Journal of Clinical Epidemiology 66 (2013) S57eS64

Simulating changes to emergency care resources to comparesystem effectiveness

Charles C. Branasa,b,*, Catherine S. Wolffa, Justin Williamsc, Gregg Margolisd,Brendan G. Carra,b

aDepartment of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, 423 Guardian Drive, Philadelphia, PA 19104, USAbDepartment of Emergency Medicine, 3400 Spruce St, University of Pennsylvania School of Medicine, Philadelphia, PA 19104, USA

cDepartment of Geography and Environmental Engineering, 300 Ames Hall, Johns Hopkins School of Engineering, Baltimore, MD 21218, USAdDivision of Health System Policy, Office of the Assistant Secretary for Preparedness and Response, US Department of Health and Human Services, 200

Independence Ave, SW, Washington, DC 20201, USA

Accepted 11 March 2013

Abstract

Objective: To apply systems optimization methods to simulate and compare the most effective locations for emergency care resourcesas measured by access to care.

Study Design and Setting: This study was an optimization analysis of the locations of trauma centers (TCs), helicopter depots (HDs),and severely injured patients in need of time-critical care in select US states. Access was defined as the percentage of injured patients whocould reach a level I/II TC within 45 or 60 minutes. Optimal locations were determined by a search algorithm that considered all candidatesites within a set of existing hospitals and airports in finding the best solutions that maximized access.

Results: Across a dozen states, existing access to TCs within 60 minutes ranged from 31.1% to 95.6%, with a mean of 71.5%. Accessincreased from 0.8% to 35.0% after optimal addition of one or two TCs. Access increased from 1.0% to 15.3% after optimal addition of oneor two HDs. Relocation of TCs and HDs (optimal removal followed by optimal addition) produced similar results.

Conclusions: Optimal changes to TCs produced greater increases in access to care than optimal changes to HDs although these resultsvaried across states. Systems optimization methods can be used to compare the impacts of different resource configurations and their pos-sible effects on access to care. These methods to determine optimal resource allocation can be applied to many domains, including com-parative effectiveness and patient-centered outcomes research. � 2013 Elsevier Inc. All rights reserved.

Keywords: Health system optimization; Access to care; Geography; Health policy; Trauma center; Wound and injuries; Location science

1. Introduction

Epidemiology, as a field, has its origins in analytic geo-graphic methods, most famously in the form of the JohnSnow narrative of water pumps and cholera in London [1].Clinical epidemiology, as a chapter in the broader field of ep-idemiology, is generally defined as the study of illness in per-sons seen by providers of medical care [2]. It is here wherethe value of the work conducted in this article converges on

Disclosures and funding: The authors have no pertinent disclosures.

This work was funded by awards from the Agency for Healthcare Research

and Quality (R01HS010914) and the Centers for Disease Control and Pre-

vention (R01CE001615).

The findings and conclusions in this report are those of the authors and

do not necessarily represent the views of the Department of Health and Hu-

man Services or its components.

* Corresponding author.

E-mail address: cbranas@upenn.edu (C.C. Branas).

0895-4356/$ - see front matter � 2013 Elsevier Inc. All rights reserved.

http://dx.doi.org/10.1016/j.jclinepi.2013.03.021

the novel approach of using spatial epidemiologic methodsfor analytic research in clinical epidemiology.

Spatial epidemiologic methods for analytic purposeshave matured over the past half century, outpacing standardgeographic information system (GIS) approaches which re-main, for the most part, descriptive methods to visually ex-plore maps of health phenomena. These GIS methods,although valuable, are generally not used to directly ana-lyze the impacts of changes to the locations of various phe-nomena in space. Although geographic variation in healthcare has been visually documented for decades and is agood example of descriptive GIS work, this line of researchoffers little in terms of direct analyses or counterfactuals,that is, what might happen if the health care system itselfwere spatially altered [3,4].

The work presented here takes this next step as a form ofcomparative effectiveness research (CER) focusing on geo-graphic changes to population-wide health care delivery

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What is new?

