A flexible simulation platform to quantify and manage emergency department crowding

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Title:
A flexible simulation platform to quantify and manage emergency department crowding
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English
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Hurwitz, Joshua E.
Lee, Jo Ann
Lopiano, Kenneth K.
McKinley, Scott A.
Keesling, James
Tyndall, Joseph A.
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Abstract:
Background: Hospital-based Emergency Departments are struggling to provide timely care to a steadily increasing number of unscheduled ED visits. Dwindling compensation and rising ED closures dictate that meeting this challenge demands greater operational efficiency. Methods: Using techniques from operations research theory, as well as a novel event-driven algorithm for processing priority queues, we developed a flexible simulation platform for hospital-based EDs. We tuned the parameters of the system to mimic U.S. nationally average and average academic hospital-based ED performance metrics and are able to assess a variety of patient flow outcomes including patient door-to-event times, propensity to leave without being seen, ED occupancy level, and dynamic staffing and resource use. Results: The causes of ED crowding are variable and require site-specific solutions. For example, in a nationally average ED environment, provider availability is a surprising, but persistent bottleneck in patient flow. As a result, resources expended in reducing boarding times may not have the expected impact on patient throughput. On the other hand, reallocating resources into alternate care pathways can dramatically expedite care for lower acuity patients without delaying care for higher acuity patients. In an average academic ED environment, bed availability is the primary bottleneck in patient flow. Consequently, adjustments to provider scheduling have a limited effect on the timeliness of care delivery, while shorter boarding times significantly reduce crowding. An online version of the simulation platform is available at http://spark.rstudio.com/klopiano/EDsimulation/. Conclusion: In building this robust simulation framework, we have created a novel decision-support tool that ED and hospital managers can use to quantify the impact of proposed changes to patient flow prior to implementation. Keywords: Simulation, Emergency department, Throughput, Crowding, Quantify, Hospital, Site-specific, Boarding times, Fast track
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Hurwitz et al. BMC Medical Informatics and DecisionMaking 2014, 14:50 http://www.biomedcentral.com/1472-6947/14/50; Pages 1-11
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doi:10.1186/1472-6947-14-50 Cite this article as: Hurwitz et al.: A flexible simulation platform to quantify and manage emergency department crowding. BMCMedical Informatics and DecisionMaking 2014 14:50.

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 http://www.biomedcentral.com/1472-6947/14/50 RESEARCHARTICLE OpenAccessAflexiblesimulationplatformtoquantifyand manageemergencydepartmentcrowdingJoshuaEHurwitz1*,JoAnnLee1,KennethKLopiano2,ScottAMcKinley1,JamesKeesling1andJosephATyndall3 AbstractBackground: Hospital-basedEmergencyDepartmentsarestrugglingtoprovidetimelycaretoasteadilyincreasing numberofunscheduledEDvisits.DwindlingcompensationandrisingEDclosuresdictatethatmeetingthischallenge demandsgreateroperationalefficiency. Methods: Usingtechniquesfromoperationsresearchtheory,aswellasanovelevent-drivenalgorithmfor processingpriorityqueues,wedevelopedaflexiblesimulationplatformforhospital-basedEDs.Wetunedthe parametersofthesystemtomimicU.S.nationallyaverageandaverageacademichospital-basedEDperformance metricsandareabletoassessavarietyofpatientflowoutcomesincludingpatientdoor-to-eventtimes,propensityto leavewithoutbeingseen,EDoccupancylevel,anddynamicstaffingandresourceuse. Results: ThecausesofEDcrowdingarevariableandrequiresite-specificsolutions.Forexample,inanationally