) resources in contiguous areas are overutilized, excessively
distant, or otherwise inaccessible. For primary care HPSA, the
specified threshold population-to-physician ratio is 3500:1 (or
3000:1 if there are unusually high needs). In addition, the HPSA
can also be designated for a population group (e.g., low-income
population) or facility (e.g., a correctional center). MUAs or MUPs
are designated on the basis of four factors of health service need:
(1) population to FTE primary care physician ratio; (2) infant
mortality rate; (3) percentage of the population with incomes
below the poverty level; and (4) percentage of the population
aged 65 and older. These four variables are applied to a rational
service area to obtain a single Index of Medical Underservice
(IMU) score ranging from 0 to 100, with 0 representing the most
underserved and 100 the best-served areas. A rational service area
with a score of 62 or less qualifies for designation as a MUA/MUP.
The rational service area concept used in both HPSA and MUA/
MUP is defined for non-metropolitan areas as (a) a whole county
or (b) groups of contiguous counties, minor civil divisions, or
census county divisions with population centers within 30 min
travel time of each other; for metropolitan areas, the rational
service area is defined as a group of census tracts that represent a
neighborhood of homogeneous socio-economic and demographic
characteristics. The existing practice of designating either an HPSA
or MUA/MUP is a tedious process that involves complicated rules
for defining the rational service area, estimating FTE, evaluating
contiguous resources, and so on. Detailed information on the
designation process is presented in DHHS (1980),Lee (1991),GAO
(1995) and the website of Health Resources and Services
Administration (HRSA), US Department of Health and Human
Services (http://bhpr.hrsa.gov/shortage/index.htm, last accessed
March 20, 2009).
Although DHHS shortage area designation methods also take
into account some non-spatial factors such as age and socio-
economic status, they are primarily regional availability measures
that quantify the distribution of supply versus demand within
a predefined region, often expressed as a ratio of population
to practitioner (or its variation; Joseph and Phillips, 1984). The
advantage of such a regional availability approach is that it
is simple and thus straightforward to implement as the data for
physicians and population are readily available and such bound-
aries can be easily located in the real world (Florin et al., 1994). In
addition, it is also convenient to administer federal funding
programs because the government infrastructure is already in
place (Florin et al., 1994).
However, two implicit assumptions found in the regional
availability approach draw sharp criticisms (e.g., Kleinman and
Makuc, 1983;Wing and Reynolds, 1988): (1) that people within
the region have equal access to the physicians within the same
region (i.e., the subregion variation of supply and demand and
‘‘distance decay’’ of utilization behavior are ignored) and (2) that
people within the region do not go beyond that region to seek care
(i.e., the boundary of the region is impermeable or self-contained).
These assumptions are not always true in the real world (Klein-
man and Makuc, 1983;GMENAC, 1980;Wing and Reynolds, 1988;
GAO, 1995;COGME, 1998). They also have different requirements
of the scale of the data. The first assumption is realistic only with
spatially disaggregated data (e.g., census tract or even smaller
areal units) as described by Bullen et al. (1996),Curtis and Taket
(1989), and Kivell et al. (1990), whereas the second assumption
requires spatially aggregating data to higher levels (e.g., groups of
counties; Makuc et al., 1991).
Although step (3) of the HPSA method is intended to consider
adjacent areas, the physician-to-population ratios are still calcu-
lated within their respective boundaries and the actual interaction
across boundaries is not accounted for. Even the recent proposed
revisions of the shortage area designation (DHHS, 1998;Ricketts
et al., 2007) are still primarily regional availability measures.
The fact that the whole county or group of contiguous counties
can still be defined as rational service areas in the current DHHS
systems suggests that the existing methods can easily lead to
overestimation in some areas and underestimation in others, and
thus funding for programs aimed at alleviating access problems
based on such designation may not be channeled to where it is
most needed (GAO, 1995).