� Emergency care system design has the potential tobe meaningfully assisted by quantitative simulationtechniques that compare the effects of different re-source configurations.

� Trauma center (TC) and helicopter depot (HD) lo-cations determine whether severely injured patientscan rapidly access TC care and, in many cases, sur-vive their injuries.

� Increases in access to trauma care following theoptimal addition of TCs or HDs can be large, po-tentially affecting substantial populations, althoughthese increases can also vary widely among states.

� Operations research and mathematical optimizationtechniques can be used in the siting of emergencycare resources, potentially improving access to careand system effectiveness for time-sensitive diseasessuch as trauma and stroke.

� The methods described here can be applied to re-source allocation questions in many domains, in-cluding comparative effectiveness research andpatient-centered outcomes research.

systems which, according to the Institute of Medicine, isa primary focus of its CER portfolio [5]. In fact, work akinto this system-wide CER has already been occurring for de-cades in operations research and topothesiology, althoughthis work has largely emerged from schools of engineeringand applied sciences with little notice from CER, thoughtleaders in health care and medicine [6]. This article partlyaims to change this by specifically using the systems oftrauma centers (TCs) and ambulances in multiple states asillustrative examples of the general value of this approach.

Trauma is amajor cause of disability,mortality, and healthcare use in the United States, resulting in millions of emer-gency department (ED) visits and hospitalizations and hun-dreds of thousands of deaths each year [1]. Prior studies[7,8] have shown that TC care and medical helicopter trans-port of severely injured patients can reduce mortality by 25%and 15%, respectively. Because trauma is such a time-sensitive disease condition, rapid access to TC care is alsoa major driver of survival outcomes for severely injured pa-tients and also consequently for system effectiveness. How-ever, about 10% of the total US population cannot accessTC care within 60 minutes, and in some states, this figure isas high as two-thirds or more of the population [9]. Thus,one of the Department of Health and Human Services’Healthy People 2020 benchmark goals is to increase accessto TC care over the next several years [10].

Improving access to TC care is a challenge for healthplanners. The time-critical and unplanned nature of severe

injury necessitates system design from the perspective ofthe population, as trauma can affect anyone at almost anytime with little, if any, warning. Trauma patients can almostnever anticipate the onset of their illness and therefore relyon the emergency care system to ensure that they receivehigh-quality health services in a timely manner followingan unplanned injury. In this context, the national emergencycare safety net requires a system to ensure that the injuredpatients quickly receive the care they need when their owndecision-making capabilities are limited by the unexpectedrapid onset of severe and often life-threatening conditions.

In time-sensitive conditions such as trauma, well-plannedgeographic access to emergency care therefore becomes vi-tal, as it affects time to treatment, survival, and overall systemeffectiveness. For decades, trauma care systems have beendeveloped to deliver trauma patients to facilities capable ofproviding them with optimal in-hospital treatment, but thesesystems have not always used evidence-based rationales forthe strategic placement of resources, such asTCs andmedicalhelicopters. The expense of maintaining these facilities [11]supports the need for a system that locates these resources ina way that maximizes rapid access to care and, by extension,patient survival. Our first goal in this study was to apply sys-tems optimization methods to determine the best initial loca-tions, and relocations, for additional trauma care resources inselect US states. Our second goal was to then compare thesesimulated changes with the existing state systems in terms ofaccess to care, a process outcome of system effectiveness fortime-sensitive conditions such as severe trauma.

2. Methods

2.1. Study design and data

This study was an optimization analysis of the locationsof TCs, helicopter depots (HDs), and severely injured pa-tients in a dozen states; optimal TC locations were calcu-lated so as to maximize the number of severely traumapatients who would be able to access them in less than60 minutes. As with prior work [12,13], the objective func-tion of the optimization models here was to maximize 60-minute access to TCs for severely injured patients usingconstraints related to the locations of existing and candidateTCs and HDs, ground and air travel networks, and the num-ber of new TCs or HDs that were to be optimally located.