averageEDenvironment,provideravailabilityisasurprising,butpersistentbottleneckinpatientflow.Asaresult, resourcesexpendedinreducingboardingtimesmaynothavetheexpectedimpactonpatientthroughput.Onthe otherhand,reallocatingresourcesintoalternatecarepathwayscandramaticallyexpeditecareforloweracuity patientswithoutdelayingcareforhigheracuitypatients.InanaverageacademicEDenvironment,bedavailabilityis theprimarybottleneckinpatientflow.Consequently,adjustmentstoproviderschedulinghavealimitedeffectonthe timelinessofcaredelivery,whileshorterboardingtimessignificantlyreducecrowding.Anonlineversionofthe simulationplatformisavailableathttp://spark.rstudio.com/klopiano/EDsimulation/. Conclusion: Inbuildingthisrobustsimulationframework,wehavecreatedanoveldecision-supporttoolthatED andhospitalmanagerscanusetoquantifytheimpactofproposedchangestopatientflowpriortoimplementation. Keywords: Simulation,Emergencydepartment,Throughput,Crowding,Quantify,Hospital,Site-specific,Boarding times,FasttrackBackgroundIntroductionHospital-basedEmergencyDepartmentsarestrugglingto providetimelycaretoasteadilyincreasingnumberof unscheduledEDvisits[1].Dwindlingcompensation[2] andrisingEDclosures[3]dictatethatmeetingthischallengedemandsgreateroperationalefficiency.However, whencomparedtootherareaswithinthehealthcaresystem,EDspresentauniqueenvironmentofcompeting *Correspondence:jehurwitz@ufl.edu 1 DepartmentofMathematics,UniversityofFlorida,GainesvilleFL,USA Fulllistofauthorinformationisavailableattheendofthearticlepriorities,limitedresources,andawidevarietyofpatients demandingcare. Understandingthecomplexityofsuchenvironments requiresmorethanexperienceandintuitionalone.There isagrowingconsensusthateffectivemanagementofcare deliveryinhospital-basedEDsrequiresthesupportof mathematicalandcomputationalmodeling.Indeed,the primaryrecommendationoftheInstituteofMedicines 2006report, Hospital-BasedEmergencyCare:Atthe BreakingPoint wasthedevelopmentofengineeringand operationsresearchtoolsforthepurposesofimproving EDefficiencyandincreasingpatientflow. Inrecentyears,therehavebeenmanyeffortsinthis direction[4].Mathematicalandcomputationalmodels 2014Hurwitzetal.;licenseeBioMedCentralLtd.ThisisanOpenAccessarticledistributedunderthetermsoftheCreative CommonsAttributionLicense(http://creativecommons.org/licenses/by/2.0),whichpermitsunrestricteduse,distribution,and reproductioninanymedium,providedtheoriginalworkisproperlycredited.TheCreativeCommonsPublicDomainDedication waiver(http://creativecommons.org/publicdomain/zero/1.0/)appliestothedatamadeavailableinthisarticle,unlessotherwise stated.

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page2of11 http://www.biomedcentral.com/1472-6947/14/50havebeenusedtoforecastEDcrowdingonascaleof hours[5],quantifyfactorscontributingtopatientsleaving withoutbeingseen(LWBS)[6-9],assesspatientstreaming mechanisms[10-15],optimizestaffandresourceallocation[16-21],conductfinancialanalyses[22-24],andstudy theimpactofreducingboardingtimes[18,23].However, becauseitisriskytoimplementmanagementoverhauls, agapremainsbetweenEDmodelsandcurrentmanagementpractice[25].ImportanceEDmanagementfaceavarietyofoptionswhendeciding howtoimproveefficiency,andseeminglystraight-forward operationalinnovationscanberenderedineffectiveby counterintuitivepatientflowdynamics[18,23,26].The utilityofpatientflowsimulationsliesnotinsimplifying thiscomplexity,butincapturingit.Adetailedmodelof EDthroughputcanaccuratelyquantifypredictionsfor managementinterventionsthatareformulatedbyexperienceandintuition.GoalsofthisinvestigationThefirstgoalofthisinvestigationwastodevelopawidelyconfigurablediscrete-eventsimulationframeworkthat allowsforquantificationoflong-termpatientflowoutcomes.Thesecondgoalwastovalidatetheabilityofthe modeltoaccuratelysimulatetwodistinctEDenvironments…oneresemblinganationallyaverageEDandone resemblinganaverageacademicED,bothintheUnited States.Thethirdgoalwastosimulateandanalyzethe additionofbedsandstaff,theimplementationofalternate carepathways,andreductionsinboardingtimesineach oftheseenvironments.MethodsPatientflowmodelToconstructamapofpatientflowthroughanED (Figure1),weconductedindepthinterviewswith providersregardingworkprocessesandoperationalcharacteristicsofanexampleED.Weassumethefollowing patientflowstructure:UponarrivaltotheED,patients arestreamedaccordingtotheirEmergencySeverityIndex (ESI)score[27].ThemostacutepatientsareimmediatelyclassifiedasESI-1andaretakendirectlytoa trauma/resuscitationbedintheMainTreatmentArea (MTA)oftheEDwheretheirtreatmentpreemptsthatof loweracuitypatientscurrentlybeingtreated.Afraction ofESI-2patientsalsobypasstriageandgodirectlytoan MTAbed.AllotherpatientsreceiveanESIscorebetween 2and5intriageandmovetothewaitingroomuntila bedbecomesavailable.Patientsinthewaitingroomare selectedforbedassignmentbasedonacuityandtimeof arrival.Insomeofourexperimentalscenarios,thereisa separateFastTrack(FT)areaavailableforusebyESI-4 andESI-5patients.Patientswhostaytoolonginthe waitingroom(i.e.whodonotreceiveabedbeforetheir toleranceforwaiting)leavewithoutbeingseen. PatientswhodonotleaveareassignedtoanMTA orFTbed,andarebrieflyassessedbyanurse.Ahistoryistakenandaphysicalexamisthenperformed byaphysician;thephysicianmightsubsequentlyorder labsorradiologicaltesting,performprocedures,ordispositionthepatient.Patientswhohavelabsorimages orderedoccupyabedandreceiveintermittentnursingattentionuntiltheresultsarereadyandaphysician returnstoreviewthem;thephysiciancanthenordermore tests,performprocedures,ordispositionthepatient.In theFT,physicianassistants(PAs)performthedutiesof physicians.Inbothtreatmentareas,patientswhoaredispositionedtodischargeexittheEDafterashortdelay toreceivedischargeinstructions;patientsdispositioned toadmitremainintheirassignedbedandreceivecare untilahospitalbedisavailable…aprocessknownas boarding.SimulationdetailsThesimulationplatformcodeiswritteninRandutilizes stochastic,event-drivenprogrammingtomodelpatient flowthroughauser-configuredEDenvironment. Inourmodel,acuity…asmeasuredbyESI…isthe primarydeterminantofpatientcomplexity,streaming, andprioritization.Assuch,parametersgoverningpatient arrivalrates,nurse-to-patientratios,tolerancebefore LWBS,treatmentsteps,admitrates,andboardingdelays aremodulatedtoreflectthisacuity-dependence. EDdynamicsareintrinsicallyvariableandsoanymodel EDmustembracerandomnessasacorefeature.Unfortunately,mostofthedataavailableforeventdurations onlyincludemeasuresofcentraltendency.Toaccount fornaturalvariationineventdurations,weusedindependentGamma-distributedrandomvariables.Thiswas motivatedbythefactthatGammarandomvariablesare completelycharacterizedbytheirmeanandvariance,and representthewaitingtimebetweenmultiplePoissondistributedevents. ThemostnotableexceptiontotheGammadistribution frameworkisinpatientarrivaltimes,whicharerandom andfluctuatedependingonthetimeofday.Wemodel patientarrivalsbyanon-homogeneous(time-dependent) Poissonprocess[28]…astochasticprocessuniquely definedbyitstime-dependentarrivalintensity.Tocreate thisintensityfunction,weusedastepfunctiongenerated fromhourlyEDarrivalratedata[29](Figure2).These arrivalrateswereadjustedtoaccountforthecontribution fromeachacuitylevel…thatis,aseparatefunctionwas generatedforeachacuitysarrivals.Wenotethatarrival intensityfunctionsforeachacuitycanbeadjustedtofit datafromanyemergencydepartment.

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page3of11 http://www.biomedcentral.com/1472-6947/14/50 Figure1 Patientflowmap. Patientpathsaredirectedbasedonacuityandresourceneeds.IfanEDdoesnotutilizeaFastTrack,allpatientsare assignedabedintheMainTreatmentArea.DataresourcesPubliclyavailabledata[29-31]providedmanykeyparametersgoverningpatientarrivalsandcomplexities,boarding delays,andrecommendedstaffinglevelsforthenationallyaveragesetting.WithpermissionfromtheAcademy ofAcademicAdministratorsinEmergencyMedicine (AAAEM),weuseddatafroma2012benchmarksurvey [32]toestimatetheseparametersfortheaverageacademic setting.EDprovidersestimatedfinerparameterssuchas labandimagingturnaroundtimesandpatient-physician interactionlengthsforbothsettings.Table1outlinesthe keyinputparametersforeachEDenvironmentandthe