1.2. Measures of potential spatial accessibility
The problems of regional availability measures have been long
recognized in geography (e.g., Openshaw and Taylor,1981), but are
still not well resolved. This is partially due to the complexity
of the issue, i.e., both the supplies and demands are spatially
distributed and are likely overlapping, and competition exists
among suppliers and consumers (e.g., Huff, 1963, 1964). The
alternative to regional availability measures is the regional
accessibility approach, which uses a gravity model formulation
to factor interaction between supply and demand located in
different regions with distance decay, thereby addressing the
problems of the regional availability approach (Weibull, 1976;
Joseph and Bantock, 1982;Joseph and Phillips, 1984;Shen, 1998;
Huff, 2000;Wang and Minor, 2002;Guagliardo, 2004;Yang et al.,
2006). The gravity model as applied to measure access to
physician usually takes the following form:
A
G
i
¼X
n
j¼1
S
j
d
b
ij
P
m
k¼1
P
k
d
b
kj
(1)
A
G
i
is the gravity-based index of accessibility at population
location i, where nand mare the total numbers of physician
locations and population locations, respectively. The denominator
term represents a measure of the availability of physicians at
location jto all population (P
k
,k¼1, 2, y,m). S
j
is the number of
physicians at location j;d
kj
and d
ij
are the distance or travel time,
and
b
is the friction-of-distance coefficient.
While conceptually more complete, a gravity model like this
is not intuitive to interpret and requires more data input to
calculate: the location of supply and demand (Joseph and Phillips,
1984), traffic network, and travel time analysis between supply
and demand. In addition, the frictional coefficient
b
in distance
decay function has to be determined by physician–patient
interaction data and may be region specific (Huff, 2000).
The two-step floating catchment area method (2SFCA), first
proposed by Radke and Mu (2000) but later modified by Luo and
Wang (20 03a, b), is a special case of gravity model. It not only has
most of the advantages of a gravity model, but is also intuitive
to interpret, as it uses essentially a special form of physician-to-
population ratio. The method is implemented in the following two
steps (Luo and Wang, 2003b;Wang and Luo, 2005):
Step1: For each physician location j, search all population
locations (k) that are within a threshold travel time (d
0
) from
location j(this is the catchment of physician location jor
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W. Luo, Y. Qi / Health & Place 15 (2009) 1100–1107 1101
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catchment j), and compute the physician-to-population ratio, R
j
,
within the catchment area:
R
j
¼S
j
P
k2fd
kj
d
0
g
P
k
(2)
where P
k
is the population at location kwhose centroid falls
within catchment j(d
kj
rd
0
), S
j
the number of physicians at
location j, and d
kj
the travel time between kand j.
Step 2: For each population location i, search all physician
locations (j) that are within the threshold travel time (d
0
) from
location i(that is, catchment area i), and sum up the physician-
to-population ratios (derived in step 1), R
j
, at these locations:
A
F
i
¼X
j2fd
ij
d
0
g
R
j
¼X
j2fd
ij
d
0
g
S
j
P
k2fd
ij
d
0
g
P
k
(3)
where A
F
i
represents the accessibility of population at location ito
physicians based on the two-step floating catchment area method,
R
j
is the physician-to-population ratio at physician location j
whose centroid falls within the catchment centered at population
location i(i.e., d
ij
rd
0
), and d
ij
the travel time between iand j.A
larger value of A
F
i
indicates a better access to physicians at that
population location. The first step assigns an initial ratio to each
catchment (or service area) centered at physician locations, and
the second step sums up the initial ratios in the overlapping
service areas where residents have access to multiple physician
locations. Note that Eq. (3) is basically a ratio of physician (supply)
to population (demand), with only selected physicians and
population entering the numerator and denominator.
The 2SFCA method has been used in a number of recent studies
measuring health care accessibility (e.g., Guagliardo, 2004;Albert
and Butar, 2005;Yang et al., 2006;Langford and Higgs, 2006;
Wang, 2007;Cervigni et al., 2008;Wang et al., 2008). However,
it has two limitations (Luo and Wang, 2003b): (1) it does not
differentiate distance impedance within the catchment (i.e., all
population locations within the catchment are assumed to have
equal access to physicians) and (2) it is a dichotomous measure
(i.e., all locations outside of the catchment have no access at all).