The states included were Colorado, Florida, Iowa, Mary-land, New Jersey, New York, North Carolina, Oklahoma,Oregon, Pennsylvania, Utah, and Washington. These 12states were selected based on the availability of ZIP codeelevel hospital discharge data, although they are also reason-ably representative in terms of topography (both land areaand elevation), demography, and health care systems.

Candidate sites for TCs were acute care hospitals with24/7 EDs, and candidate sites for HDs were all existing ci-vilian airports, TCs, or acute care hospitals that could

Fig. 1. Map of geometric ellipses demonstrating access to care within45 minutes, in gray, based on trauma center and helicopter depot lo-cations in Pennsylvania.

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accommodate a base helipad. Cost and capacity were notincluded in the model.

Data onTC locationswere obtained from the 2005TraumaInformation Exchange Program national TC registry, whichcontains the name, address, and certification level of everyTC certified by the American College of Surgeons or a statecertification agency [14]. Data on non-TC acute care hospitallocationswereobtained from the 1999AmericanHospitalAs-sociation annual survey, which is administered annually tomore than 6,000 hospitals and health care systems nation-wide. These data were used to determine the locations of can-didate sites (acute care hospitalswith 24/7 EDs) for TCs in theanalysis. This was the basic level of entry that we set for theexisting non-TCs to be considered as candidate TCs; it effec-tively eliminated hospitals in which the most basic resourceneeds of a TC were absent (e.g., noneacute care hospitalswith no ED, such as rehabilitation hospitals, long-term carehospitals, etc). The 2004 Atlas and Database of Air MedicalServices (ADAMS) was used to obtain the locations of civil-ian air ambulance depots and flying speeds for helicoptersbased at each location [15]. The 2004 ADAMS and the2005 Airport Data & Contact Information database from theFederal Aviation Administration provided the locations ofthe civilian airports used as candidate sites for additional airmedical depots. Although additional HDs can be sited asstand-alone helipads in locations other than only hospitalsand airports, this would create a list of possible candidate sitesthat is likely too large to obtain solutions within reasonablecomputation times. In addition, it may be desirable to locatehelipads at airports and hospitals (for instance, in terms of fuelavailability, preexistingmechanical and repair services, staff-ing support, ease of transport to other facilities, etc).

The 1998e1999 state inpatient databases from theAgency for Healthcare Research and Quality as well asfrom individual state providers were used to identify se-verely injured patients (those with an injury severity score(ISS) O15) along with their residential ZIP codes. Theseseverely injured patients were then aggregated into ZIP co-des, which summed to the optimization model’s objectivefunctionethat is, maximization of the number of severelyinjured trauma patients, within ZIP codes, who had accessto a TC within an hour [12,13]. Vital statistics data on themultiple causes of death were obtained from the NationalCenter for Health Statistics to identify and include patientswho had died from an injury and had required some amountof medical care, defined by the ED as the documented placeof death. Trauma patients were defined as those with prin-cipal and/or secondary diagnoses of trauma: InternationalClassification of Diseases, Ninth Revision, Clinical Modifi-cation, codes between 800.00 and 959.90, excluding thosefor foreign bodies (930e939), traumatic complications(958), and late effects of injuries (905e909). Data fromthe Neilsen Claritas Demographic Estimation Program pro-vided the geographic location of the population-weightedcentroid point of each ZIP code in the included states.The location of the population-weighted centroid was the

point in the ZIP code closest to where most of the ZIP co-de’s population resided, and it was used as the geometricmean location assigned to all patients in the ZIP when cal-culating time to the nearest TC or candidate facility. ThisZIP code centroid served as a proxy location of each pa-tient’s injury, given that actual data on the specific addresslocations of patient injuries were not available across mul-tiple states.

