Measuring spatial accessibility to healthcare for populationswith multiple transportation modes

Liang Mao n, Dawn NekorchukDepartment of Geography, University of Florida, P.O. Box 117315, 3142 Turlington Hall, Gainesville, FL 32611, USA

a r t i c l e i n f o

Article history:Received 17 March 2013Received in revised form21 August 2013Accepted 25 August 2013Available online 12 September 2013

Keywords:Healthcare accessibilityTransportation mode2 Step Floating Catchment Area Method(2SFCAM)Geographic information system (GIS)

a b s t r a c t

Few measures of healthcare accessibility have considered multiple transportation modes when peopleseek healthcare. Based on the framework of the 2 Step Floating Catchment Area Method (2SFCAM), weproposed an innovative method to incorporate transportation modes into the accessibility estimation.Taking Florida, USA, as a study area, we illustrated the implementation of the multi-mode 2SFCAM, andcompared the accessibility estimates with those from the traditional single-mode 2SFCAM. The resultssuggest that the multi-modal method, by accounting for heterogeneity in populations, provides morerealistic accessibility estimations, and thus offers a better guidance for policy makers to mitigate healthinequity issues.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Inequitable access to healthcare has long been recognized as aproblem in the United States. For example, Rosenblatt and Lishner(1991) had estimated a tenfold difference in the physician supplybetween urban and rural populations in the US. Meade and Emch(2010) had revealed a shortage of general practitioners in Mid-western and southern counties, but a surplus in northern andeastern counties. Lovett et al. (2002) reported extremely lowaccessibility to general practitioners in remote rural areas due to alack of public transportation services. Many of these health inequityissues can be attributed to uneven distributions of populations,health facilities, and transportation networks between them, all ofwhich pose a critical challenge to regional health planning andinterventions (Rosenblatt and Lishner, 1991; Todd et al., 1991;Wang, 2012). For those health planners, measuring healthcareaccessibility of populations are often the essential first step towardany meaningful and effective government intervention programs(Guagliardo, 2004; Luo, 2004).

Spatial accessibility to healthcare refers to the ease with whichresidents of a given area can reach medical services and facilities(Hewko et al., 2002). Different from its aspatial counterpart, thespatial accessibility emphasizes the role of geographic distance inthe interactions between health services and population demands(Joseph and Bantock, 1982; Luo and Wang, 2003). In recent years,

measurements of spatial accessibility to healthcare have receivedincreasing attention, due to their capability of describing geo-graphic variations within large regions, for example, within countiesor states (Guagliardo, 2004; Wang, 2012). Since the spatial acces-sibility is primarily calculated by geographic information systems(GIS), it has also been referred to as the GIS-based accessibility(Langford and Higgs, 2006; Luo, 2004). Simple measures of spatialaccessibility could be travel distance or travel time of a populationto the nearest health service (Brabyn and Skelly, 2002; Dutt et al.,1986). More sophisticated methods include: the gravity model(Joseph and Bantock, 1982), the Two Step Floating CatchmentArea Method (2SFCAM) (Luo and Wang, 2003), and the kerneldensity method (Guagliardo et al., 2004), as well as their variants(Luo and Qi, 2009; McLafferty and Grady, 2004; Wang and Rois-man, 2010). In general, these methods attempt to formulatedistance-dependent interactions between health services andpopulation demands, while representing competition amongpopulations for limited resources. A service-to-population ratio isfinally calculated for each population of interest to gauge itshealthcare accessibility (Yang et al., 2006). These accessibilitymeasures, then, help identify under-served areas and suggestoptimal allocation of health resources (Ayeni et al., 1987; Oppongand Hodgson, 1994; Rosero-Bixby, 2004).

Of these traditional methods, an intrinsic assumption is that allpeople are traveling to health facilities by a single (or uniform)transportation mode, in most cases, traveling by car. This uniformassumption is unrealistic in many populations, such as low-income populations which lack means for car ownership, ormetropolitan populations which favor public transportation due

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n Corresponding author. Tel.: þ1 352 392 0494; fax: þ1 352 392 8855.E-mail address: liangmao@ufl.edu (L. Mao).