Several studies since then have attempted to address the short-
comings. Guagliardo (2004) proposed using a kernel density (KD)
function to approximate the distance decay for both physician and
population and obtaining provider-to-population ratio based on
physician density raster and population density raster. Yet, his
study used a uniform base radius (3 miles) for the KD function,
which is equivalent to the straight-line distance for the catch-
ment. Yang et al. (2006) compared the KD method with 2SFCA and
found that 2SFCA performs better than KD, but pointed out the
need to vary the radius of service area according to the type of
provider or the type of neighborhood.
In their study of measuring access to cancer care facilities in
the US, Alford et al. (2008) introduced Gaussian weights to the
demand side (second step) of 2SFCA to account for the distance
decay and they used the gridded raster population data LandScan
developed by the Oak Ridge National Laboratory (ORNL). None-
theless, they did not apply Gaussian weights to the supply side
(first step), nor did they offer any theoretical linkage to gravity
model.
The University of New Mexico Division of Government
Research developed an unpublished model that divides the space
around each physician zip code centroid into three circular zones
(http://www.unm.edu/dgrint/dgr.html, last accessed March 20,
2009). The closest zone (o35 miles) is friction -free. The farthest
zone (4100 miles) is considered inaccessible, and for the zone in
between, physician service is discounted by the inverse of square
of distance. This method uses zip code for both population and
physician, which may result in loss of resolution and the
introduction of errors. It uses straight-line distance, rather than
street network distance or travel time, which are better measures
of impedance (Wang and Minor, 2002).
Next we will synthesize these previous ideas in the enhanced
two-step floating catchment area method to address the short-
comings, while maintaining theoretical association with the
gravity model and its accompanying advantages.
2. Methodology
Building on previous research, this paper presents an enhance-
ment to the 2SFCA method by applying weights to differentiate
travel time zones, in both the first step and the second step,
thereby accounting for distance decay. In the following discussion,
we assume that the population data is in the gridded raster format
such as LandScan. The same principle applies to vector-based
population data. In order to differentiate accessibility within a
catchment, multiple travel time zones within each catchment are
obtained using the ArcGIS Network Analyst and assigned with
different weights according to the Gaussian function (Kwan, 1998;
Wang, 2007). The method is implemented in two steps:
Step 1: The catchment of physician location jis defined as the
area within 30-min driving zone (Lee, 1991). Within each
catchment, compute three travel time zones with minute breaks
of 0–10,10–20 and 20–30 min (zones 1–3, respectively). Search all
population locations (k) that are within a threshold travel time
zone (D
r
) from location j(this is catchment area j), and compute
the weighted physician-to-population ratio, R
j
, within the catch-
ment area as follows:
R
j
¼S
j
P
k2fd
kj
2D
r
g
P
k
W
r
¼S
j
P
k2fd
kj
2D
1
g
P
k
W
1
þP
k2fd
kj
2D
2
g
P
k
W
2
þP
k2fd
kj
2D
3
g
P
k
W
3
(4)
where P
k
is the population of grid cell kfalling within the
catchment j(d
kj
AD
r
), S
j
the number of physicians at location j,d
kj
the travel time between kand j, and D
r
the rth travel time zone
(r¼1–3) within the catchment. W
r
is the distance weight for the
rth travel time zone calculated from the Gaussian function,
capturing the distance decay of access to the physician j.
Step 2: For each population location i, search all physician
locations (j) that are within the 30 min travel time zone from
location i(that is, catchment area i), and sum up the physician-to-
population ratios (calculated in step 1), R
j
, at these locations as
follows:
A
F
i
¼X
j2fd
ij
2D
r
g
R
j
W
r
¼X
j2fd
ij
2D
1
g
R
j
W
1
þX
j2fd
ij
2D
2
g
R
j
W
2
þX
j2fd
ij
2D
3
g
R
j
W
3
(5)
where A
F
i
represents the accessibility of population at location ito
physicians, R
j
the physician-to-population ratio at physician location
jthat falls within the catchment centered at population i(that is,
d
kj
AD
r
), and d
ij
thetraveltimebetweeniand j. The same distance
weights derived from the Gaussian function used in step 1 are
applied to different travel time zones to account for distance decay.