2.2. Access to trauma care

To calculate optimal TC locations, it was necessary todetermine population access to the existing and then candi-date TC sites. Access to trauma care was defined as the per-centage of severely injured patients (those who had an ISSO15 or who died from their injuries) who could reacha level I or II TC within 45 or 60 minutes. These access cal-culations were completed using the Trauma Resource Allo-cation Model for Ambulances and Hospitals (TRAMAH).The TRAMAH is a deterministic (i.e., non-stochastic) opti-mization model that uses a TCeHD pairing mechanism toessentially produce geometric ellipses of geographic accessthat vary in size depending on the distance between the TCand HD in each pairing. Several examples of pairings aregiven in Fig. 1, with differently sized ellipses and underly-ing population access to care shown as dependent on thedistances between pairs. The TRAMAH optimization algo-rithm basically considers these geometric ellipses in its for-mulation and then makes adjustments to these ellipseswhen presented with new facilities to locate in ultimatelymaximizing access to trauma care. This algorithm can re-sult in co-location of helicopter ambulances with TCs, assame-site pairings, or it can locate helicopter ambulancesas satellites to TCs. In either situation, through the pairingstrategy of the TRAMAH, TCs may be located such thatthey can be serviced by multiple helicopter ambulancesand/or any one helicopter ambulance can be located such

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that it can service multiple TCs, depending on flight speedand distance.

The TRAMAH can be used to calculate the existing geo-graphic access to TCs by ground and/or air ambulanceswithin user-defined, out-of-hospital response time standards,typically 45 or 60 minutes. Up-to-date, interactive versionsof these existing access calculations for all US states areavailable for the public and policymakers to view at www.traumamaps.org. The TRAMAH has also been designed tosimulate and assess changes to the geographic configurationsof TCs and ambulanceswithin defined geographic areas (typ-ically states), including the optimal addition, removal, or re-location of TCs and ambulances with the objective ofmaximizing access for defined populations such as severelyinjured people or all residents living in a defined area. As thisarticle addresses, the application of the TRAMAH to com-pute optimal access calculations in multiple states, specificdetails of the full TRAMAH, its formulation, and its applica-tion are only summarized here and can be found in greater de-tail elsewhere [12,13,16]. This article is, however, a newapplication of the TRAMAH in multiple states for specifi-cally sized problems of up to two facility modifications.

Numerical inputs that are part of the calculation of theTRAMAH include pre-hospital time intervals and travelspeeds that were determined from a large series of priorstudies of ambulance transport for trauma [17]. Ground am-bulance access calculations include activation, response,and on-scene pre-hospital time intervals, as well as trans-port time. Time intervals and transport times are adjustedbased on urban, suburban, or rural location. Air ambulancecalculations used in the TRAMAH include the typicalcruise speed of the specific helicopter in use at each HDas well as warm-up, response, on-scene, and transport timeintervals. For the purposes of this article, any single ZIPcode containing severely injured patients will be assignedas having access to care if it can reach a TC within the re-sponse time standard, by either ground or air ambulance.

2.3. Optimal locations for additional TCs and HDs

Geographic access calculations completed using theTRAMAH were used to determine the optimal locationsof added or relocated TCs and/or HDs. Because the prob-lems considered here had relatively small numbers of po-tential solutions, we used a basic enumeration algorithmto obtain optimal solutions and compare all possible candi-date resource locations to find the one or two best locationsthat would maximize the number of severely injured pa-tients with access to a level 1 or 2 TC by air or groundambulance. Basic enumeration algorithms are simplebrute-force search algorithms that can find optimal solu-tions for smaller problems by fully enumerating and thensearching all possible solutions for the one best solutionto any given problem. Prior work using the TRAMAH ina single state considered problems with a much larger uni-verse of potential solutions to explore (in finding the one

optimal solution) and therefore higher computational com-plexity, increasing the probability that the one global opti-mal solution could not be found.

Based on these data inputs, we ran optimization scenar-ios that simulated the marginal impact of one to two ad-ditional and one to two relocated TCs and one to twoadditional and one to two relocated HDs on the access toTC care for severely injured people within each state. Ad-dition scenarios optimally added the best new TCs and/orHDs, from among the list of candidate locations, to theexisting system. Relocation scenarios optimally replacedexisting TCs and/or HDs with the best TCs and/or HDsfrom among the list of candidate locations. The mathemat-ical objective function that was optimized for all these ad-dition and relocation scenarios was maximization of accessto level 1 and 2 TCs within 45 and 60 minutes for severelyinjured people within each state. We calculated mean sum-mary statistics across all 12 states in which the various op-timization scenarios were completed.