Health & Place 24 (2013) 115–122

to traffic and parking issues. Neglecting various transportationmodes of the populations, these methods would inevitably intro-duce errors into the accessibility estimation. To date, little atten-tion has been paid to incorporating multiple transportation modesinto accessibility measures. Without such an improved measure,health planners may unintentionally misidentify underservedareas, and design less-effective mitigation programs.

To fill this knowledge deficit, we propose a multi-modeaccessibility measure based on the framework of 2SFCAM. Weapplied our multi-mode measure to estimate the spatial accessi-bility of residents to hospitals in the state of Florida, United States,and compared the results to those from a traditional single-modemethod. The remaining of this article is organized as follows: thenext section reviews the traditional 2SFCAM and describes theprinciples of multi-mode accessibility measure. The third sectionillustrates the data preparation and implementation of multi-mode method. The fourth section presents the results and discus-sion. The last section summarizes findings and concludes thearticle.

2. Multi-mode measure for spatial accessibility to healthcare

2.1. Review of traditional 2SFCAM

The traditional 2SFCAM is based on a threshold effect of traveltime and implemented in two steps (Luo and Wang, 2003). First,for each health facility j, search for all populations that fall within athreshold travel time (d0) from j (that is, catchment area j), andcompute a service-to-population ratio Vj within the catchmentarea .

Vj ¼Sj

∑kAdkj rd0

Pkð1Þ

where dkj is the travel time between k and j, Pk is the population atlocation k that falls within the catchment area j (that is, dkjrd0),and Sj is the capacity of service at health facility j.

Secondly, for each population at location i, search for all healthfacilities (j) that fall within the threshold travel time (d0) fromi (that is, catchment area i), and sum all service-to-populationratios, Vjs, included in the catchment area (Eq. (2)). The outcome

Ai indicates the healthcare accessibility of population at location i.

Ai ¼ ∑jAdij rd0

Vj ð2Þ

The 2SFCA method has been widely used in recent studies thatevaluate healthcare accessibility to physicians, cancer care facil-ities, pediatric providers, etc. (Albert and Butar, 2005; Wang et al.,2008; Wang and Roisman, 2011). It has also received criticisms inthe literature due to its equal access assumption, i.e., all popula-tions within the same catchment area have equal access tohealthcare (Guagliardo, 2004; Wang, 2012). This assumption isnot always true, particularly when people take a variety oftransportation modes to seek healthcare. An improved measureis called for to address this shortcoming.

2.2. Design of multi-mode 2SFCAM

Following the framework of 2SFCAM, we propose a multipletransportation mode method called the multi-mode 2SFCAM.To incorporate n (nZ1) transportation modes {M1, M2, M3, …, Mn},each population Pk at location k is divided into n subpopulationsby mode, denoted as Pk¼{Pk,M1, Pk,M2,…, Pk,Mn}. This informationon transportation modes could be derived from regional travelsurveys or census data, such as the census transportation planningproducts (CTPP). Our multi-model method is implemented infollowing two steps.

Step 1: we added the subpopulation structure into Eq. (1) of thetraditional 2SFCAM, and formulated it into

Vj ¼Sj

∑kAdkjðM1Þrd0ðM1Þ

Pk;M1þ ∑

kAdkjðM2Þrd0ðM2ÞPk;M2

þ⋯þ ∑kAdkjðMnÞrd0ðMnÞ

Pk;Mn

ð3Þ

where dkj(Mn) is the travel time by the mode Mn betweenlocation k and facility j. d0(Mn) is a predefined threshold traveltime from j by mode Mn. To build a working model, thesethreshold travel times (by mode) can be empirically estimatedfrom statistics of regional travel surveys. In this way, a numberof catchment areas by mode could be drawn around facility j,and the subpopulations of corresponding modes are includedas the demands for health services Sj (Fig. 1a). For example, allpeople in Population 1 (in Fig. 1a) have access to facility j,because the population falls within all three catchment areas(of different modes) around facility j. However in Population 3,

Fig. 1. A sketch map of multi-mode 2SFCAM for healthcare accessibility. (a) Step 1: create multiple catchment areas by mode around a facility and estimate service-to-population ratio for the facility. (b) Step 2: draw multiple catchment areas by mode around a population, and calculate the overall accessibility of the population.