Just as 2SFCA has proven to be a special case of the gravity
model, where the friction-of-distance exponent equals 1 in the
catchment and 0 outside (Luo and Wang, 2003b), E2SFCA is also a
special case of gravity model. The Gaussian weight used in E2SFCA
is a way to implement the distance decay term (d
b
kj
and d
b
ij
)in
gravity model. If we assume equal access within each of the three
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W. Luo, Y. Qi / Health & Place 15 (2009) 1100–1107110 2
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travel time zones, zero access beyond the third zone, and replace
the distance decay terms with corresponding weights, Eq. (1)
becomes Eq. (5).
The advantage of E2SFCA is that multiple distance decay
weights substitute the dichotomous 0 and 1 in 2SFCA; so it solves
the problem of not differentiating accessibility within the
catchment and thus is theoretically more analogous to the gravity
model. The discretized consideration of distance decay (by travel
time zones) in E2SFCA is a reasonable approximation to the
continuous gravity model because, in reality, people would not
mind a few minutes of difference in travel time to seek care. This
approximation makes the result of E2SFCA straightforward to
interpret and easy to use, because it is essentially a weighted
physician-to-population ratio. With the advances in GIS technol-
ogy and availability of street network data, E2SFCA can be easily
implemented with GIS software.
3. Study area and data
To illustrate the advantages of the E2SFCA method, we apply it
to examine the spatial accessibility to primary care physicians in a
group of nine counties surrounding DeKalb in northern Illinois
(Luo and Wang, 2003a;Luo, 2004) and compare the results with
those derived from 2SFCA and the HPSA of 2000 (DHHS, 2000).
The nine counties are: Winnebago, McHenry, Boone, Ogle, Kane,
DeKalb, Lee, Kendall, and La Salle and are mostly suburban or
rural, located west of Chicago. (See Fig. 1 for location.) The 2000
census data show that there are 1,239,363 people living in the
study area.
The primary care physician data of Illinois in 2000 were
purchased from the Physician Master File of the American Medical
Association (AMA) via Medical Marketing Service Inc. Primary
care physicians include family physicians, general practitioners,
general internists, general pediatricians, and some obstetrician
gynecologists (Cooper, 1994). This research uses the same dataset
as that in Luo and Wang (2003a) and approximates physician
location with the zip code centroid of the physician’s work
address. The zip code data are used because a significant number
of records in the Physician Master File have only PO Box addresses,
which are not feasible for geocoding. There are 1748 primary care
physicians located in the 163 facilities in the study area. The
analysis of multiple-site practices is important for the accurate
assessment of medical service availability (Cromley and Albertsen,
1993), but since the main focus of the paper is on methodology of
measuring potential spatial access we did not consider multiple-
site practices. The same dataset is used with both 2SFCA and
E2SFCA for comparison. Fig. 1 shows the location of the study
areas, the physician locations by zip code centroids, and the
gridded population data.
Unlike previous work, this research uses US 2000 Census Grid
data created in SEDAC project at Columbia University because
LandScan data are available only for the current year. The data
were derived from the original 2000 census data by taking
population and housing counts to the block level and proportion-
ally allocating the count in the census blocks to a latitude–
longitude quadrilateral grid. The resolution is 30arc-second
(1 km). The regular grid cell in raster data is better for
overlapping travel time zone analysis than vector data, and the
graphic output is usually more aesthetically pleasing. Detailed
information of the US 2000 Census Grid can be found at http://
sedac.ciesin.columbia.edu/ (last accessed, March 20, 2009).
Unlike most prior work using straight-line distances or travel
time estimation, this research uses detailed and updated street
network data that come from 2008 ESRI data CD and ESRI ArcGIS
Network Analyst 9.3 to accurately estimate travel time zones
around physician locations.
4. Results
The result of applying 2SFCA to the study area is shown in
Fig. 2. Two sets of weights are used in the E2SFCA method. Weight
set 1 ( ¼1.00, 0.68, and 0.22 for the three travel time zones)
represents a slower distance decay (Fig. 3), whereas weight set 2
(¼1.00, 0.42, and 0.09) represents a sharper distance decay
(Fig. 4). A comparison of Figs. 2 and 3 shows that, overall, the
two methods generate similar physician accessibility patterns.