3. Results

Existing access to trauma care within 60 minutes rangedfrom 31.1% to 95.6% across the 12 states we studied, witha mean of 71.5%. Existing access to trauma care within45 minutes ranged from 13.9% to 84.6% across the 12states we studied, with a mean of 49.9%.

The effect of adding additional resources varied amongthe 12 states under study. Increases in 60-minute access fol-lowing the addition of one to two TCs ranged from 0.8% to35.0% (45 minutes: 0.8%e24.6%), whereas additional cov-erage following the addition of one to two HDs rangedfrom 1.0% to 15.3% (45 minutes: 0.8%e12.2%). On aver-age across all states, access was increased most by the ad-dition of TCs (60 minutes: two TCs 5 9.6%, one TC 56.8%; 45 minutes: two TCs 5 10.9%, one TC 5 7.8%).The addition of HDs provided smaller increases in accesson average (60 minutes: two HDs 5 5.5%, one HD 53.4%; 45 minutes: two HDs 5 6.8%, one HD 5 4.2%). So-lutions for all states within the 60-minute response timestandard are shown in Table 1.

Select state maps have been included in Fig. 2 to visuallydepict some of these optimal additions and highlight thestate-specific nature of optimal additions of TCs and HDs.In these maps, the white areas have no access to trauma care,whereas the gray- and dark gray-shaded areas show the exist-ing access and increased access, respectively. As an ex-tension of the map showing the optimal siting of oneadditional HD in North Carolina, the percent increases ofall candidate locations across the state were also calculated.This produced a map showing the range of choices availablethroughout the state, possibly to offer alternative, near-optimal choices to a policymaker or planner (Fig. 3).Figures 2B and 3 show the same, single optimal locationfor a new HD, but the map in Fig. 3 extends this to also showall other near-optimal and inferior solutions across the state.

Table 1. Increases in 60-minute access from optimal addition of TCs and HDs in a dozen states

States Existing access (%)

Adding

D1 HD (%) D2 HD (%) D1 TC (%) D2 TC (%) D1 HD and 1 TC (%)

Colorado 84.69 þ1.35 þ2.18 þ0.79 þ0.86 þ2.14Florida 78.34 þ3.22 NS þ11.02 þ13.29 NSIowa 31.13 þ9.59 þ15.29 þ5.72 þ10.19 þ16.02Maryland 84.15 þ2.51 þ3.72 þ7.82 þ13.87 þ8.56New Jersey 95.38 þ2.65 þ4.62 þ2.45 þ4.34 þ4.53New York 95.59 þ0.97 NS þ0.88 þ1.71 þ1.80North Carolina 55.58 þ5.83 þ9.72 þ6.72 þ12.49 þ12.55Oklahoma 36.03 þ2.86 þ4.45 þ30.37 þ34.98 þ33.23Oregon 69.50 þ2.59 þ5.06 þ8.74 þ11.89 þ12.01Pennsylvania 94.25 þ2.22 þ3.00 þ1.63 þ3.14 þ3.73Utah 54.14 þ3.21 þ4.37 þ2.92 þ4.94 þ7.86Washington 79.44 þ0.00 þ2.15 þ1.99 þ3.72 þ5.11

Abbreviations: TC, trauma center; HD, helicopter depot; NS, no solution found within reasonable processing times.

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Relocation scenarios for TCs and HDs produced resultssimilar to the addition scenarios for these resources, and forsome states, increases in percent access were equivalent,that is, the same optimal locations were obtained as solu-tions. The effect of relocating resources also varied amongthe 12 states under study. Increases in 60-minute access fol-lowing the relocation of one to two TCs ranged from 0.8%to 13.9% (45 minutes: 4.3%e11.2%), whereas additionalcoverage following the relocation of one to two HDs rangedfrom 1.0% to 14.9% (45 minutes: 1.7%e7.6%). On averageacross all states, access was increased through the reloca-tion of TCs (60 minutes: two TCs 5 6.8%, one TC 55.5%; 45 minutes: two TCs 5 7.8%, one TC 5 7.8%) aswell as through the relocation of HDs (60 minutes: twoHDs 5 7.1%, one HD 5 3.3%; 45 minutes: two HDs 5no solution, one HD 5 4.2%).