L. Mao, D. Nekorchuk / Health & Place 24 (2013) 115–122116

only people with cars have access to facility j, while all otherpeople (traveling by bus or walking) cannot reach the facilitywithin 30 min. The resultant Vj reflects the amount of servicesthe facility j can offer to a person who is able to reach it by his/her transportation mode.Step 2: We further augmented Eq. (2) to take into accountmultiple transportation modes, and developed Eq. (4):

Ai ¼Pi;M1

∑jAdijðM1Þrd0ðM1Þ

VjþPi;M2∑

jAdijðM2Þrd0ðM2ÞVjþ :::þPi;Mn ∑

jAdijðMnÞrd0ðMnÞVj

∑n

v ¼ 1Pi;Mv

ð4Þ

Instead of directly adding all Vjs within a catchment area (Eq. (2)),our multi-mode method first weights Vj of each facility by thesizes of subpopulations according to the catchment area(s) it fallswithin. Then, the weighted values are summed to calculate theoverall accessibility (Ai) of population i. For example in Fig. 1b, allpeople in Population i would have access to facility 1, because it islocated within all three catchment areas (of different modes)around location i. Therefore, the weight for facility 1 is 100%.In contrast, only people with cars can access to facility 3, whilepeople traveling by bus or walking cannot reach that far within30 minutes. The weight for facility 3 is the proportion of peoplewith cars in Population i. In such a manner, the accessibility of apopulation is dependent not only on the distribution of healthfacilities around it, but also on its population structure in terms oftransportation modes.

3. Illustration: a case study in Florida, USA

To illustrate the proposed multi-mode 2SFCAM, we took the USstate of Florida as a study area, and estimated the accessibility ofresidents to hospital beds. We then compared the results to thosefrom the traditional single-mode 2SFCAM to examine how muchthe estimation can be improved.

3.1. Data collection

Spatial datasets regarding to this research included: informa-tion on 346 hospital facilities obtained from the Florida Geo-graphic Data Library (FGDL, 2012), a transportation network with1,747,524 road segments (TIGER, 2000), and population data from11,442 block groups (US Census (2000)). The U.S. Census blockgroup is the smallest geographic unit for which the Census Bureaupublishes sample data about demographics and socio-economy ofa population. A census block group usually contains a populationof 600–3000 people with an optimal size of 1500. The block groupwas chosen as the basic unit of analysis because it is the finestgeographic level available with information about vehicle owner-ship. We used the vehicle ownership later to define populationstraveling with and without cars. For accessibility estimation, thenumber of beds in a hospital was regarded as the amount ofservices provided by this facility (Fig. 2a), replacing the variable Sjin Eq. (3). The total households of each block group represent thepopulation that would potentially seek (or demand) healthcarefrom hospitals, replacing the variable P in Eqs. (3) and (4). Similarto previous studies, the population centroids of block groups wereused to represent the locations of populations. In other words, allhouseholds in a block group were collapsed onto the centroid ofthis block group. To consider the uneven distribution of house-holds in a block group, we first extracted the geometric centroidsof census blocks, as our best knowledge of population distribution.Then, we weighted each census block centroid by the number of

households in this block, and calculated the weighted centroids ofblock groups with

xc ¼∑pixi∑pi

yc ¼∑piyi∑pi

ð5Þ

where xc and yc denote the coordinates of population centroid of acensus block group c; xi and yi are the coordinates of the ith blockcentroid within that block group; pi is the number of householdsin the ith census block.

To incorporate transportation modes in the measurement, wedivided households of each block group into two categories:households with and without cars (Fig. 2b). We assumed thatonly people living in households with cars would travel tohospitals by car, while people living in households without carstravel by bus. To estimate travel time to hospitals, each roadsegment was assigned a car speed limit based on road types andsubtypes (Table 1), and a constant bus speed of 10 mile/h (Metro,2010). The travel time through a road segment by car or by buswas computed by dividing the segment length by the speed.An algorithm was implemented to find the shortest route betweeneach pair of population centroid and hospital facility, and then toaccumulate the travel time through each road segment on theroute. As a result, the shortest travel time between any pair ofpopulation centroid and hospital facility was calculated, replacingdkj and dij in Eqs. (3) and (4).