The majority of the low accessibility areas are rural areas outside
the major population centers (e.g., Rockford and DeKalb). The
result of E2SFCA reveals more details of accessibility than 2SFCA,
because 2SFCA does not differentiate the spatial variation within
each catchment. For example, in the area around Rockford,
E2SFCA shows a concentric pattern of accessibility with higher
values near the population center and lower values at its
periphery (Fig. 3), whereas 2SFCA displays relatively uniform
high accessibility from the center to periphery (Fig. 2). Clearer
hierarchy structures can be observed in the other urban and
suburban areas in E2SFCA (compare Figs. 2 and 3).
One criticism on 2SFCA is that the accessibility is overrated in
the overlapping areas of physician catchments, as the residents in
those areas are assumed to have services from all physicians
whose service areas are overlapping there. This might not always
be true because people at the outer rim of a catchment may not be
fully served by the physicians near the center of the catchment.
This problem is solved in E2SFCA, since distance decay within the
ARTICLE IN PRESS
Fig. 1. Physician locations and 2000 census grid in study area.
W. Luo, Y. Qi / Health & Place 15 (2009) 1100–1107 1103
Author's personal copy
catchment is taken into consideration through the distance decay
weights. For example, according to the 2SFCA method, the rural
area northwest of DeKalb actually has accessibility equal to or
higher than that of the area closer to the City of DeKalb (see the
area labeled H in Fig. 2), a result that is counterintuitive. With the
E2SFCA method, the accessibility of the same area becomes equal
to or lower than that of areas closer to DeKalb (see the area
labeled with L in Fig. 3). With a sharper distance decay structure
(weight 2), the accessibility pattern is more of a concentric
pattern around DeKalb, the highest near population center and
the lowest farther away (compare Figs. 1, 3, and 4). This
observation holds true for the rest of the study area, with low
accessibility in suburban and rural regions and high accessibility
around urban centers (hot spots; See Fig. 4).
Fig. 5 shows the plot of accessibility at each population grid
cell, as generated by the 2SFCA and E2SFCA methods. The 2SFCA
method tends to overestimate accessibility compared with the
E2SFCA method (more data points above the 1:1 line), especially
in areas with low accessibility. This is because of the equal
access within catchment assumption in 2SFCA. In fact, using the
commonly used 1:3500 physician-to-population ratio as standard,
the 2SFCA method identifies 42,916 persons without adequate
access to primary care physician in the study area, whereas 60,079
persons are identified without adequate access by the E2SFCA
method with the preferred weight set 2 distance decay structure
(see Table 1).
What is more informative is the comparison of spatial
distribution of shortage areas identified with different methods:
2SFCA, E2SFCA (with two different weights), and the 2000 HPSA
as published by DHHS (DHHS, 2000). HPSAs in the study area are
mostly partial counties (DHHS, 2000) represented as townships
(in Ogle and Lee counties) and census tracks (west Rockford area
in Winnebago County). The west Rockford HPSAs are apparently
related to non-spatial factors (low-income population groups),
not explicitly considered in this paper. The HPSAs in Ogle and Lee
counties generally covered the shortage areas identified by 2SFCA
and E2SFCA, but overestimated their spatial extents. In addition,
the HPSAs also missed many other shortage areas identified by
2SFCA and E2SFCA methods. These shortage areas are usually
located between the population centers and along the edge of the
study area. Since the study area is limited to the DeKalb and
surrounding counties, the actual health care status for the areas
on the edge of the study area may need further examination
as physician data from the neighboring states/counties are not
included (i.e., these areas are subject to the classical edge effect
arising in spatial analysis).
As shown in Fig. 5, the 2SFCA method tends to overestimate
accessibility because distance decay is not considered, and thus
identifies smaller total shortage areas (compare Figs. 6(a) and (b),
see also Table 1). The sharper distance decay weight (weight 2)
used in E2SFCA identifies greater total shortage area (in terms of
both physical area and population) than a slower distance decay
weight (weight 1). The policy implication is that using the E2SFCA
method would more explicitly identify and delineate HPSAs. This
would help allocate the limited resources to the most needy
places.