4. Discussion

TC and HD locations play a major role in determiningwhether severely injured patients can rapidly access TC careand, in many cases, survive their injuries. Our analysesshowed that access to trauma care could be substantially in-creased by the optimal addition of TCs or HDs, potentiallyaffecting sizable groups of severely injured people, althoughthese increases were also found to vary widely among states.Operations research and mathematical optimization tech-niques, such as those used here, can be applied to the sitingof emergency care resources, potentially improving accessto care and system effectiveness for time-sensitive diseasessuch as trauma.

The variability in results among states underscores theimportance of incorporating some sort of prospective,data-driven system planning techniques. Organic systemdevelopment is prone to inefficiencies, if not guided, atsome level by data-driven considerations of the need forrapid geographic access to care across the population. Todate, trauma systems have been developed largely withoutprospective, data-driven planning for the placement of

resources, sometimes resulting in state systems of care inwhich select areas are highly under-resourced and an equalnumber of areas are highly over-resourced [11]. This is inpart illustrated by the finding in our analyses that for manystates, the access provided by optimally relocating a givenresource was exactly the same as for adding that resourcedmeaning that in the existing system, some resources wereproviding access to populations that already had access totrauma care through one or more potentially redundantTCs or HDs. Such redundancy may be appropriate in largeurban areas where the capacity of one TC or air ambulanceagency cannot meet the demand of the population but mayalso be an unnecessary use of resources in urban, suburban,or rural areas where the supply of trauma care resources ex-ceeds, or in some cases far exceeds, the demand for theseresources in terms of severely injured patients.

The results of this analysis also underscore the impor-tance of evaluating system development in a given area,such as a state, using geographic data and evidence specificto that location. When considering trauma care, differencesbetween states in existing access to care, the distribution ofpopulation demand for care, and locations of existing andpotential health care resources (TCs and ambulances) makestate-specific guidance of vital importance in terms of thebest way to improve geographic access to care. This spec-ificity consideration is further magnified if additional non-geographic factors relating to access to care, such ascapacity considerations of TCs and pre-hospital responseagencies, are considered. In such cases, even a small statewith the intent of siting a modest number of resourcescan generate many more configuration choices (over andabove those that are simply geographic in nature) thancan effectively, much less optimally, be evaluated by thecurrent technology. For this reason, the model we used heredid not include any of these additional elements. Neverthe-less, rapid advances in computing may soon alleviate thisproblem, and when considering the geographic aspects ofthese policy problems, quantitative location techniquescan often produce optimal or near-optimal solutions fasterthan human judgment alone.

Fig. 2. Maps of increased access, in dark gray, within 60 minutes after optimally adding trauma centers and helicopter depots in select states.Light gray areas show existing access, and white areas show no access within 60 minutes.

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Other study shortcomings deserve mention. Our esti-mates of access were based on where people lived andnot where they were injured. Although people are certainlyinjured outside their residences, no national data exist onthe locations of all types of severe injuries at a very smalllevel of aggregation (such as ZIP codes). The advantages ofthe state-level, readily available databases that we used out-weighed this shortcoming (e.g., hospital discharge datahave a high level of geographic accuracy in terms of patientZIP codes because they are primarily intended for financialand billing activities). Although other databases could beused or a scheme to adjust hospital discharge data mightbe formulated, the return in better ZIP code data resultingfrom these strategies would be small compared with the siz-able investment in time and resources that such an effortwould require. Nongeographic issues that could have po-tentially changed access were also shortcomings in our

analyses. These issues included areas with no 9-1-1 tele-phone service, inclement weather, roadway congestion,and out-of-service times for ambulances and TCs. Never-theless, the impact of these issues on our results was prob-ably minimal: the vast majority of people in the UnitedStates have 9-1-1 access [16], relatively few helicopterflights are precluded by weather [18,19], traffic conditionsreportedly have only minor effects on ground ambulanceemergency response speeds on average [20], and helicoptersare estimated to be fully out-of-service only a small percentof the time [21]. Finally, cost constraints were potentiallyimportant considerations that were not included in themodels presented here. The individual conversion costs ofany single hospital into a TC or the construction of a newbase helipad can be significant, and the relative impact ofsuch costs, in the form of cost-versus-access trade-offcurves, has been reported in the past for a single-state