In order to estimate the threshold travel time (d0), we obtainedFlorida household travel records from the National HouseholdTravel Survey 2001 (NHTS, 2001). This survey provided detailedinformation about 12,110 individual trips in Florida during thesurvey period. Of these trips, 118 were associated with a purposefor ‘Medical/Dental Service’, and were selected to derive thefrequency distribution of trips against travel time. It was foundthat the number of medical trips decays exponentially as the traveltime increases (Fig. 3a). The average travel time of a medical trip inFlorida is 22.8 min, and 75% of the trips (the 3rd quartile) took lessthan 30 min (Fig. 3b). The 30 min have also been used as cut-offtime in several previous works (e.g. Wang and Roisman, 2011).Therefore we set the threshold travel time (d0 in Eqs. (3) and (4))as 30 min for both transportation modes.

3.2. Comparison analysis

After model parameterization, we implemented both single-mode (by car) and multi-mode 2SFCAMs to Florida census blockgroups. The outcomes from the two methods were comparedvisually and statistically. First, we evaluated a set of accessibilitystatistics estimated from the two methods, including the meanvalue, standard deviation, underserved area, and population. The“underserved” is defined by a threshold rate of 8 beds per 1000households. This threshold was calculated according to the factsthat on average 3.1 hospital beds were available for every 1000person in US between year 2005 and 2006 (WHO, 2013), and theaverage household size during this period was 2.59 persons(US Census, 2010). In addition, a scatterplot between outcomesfrom these two methods was drawn to depict the trend of under-estimation or over-estimation.

Secondly, we investigated the relative differences in outcomesbetween two methods. A percent difference was calculated foreach census block group using Eq. (6), and for each hospital facilitywith Eq. (7):

PctDif f ðAiÞ ¼AiðsÞ�AiðmÞ

AiðmÞ 100 ð6Þ

PctDif f ðVjÞ ¼VjðsÞ�VjðmÞ

VjðmÞ 100 ð7Þ

L. Mao, D. Nekorchuk / Health & Place 24 (2013) 115–122 117

where Ai(s) and Ai(m) denote the accessibility of census blockgroup i estimated from the single-mode and multi-mode 2SFCAM,respectively. Vj(s) and Vj(m) are the service-to-population ratio offacility j estimated from the two methods. The percent differenceswere mapped to show the spatial distribution of over- and under-estimations, and suggest potential explanatory hypotheses.

4. Results and discussion

A quick comparison in Fig. 4 suggests that both single-modeand multi-mode 2SFCAMs estimated a similar pattern of health-care accessibility. People in urbanized areas have higher accessi-bility than those who live in suburban and rural areas. Thishierarchical pattern has been reported in previous literature, andcan be explained by a concentration of hospitals and roads inurbanized areas (Luo and Qi, 2009; Wang and Roisman, 2011).A further examination at a finer scale (insets of Fig. 4) showed thatthe two methods produced distinct estimates in urbanized areas,although their estimates were similar in rural areas.

Statistics in Table 2 indicate that the single-mode 2SFCAMestimated a slightly higher average value than the multi-modemethod, but with a lower variability. A potential reason is becausethe single-mode method assumed all people seek healthcare bycar, thus increasing their ability to access healthcare centers.Meanwhile, this uniform assumption smoothed the variability of

estimates, leading to a lower standard deviation. By representingmore heterogeneity in populations, our multi-mode methodproduced a lower mean accessibility but with more variability.It is noteworthy that the single-mode method, by assuming auniform transportation mode, identified a larger underserved areaand population than the multi-mode method did. The explanationis presented later in the discussion.

Fig. 2. Study area, health facilities, and population demands: (a) Geographic location of Florida in the United States, hospital facilities, and the amount of services beingoffered; (b) census block groups shaded by the percentage of households without cars. The inset map shows details in the Jacksonville, the largest urbanized area in Florida.