outputvaluesusedtovalidatetheaccuracyofeachmodel. WestressthatthedatacomparedtothesimulationoutputsinthebottomofTable1 wasnotusedtoconstruct eithermodel …rather,thisdatawasusedonlytovalidate theaccuracyofeachmodel. Incomparingnationallyaveragestatisticstodatacollectedfromacademichospitals,itisimmediatelyclear thatacademicenvironmentsonaverageexperiencehigher patientarrivalrates.Moreover,themixofpatientstends tobemoreacuteinacademicsettings(seetoptwopanels ofFigure2).Becauseofthis…andthefactthattheyare typicallyassociatedwithlargehospitals…academicEDs havehigheradmitratesandlongerboardingtimesrelative tothenationalaverage.Toaccommodatethis,academic EDstendtohavemorebedsandhigherstaffinglevels. Sincealldatausedinthisexperimentwaspubliclyavailable,approvalbyanethicscommitteewasnotrequired.LimitationsOurmodelmakesnoassumptionsregardingfactorscontributingtotriageorregistrationdelays.Instead,simulatedpatientsareassignedalengthoftimedrawnfroma Gammadistributiontocompletetriageandregistration. Becauseourmodelassumesshortdoor-to-triagetimes, weassumeanyerrorisnegligible;itisalsocomputationallyefficienttoassumethisdistributionisstate-and time-invariant. Whileapatientsdecisiontoleavewithoutbeingseenis influencedbymanyfactors[33],ourmodelalsoassumes thateachpatientsdecisiontoLWBSdepends only on waitingtime.Tothatend,eachsimulatedpatientarrives withatoleranceforwaitingthatisdrawnfromanacuitydependentGammadistribution.Ifapatientdoesnot receiveabedbeforetheirtoleranceforwaiting,theyexit theEDandaremarkedasLWBS. Topologyandlayoutareimportantfactorsthataffect EDthroughput.Ourmodelaccountsforthisbyincorporatingthetimeittakesforaprovidertomovefrom roomtoroom.Thisismodeledusingtime-andproviderdependentexponentialrandomvariables. Amoresignificantlimitationisthatourmodelassumes thatphysiciansarenotassignedtospecificpatients. Rather,whenpatientsdemandaphysician,anyavailable physiciancanprovidecare.Intheacademicenvironment, physician-providerstypicallyworkinteamsoffaculty pairedwithresidents.Forthepurposesofthissimulation, weassumethatasinglephysicianintheacademicsetting

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page4of11 http://www.biomedcentral.com/1472-6947/14/50 Figure2 AdayinthelifeofanED. Generatedarrivalfunctions(top),and30-daysimulatedlocationofpatients(middle)andidleresources (bottom)fornationallyaverageandaverageacademicEDsettings.Thenationallyaveragesettingislimitedbyproviders,whilebedsaretheprimary bottleneckintheaverageacademicsetting.adequatelyrepresentsaphysician-residentteam.Wenote thatthesimulatedpatientsperdoctorperhourstatistic(Table1)isaconsistentvalueinbothsettings[32,34]. ThedevelopmentofanefficientalgorithmtoassignphysicianstospecificpatientswillimproveEDsimulationsand deservesfurtherstudy. NursingattentioninanEDisamuchmorevariedand continuousprocessthanpatientinteractionswithaphysician.Ratherthanmodelpatientsdemandfornursingcare asmultiplediscreteintervals,simulatedpatientsoccupy afractionofanurse(correspondingtonurse-to-patient ratios)atalltimeswhileinanEDbed.Ourmodelfor

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page5of11 http://www.biomedcentral.com/1472-6947/14/50Table1Inputparametersandoutputvalidationforthenationallyaverageandaverageacademicenvironments InputparametersNationalaverageAcademicaverage MTABeds321415FTBeds0162Physicians3242PAs0212Nurses82132NursetoPatientRatio†1:431:43MeanArrivalsperDay15511955MeanLWBSThreshold†3.5hrs23.5hrs2MeanNursingAssessment†5min25min2MeanPhysicianAssessment†10min210min2MeanLabTAT†30min245min2MeanImagingTAT†75min290min2AdmitRate†12.8%125.8%5MeanBoardingDelay†1.63hrs44.43hrs5 OutputsSimulatedActual1SimulatedActual5 LWBSRate(%)3.06(1.03)3.004.54(0.88)4.50 Door-to-EventTime(hrs)„„„„ Doctor 0.98(0.10)0.971.25(0.07)1.31 Disposition 3.06(0.15)3.083.41(0.08)3.41 Exit 3.71(0.15)3.735.63(0.10)5.67 Patients/Doctor/Hour2.41(0.02)1.8-2.832.21(0.01)2.51 Patients/Bed/Year1764.5(16.8)nodata1513.8(9.67)1360.3 Inputparametersforthenationallyaverageandaverageacademicenvironments(above).Simulatedoutputsreportedasmean(sd)of30one-monthsimu lations closelyapproximateactualdata(below).Note:between2:00amand10:00am,thenumberofphysiciansisreducedby1andthenumberofnursesisreduced by3.