Fig. 3. Map of a range of increases in 60-minute access that result from adding one helicopter depot successively to all candidate sites acrossNorth Carolina. The one, optimal new helicopter depot location (same as in Fig. 2B) is also shown.

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trauma care system [13]. These trade-off curves may be thefocus of future multi-state analyses although it is worth not-ing that they are more computationally complex than thecalculations reported here (and, as such, may also thereforebe less appealing to policymakers).

Important next steps in this line of research include ana-lyzing other time-critical diseases, such as stroke, ST-segment elevation myocardial infarction, and cardiac arrest,as well as exploring cost and outcome projections, includingpotentially negative health consequences, for various solu-tions. Including system capacity constraints into future cal-culations will be important to ensure not only that thepopulation has geographic access but also that available sys-tem resources are sufficient and appropriately matched tomeet population need. Related policy questions will alsoneed to be addressed, such as how policymakers and plannerscan have their decisions best supported by mathematicalmodels such as those presented here and what role thesemodels should play in dictating how and where severely in-jured patients receive care. Additionally, it will be importantto consider whether trauma system resources should be sitedwith the general population in mind, which may favor urbanareas and increase rural disparities, or whether resourcesshould instead be located near populations at higher riskfor severe injury, which may favor areas with high injuryrates in specific populations (e.g., populations near highwayswith elevated motor vehicle crash rates) and higher overalldemand for trauma care. Finally, for analysts interested in in-strumental variable regression techniques, the percent calcu-lations of additional coverage might serve as usefulinstruments (as simulated data, they can be readily defendedas being orthogonal to many outcomes) in dealing with situ-ations of reverse causality or interdependence in varioushealth services research analyses.

The Centers for Disease Control and Prevention’sHealthy People 2020 objectives include the goal of increas-ing national access to trauma care by 8.3% [10]. Given theexpenses and often intense political arrangements associatedwith creating (or removing) TCs and HDs, as well as thecurrent national focus on eliminating wasteful health carespending, successfully achieving this goal necessitates in-formed, data-driven consideration of the geographic place-ment of additional resources. This analysis shows theimportance of using state-specific optimization methods toevaluate the types, locations, and expansion of resources,as impact varies greatly from state to state. These methodscould help systems planners compare the effectiveness ofvarious resource configurations and thus engineer the effec-tive placement of these resources to best enhance populationaccess to care.

5. Conclusion

Emergency care system design can bemeaningfully assis-ted by quantitative simulation techniques that compare theeffects of different resource configurations. In the states in-cluded in this analysis, the addition or relocation of TCs pro-vided greater increases in access to trauma care than did theaddition or relocation of HDs. However, these results variedfrom state to state, showing the importance of conductingstate-specific analyses to guide the placement of limitedresources. The results of this analysis suggest that state-specific optimization methods can be used to informpolicymakers and planners interested in determining optimallocations for trauma system resources in their specific states.

Rapid access to life-saving trauma care is a real-worldconsideration and a top priority for stakeholders. However,

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other real-world considerations such as cost and unintendedconsequences (e.g., reduction of patient volumes creatingdilution of provider experience and poor outcomes) are alsoof importance. Multiobjective models that extend beyondwhat is presented in this article and that account for accessto care as well as these other real-world considerations arebeing explored, some by our research team. Thus, impor-tant additional capabilities are possible and can be appliedto health care location problems such as the one presentedhere. Care should be taken, however, in not making suchmodels overly complex if the intent is for real-world stake-holders, such as state health planners, to become engagedand use the CER results that are produced. In this way,health care systems optimization can further help healthsystems planners compare the impacts of different resourceconfigurations and their possible effects on access to careand other outcomes of interest.