ARTICLE IN PRESS
Fig. 2. Result of 2SFCA method. Fig. 3. Result of E2SFCA method applying weight 1.
W. Luo, Y. Qi / Health & Place 15 (2009) 1100–1107110 4
Author's personal copy
5. Discussion
The E2SFCA method as shown in the above case study
addresses the shortcomings of 2SFCA but maintains its advan-
tages. Several issues remain for further study. First, what is the
appropriate functional form for the distance decay weights? In
this study we used the Gaussian function weight to account for
the distance decay and we compared two sets of weights. Other
functional forms can also be used depending on the type of
accessibility. For example, for access to cancer care facility, a
slower decay function could be used; for access to pharmacy,
a sharper decay function could be used. Second, what is the scale
of temporal resolution for estimating travel time? In this study,
we used 10-min interval travel time for the subzones within the
catchment. This can be varied according the type of accessibility
and the resolution needed. Third, what is the appropriate
catchment size? As pointed by Yang et al. (2006), the catchment
size may also be varied according to the type of provider or the
type of neighborhood. For example, in rural areas, the catchment
size may be bigger; in urban areas smaller. The optimal size can be
determined by incrementally increasing the size of catchment
until the base population within the catchment meets a threshold
value (Tiwari and Rushton, 2005). In addition, the size of the
catchment does not have to be the same for step 1 and step 2.
Physicians in an urban center may serve a large area including
surrounding small towns, requiring large catchment for step 1, but
population in an urban center is less likely to seek care in a nearby
small town, resulting in small catchment for step 2. To properly
address these issues, detailed surveys of actual utilization of
health services would be necessary.
6. Conclusion
Built on previous research, this paper presents an enhance-
ment of the existing 2SFCA method for measuring spatial
accessibility by introducing weights to different travel time zones
within a catchment to account for the distance decay. The
discretized consideration of distance decay (by travel time zones)
ARTICLE IN PRESS
Fig. 4. Result of E2SFCA method applying weight 2.
Fig. 5. Comparison of accessibitliy by 2FSCA and E2FSCA: (a) weight 1 and (b)
weight 2.
Table 1
Physician shortage area statistics.
Method Area of shortage area
(km
2
)
Population under
physician shortage
HPSA (2000) 21,162.9 44,811
2SFCA 23,418.5 42,916
E2SFCA (weight1) 27,951.3 42,685
E2SFCA (weight2) 42,209.8 60,079
W. Luo, Y. Qi / Health & Place 15 (2009) 1100–1107 1105
Author's personal copy
in E2SFCA is justified because, in reality, people would not mind a
few minutes of difference in travel time to seek care. The travel
time zones can be easily derived with ArcGIS Network Analyst
tool. The advantage of E2SFCA is that it considers distance decay
in both steps, which has solid theoretical foundation in gravity
model as it is another special case of gravity model. Furthermore,
E2SFCA is much easier to implement in GIS and more straightfor-
ward to interpret because it is an elaborated form of the familiar
ratio between supply and demand (i.e., weighted ratio). The
weight can take different forms and can be adjusted for different
applications. For example, for measuring accessibility to cancer
care facility, the weight might change slowly with distance; for
measuring accessibility to pharmacy services, the weight may
decay more sharply with distance. In addition, the catchment size
can also be varied to account for the difference in base population
in rural vs. urban areas and in step 1 vs. step 2. More survey-based
studies are needed to determine the proper decay function and
catchment size. The case study of applying this new method in
northern Illinois showed that E2SFCA reveals a spatial accessi-
bility pattern that is more consistent with intuition than the
2SFCA method and identifies more persons with inadequate
access to primary care physicians. Incorporating E2SFCA into
existing practices of designating physician shortage area would
allow the government agencies to more precisely allocate limited
healthcare resources to the most needy populations. In addition,
the E2SFCA has great potential to be used in other areas such as
measuring job accessibility.
Acknowledgements
We would like to thank the two anonymous reviewers for their
helpful and constructive reviews and Dr. Andrew Krmenec for
editorial help.
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