Table 1Criteria for assigning car speed limits to road segments.

Road Typea Road Subtypea Speed limit (miles/h)b

Primary Interstate highway 70US route 65

Secondary State highway 60State route 55County highway 50County route 45

Local Local, neighborhood,and rural road, city street

40

Ramp N/A 35

Others N/A 20

a Road types and subtypes are classified by the Florida Geographic Data Library.b Speed limits are assigned according to the Florida Department of Transporta-

tion (http://www.dot.state.fl.us/trafficoperations/FAQs/SpeedLimitFAQ.shtm).

Fig. 3. (a) Frequency distribution and (b) cumulative frequency distribution of 118health-oriented trips against the travel time.

L. Mao, D. Nekorchuk / Health & Place 24 (2013) 115–122118

For a majority of census block groups (Fig. 5a), the single-modemethod resulted in higher estimation than the multi-modemethod did. The differences in estimates were not significantwhen the accessibility rate is low, but became more marked as theaccessibility rate increased. The magnitude of difference waspositively associated with the percentage of non-car householdsin a population (Fig. 5b). A regression analysis indicated that theabsolute value of percent difference, |PctDiff (Ai)|, would rise by0.48 if the non-car households increased by 1%. A possibleexplanation is that the higher the proportion of non-car house-holds in a population, the weaker the uniform assumption wouldbe, and thus the more miscalculations are introduced by thesingle-mode method.

A differential map between the two methods (Fig. 6a) showsthat in the urban areas, the single-mode method produced scoreshigher than the multi-mode method by 10–15%. In contrast, inmost rural areas, it was the multi-mode method that scored up to5% higher. To explain the observed pattern, we further examinedthe difference in Vjs from two methods (Fig. 6b), which came fromthe first step of 2SFCAM. It is interesting that the Vjs for allhospitals were under-estimated by the single-mode method, ascompared to the multi-mode one. Hospitals in urbanized areaswere significantly under-estimated by roughly 8�10%, while thosein rural areas were slightly under-estimated by about 2%. This isbecause the single-mode method presumed that all people seekhealthcare by car. As a result, more people have access to ahospital and compete for a certain amount of services, leading toa larger denominator in Eq. (1) and thus lower service-to-population ratio Vj. By considering various transportation modes,the multi-mode method reduced the number of competitors for acertain amount of services (Eq. (3)), resulting in higher Vjs.

Turning to the 2nd step of 2SFCAM, the single-mode methoddirectly summed all Vjs falling within a catchment area (Eq. (2)),

whereas the multi-mode method weighted or discounted Vjs bysubpopulations of various transportation modes and then summedthem together (Eq. (4)). In rural areas where more than 95% of

Fig. 4. Accessibility of census block groups estimated by (a) the single-mode 2SFCAM and (b) the multi-mode 2SFCAM. The insets magnify an urbanized area to show details.

Table 2Statistical comparison between the single-mode and mu lti-mode 2SFCAM.

Method Mean (beds/1000households)

Standarddeviation(beds/1000households)

Underservedarea (km2)a

Underservedpopulation(Households)a

Single-mode2SFCAM

11.84 11.95 122,580 1,939,602

Multi-mode2SFCAM

11.81 12.06 122,572 1,923,984

a The under-service is defined as the accessibility rate lower than 8 beds perthousand households calculated above.

Fig. 5. (a) Scatter-plot between estimates from the single-mode and multi-mode2SFCAMs; (b) Scatter-plot of the difference percent against the percent of house-hold without cars.