Acknowledgments

Dr. Carr is supported by a career development awardfrom the Agency for Healthcare Research and Quality(K08HS017960).

References

[1] Koch T. The map as intent: variations on the theme of John Snow.

Cartographica 2004;39(4):1e14.

[2] Weiss NS. Clinical epidemiology. In: Rothman KJ, Greenland S, ed-

itors. Modern epidemiology. Philadelphia, PA: Lippincott; 1998:

519e28.

[3] Welch HG, Sharp SM, Gottlieb DJ, Skinner JS, Wennberkg JE. Geo-

graphic variation in diagnosis frequency and risk of death among

Medicare beneficiaries. JAMA 2011;305:1113e8.

[4] Luft HS. From small area variations to accountable care organiza-

tions: how health services research can inform policy. Annu Rev Pub-

lic Health 2012;33:377e92.[5] Committee on Comparative Effectiveness Research Prior-

itization, I.o.M., Initial national priorities for comparative

effectiveness research. Washington, DC: National Academies

Press; 2009.

[6] ReVelle C. A perspective on location science. Location Sci 1997;

5(1):3e13.

[7] MacKenzie EJ, Rivara FP, Jurkovich GJ, Nathens AB, Frey KP,

Egleston BL, et al. A national evaluation of the effect of trauma-

center care on mortality. N Engl J Med 2006;354:366e78.

[8] Galvagno SM, Haut ER, Zafar SN, Millin MG, Efron DT,

Koenig GJ Jr, et al. Association between helicopter vs ground emer-

gency medical services and survival for adults with major trauma. JA-

MA 2012;307:1602e10.

[9] Branas, C.C., Carr B.G. Trauma center maps; 2010 cited 2012; Avail-

able at www.traumamaps.org. Accessed May 24, 2013.

[10] Centers for Disease Control and Prevention. Healthy People 2020

goals: improve access to trauma care in the United States; 2012;

Available at http://healthypeople.gov/2020/topicsobjectives2020/

objectiveslist.aspx?topicId524. Accessed May 24, 2013.

[11] Taheri PA, Butz DA, Lottenberg L, Clawson A, Flint LM. The cost of

trauma center readiness. Am J Surg 2004;187:7e13.

[12] Branas CC, MacKenzie EJ, ReVelle CS. A trauma resource allocation

model for ambulances and hospitals. Health Serv Res 2000;35:

489e507.

[13] Branas CC, ReVelle CS. An iterative switching heuristic to locate

hospitals and helicopters. Soc Econ Plann Sci 2001;35(1):11e30.

[14] MacKenzie EJ, Hoyt DB, Sacra JC, Jurkovich GJ, Carlini AR,

Teitelbaum DS, et al. National inventory of hospital trauma centers.

JAMA 2003;289:1515e22.

[15] Flanigan M, et al. Assessment of air medical coverage using the Atlas

and Database of Air Medical Services and correlations with reduced

highway fatality rates. Air Med J 2005;24(4):151e63.

[16] Branas CC, et al. Access to trauma centers in the United States.

JAMA 2005;293:2626e33.

[17] Carr BG, Caplan JM, Pryor JP, Cranas CC. A meta-analysis of preho-

spital care times for trauma. Prehosp Emerg Care 2006;10(2):

198e206.

[18] Whitney CL, Brown LH, Hunt RC. Use of local climatic data to de-

termine if weather precludes the operation of an air medical system.

Air Med J 2000;19:22e4.

[19] Askue V. Flying with ice. Air Med J 2001;20:10e1.

[20] Kolesar P, Walker W, Hausner J. Determining the relationship be-

tween fire engine travel times and travel distances in New York City.

Oper Res 1975;23:614e27.

[21] Stanhope K, Falcone RE, Werman H. Helicopter dispatch: a time

study. Air Med J 1997;16:70e2.