L. Mao, D. Nekorchuk / Health & Place 24 (2013) 115–122 119

households travel by car (Fig. 2b), the discounts on Vjs were quitesmall, and thus Eqs. (2) and (4) tended to be similar. Since Vjs areunder-estimated in the 1st step, the single-mode method (Eq. (2))produced lower accessibility rates than the multi-mode one inrural areas. This explains why the single-mode method may over-identify the underserved area and population (Table 2). Popula-tions living in rural areas are more likely to be underservedaccording to many empirical studies, and the single-mode methodtends to under-estimate in these areas, thus leading to a largerunderserved population. The two methods differ greatly in urba-nized areas where car travel is no longer the predominanttransportation mode (only accounts for 60–70% households asshown in Fig. 2b). Even though the multi-mode method estimatedhigher Vjs, the discounts on Vjs were so large that they overrodethe elevated Vjs in Eq. (4), and thus pulled down the overallaccessibility. Consequently, the single-mode method estimatedhigher accessibility in urbanized areas than the multi-modemethod. The results imply that when targeting health resourcesto rural areas, health planners should be cautious if using the

single-mode method for estimation, because it asks for moreresources than is actually needed.

Another concern of this multi-mode method is its extension tothe gravity model of spatial accessibility, of which 2SFCAM is aspecial case (Luo and Wang, 2003). Following similar patternsfrom Eqs. (3) and (4), the multi-modal gravity model could beformulated as Eqs. (8) and (9). The accessibility score can becomputed as:

AGi ¼

Pi;M1∑jðSjdijðM1Þ�βM1 =VG

j ÞþPi;M2∑jðSjdijðM2Þ�βM2 =VG

j Þþ :::þPi;Mn∑jðSjdijðMnÞ�βMn=VG

j Þ

∑n

v ¼ 1`Pi;Mv

ð8Þ

where {M1, M2, …, Mn} represent n transportation modes in astudy area. Pk¼{Pk,M1, Pk,M2,… Pk,Mn} denote n subpopulations bymode. The travel friction coefficients {βM1, βM2,… βMn } varies bytransportation mode, and specify different distance decay effectsof accessibility. The service-competition intensity VG

j is estimatedas a sum of multi-modal population potentials in Eq. (9), andrepresents a discount to the service availability.

VGj ¼∑

k

Pk;M1

dkjðM1ÞβM1þ∑

k

Pk;M2

dkjðM2ÞβM2þ :::þ∑

k

Pk;Mn

dkjðMnÞβMnð9Þ

Eqs. (8) and (9) could be a more general form of our multi-modeaccessibility model, and are expected to produce a more smoothaccessibility map by weakening hard traveling thresholds. Esti-mating the travel-friction coefficient βs becomes more challenging,as now each travel mode has its own β parameter. Derivingestimates of these coefficients would involve generating andanalyzing the statistical distributions of travel times based ontravel surveys of each travel mode to be considered.

Several limitations should be mentioned with this illustration.First, our model application only considered two major transpor-tation modes: by car and by bus. This was the best information wecan derive from the census block group data, and was thought tobe sufficient for illustration purposes. In reality, the transportationmodes of a population are far more complicated. Some people, forinstance, may choose to walk to hospitals in urban centers due toclose proximity. By restricting our analysis to car and bus travelonly, we would expect less heterogeneity of accessibility in finalresults than the reality. However, the representation of all modesrequires detailed datasets that record travel behavior of all people/households. Few such datasets exist due to the time and costs tocollect them, as well as individual privacy issues. The alternative isto use transportation simulation models, such as the transporta-tion Analysis and Simulation System (TRANSIMs), to generate suchdatasets based on statistical distributions established from censusdata and travel behavior surveys. Second, the bus transit systemswere simplified by allowing the bus to travel along the same pathas a car would, i.e., the shortest path to the hospital. We made thisassumption because the data for public transits is limited to a fewmetropolitan areas, while the extensive rural and small urbanareas are not covered. To offset our assumption, a slower speedwas set for bus travel to help account for bus routes that oftenfollow non-shortest paths between origins and destinations. Thisapproach is a compromise that allows us to encompass the entireFlorida state into analysis. Future work may wish to explicitlyconsider the bus routes and stops of that particular region. Third,we set a uniform time threshold for both traveling by car and bybus to health facilities. This assumption is acceptable for illustra-tion purposes, but not always true in reality. The subpopulationswith different transportation modes may differ in the travel timethresholds. For example, people traveling by car may be willing totravel for longer time periods than those walking because of therelative ease and comfort of car travel. A possible solution is to

Fig. 6. Geographic comparison of single-mode and multi-mode 2SFCAMs.(a) Percent difference of accessibility by census block group, PctDiff (Ai), fromEq. (6). (b) Percent difference of service-to-population ratio by hospital, PctDiff (Vj),from Eq. (7).

L. Mao, D. Nekorchuk / Health & Place 24 (2013) 115–122120

split trip records in the travel survey by mode, and analyze thefrequency distribution of each mode by travel time. Fourth, bothhospitals and populations were simplified to some extent in thisresearch. We treated all hospitals the same except for the numberof beds, but neglected the quality and variety of services they offer.We also used the population centroids to represent the populationdistribution, and collapsed all populations on those centroids.The results may not reflect the exact true accessibility, but areenough to show the differences between the two methods.Potential improvement is to use finer population datasets, suchas residential parcel data, population grid data estimated fromsatellite imagery, and fine-scale dasymetric population maps. Fifth,although the study area is a peninsula surrounded by water bodies(as shown in Fig. 2), edge effects are a concern along the northernand panhandle (north-west salient) state border lines. People wholive close to state borders may choose to cross state lines to seekhealthcare, and therefore the final results should be interpretedwith caution. However, many US health insurance plans encouragetheir subscriber to seek healthcare locally, and not to cross statelines if unnecessary, which minimizes inter-state travels andnaturally limits edge effects to the northern borders. All theselimitations warrant future extensions and applications of ourmulti-modal method.

5. Conclusions and Implications

Based on the framework of 2SFCAM, we proposed an innova-tive method to incorporate transportation modes into the estima-tion of healthcare accessibility. Taking the Florida state as a studyarea, we illustrated the implementation of our multi-mode2SFCAM, and compared the accessibility estimates with thosefrom the traditional single-mode 2SFCAM. The comparison analy-sis suggested that the single-mode method tends to over-estimateaccessibility in urbanized areas where the transportation modesare heterogeneous, but under-estimate in rural areas where thetransportation modes are homogeneous. These misestimates lie inthe assumption of a uniform mode, and lead to a larger under-served population being identified. By accounting for varioustransportation modes within populations, our multi-mode methodprovided a more realistic estimation, and thus offers betterguidance for health policy makers to design cost-effective mitiga-tion programs.

The contribution of this research to the literature is twofold.First, few accessibility measures have explicitly considered multi-ple transportation modes when people seek healthcare. Our multi-mode method fills this knowledge gap and relaxes the previousassumption of equal access within catchment areas. By consider-ing various transportation modes, our method adds more realityinto the accessibility modeling and offers more reliable estimatesto pinpoint underserved populations. Secondly, our multi-modemethod is superior to the enhanced 2SFCAM recently proposed byLuo and Qi (2009). Their enhanced 2SFCAM divides a catchmentarea into several time zones, and assigns each zone a weight. Theirconcept is close to our method, but the delineation of time zonesand assignment of weights remain arbitrary. Furthermore, theweights used in their application were uniform over the entirestudy area, which is simple and problematic. Our method offers anobjective way to define zones and assign weights. The zones canbe replaced by the catchment areas of various transportationmodes, and the weights can be expressed as the proportions ofsubpopulations with different modes. Weights can vary overdifferent populations in the study area, such as census blockgroups or tracts. In this sense, our method provides more objec-tivity and flexibility.

In general, the transportation mode is an important factor todetermine the ease of access, and should not be simplified in theaccessibility measures. The proposed multi-mode method allows amore realistic estimation of accessibility, but meanwhile requires alarge amount of information about individual travel behavior.Thanks to the fast growth of information technology, the collectionof such large datasets can now be made easier by tracking mobilephones of a large population (Asakura and Hato, 2004; Gonzalezet al., 2008), or extracting blog records from social networkingwebsites, such as Facebook, Twitter, and Foursquare (Handy, 1996;Noulas et al., 2011). With this type of information, the applicationsof the multi-mode method are not limited to public health, but canbe readily extended to economics and urban planning, for examplemeasuring accessibility to markets or urban amenities.

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