†Theseparametersaremodulatedtobeacuity-dependentaccordingtoanEDproviderheuristic;thefiguresreportedarethemeanoverallpatients. TAT :turnaround time.Sources:1CDC[29],2EDProviderEstimate,3ACEP[31,34],4CMS[30],5AAAEMSurvey[32].managementassumesthatapatientcannotbeplacedina bedwithoutsufficientnursingstaffing.Therefore,inour model,anursingshortagewillmanifestitselfasalackof usablebeds. BoardingtimesinarealhospitalsettingaredependentonmanyfactorsoutsideoftheED,suchashospital capacity,transportefficiency,anddischargeschedules. Ourmodeldoesnotsimulatethesedirectly.Rather,when asimulatedpatientisdispositionedtoadmit,aGamma distributionisgeneratedandaboardingtimedrawnfrom thisdistributionisassignedtothepatient.Themodel allowsforacuity-andtime-dependentdistributions,but duetoalackofconcretedata,thesimulationswereport hereusedaboardingtimedistributionthatwasacuityandtime-invariant.ResultsAsistobeexpectedwithasimulationofthismagnitude, thereareaverylargenumberofparameters.Inparticular,wefocusedontwoparameterregimes:onedictated byalackofproviders,theotherbyalackofbeds.Interestingly,equippingthesystemwithnationallyaverage statisticsledtoprovider-limiteddynamics,whileusing averageacademichospitalstatisticsledtobed-limited dynamics. Theresultsflowfromthreephasesofanalysis: validation explication ,and experimentation .In validation wecomparetraditionalmetricsofEDthroughputto simulatedoutputstatisticstoensurethemodelissufficientlyaccurate.ThesimulationalsoproducesnumerousstatisticswhicharedifficulttotrackinarealED setting,butproveusefulinunderstandingEDprocess ofcare.In explication ,weuseminute-by-minutetrackingofresourceutilization,patientlocations,andacuityspecificdoor-to-eventstatisticstoidentifycausesof delaysinEDthroughput.Finally,weconductedaseries ofrigorous numericalexperiments totesttheeffectivenessofintroducingadditionalresources,implementing

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page6of11 http://www.biomedcentral.com/1472-6947/14/50alternatecarepathways,andreducingboardingdelays inboththenationallyaverageandaverageacademicED settings.Validation:themodelprovidesconsistentandfaithful outputsWeconstructedandtunedthemodeltomatchnationally averagedata.Afterappropriatelyupdatingdata-driven parameterssuchaspatientarrivals,patientcomplexitiesandEDresourcelevels,wemodifiedthemeanlab turnaroundtimefrom30minutesto45minutesand themeanimagingturnaroundtimefrom75minutesto 90minutesbasedonEDproviderestimates.Theresult closelyapproximatedaveragethroughputmetricsfrom theacademichospitalsurvey(Table1). Wereportourresultsforeachenvironmentinterms oftheoutcomeof30-daysimulations.TheoutputstatisticsweusedforvalidationareLWBSrate,door-to-doctor, door-to-disposition,door-to-exit,patientsperdoctorper hour,andpatientsperbedperyear.Thestandard deviationsreportedintheOutputssectionofTable1 reflectvariationinthemonthlyaveragestatistics.We stressthatwhereasthestatisticsfromtheupperhalfof Table1aredirectlyinputtothemodelasparameters, thereportedOutputbenchmarksareoutcomesofthe simulation. Tocheckforconsistencywithotherexistingmodels, wecomparedourresultstothosereportedbyKhare etal.[18],whopublishedamodelusingparameters characterizingacuity-dependentarrivals,LWBStolerance,treatmentlengths,andadmitrates.Accountingfor EDbeds,physicians,andboardingtimes,theyconcluded thatreducingboardingtimesby25%decreasedmean lengthofstayby22minutes,whilefiveadditionalbeds increasedmeanlengthofstaybysevenminutes.Using theirinputparameters,wewereabletosimulateanED withasimilarmeanlengthofstayandLWBSrate,and thenreplicatetheirresults:ourmodelpredictedthat reducingboardingtimesby25%reducedmeanlengthof stayby23.4minutes,whilefiveadditionalbeds(andsufficientnursingcoverage)hadnoeffectonmeanlength ofstay.Explication:identifyingsite-specificcausesofcrowdingOurmodelproducesanovelbreakdownofwell-known statisticalbenchmarksintermsofpatientacuity.In Figure3,wedisplaykeydoor-to-eventtimesinboth thenationallyaverageandtheaverageacademicenvironments.Thecolorsindicatepatientacuityandthe radiiofthecirclesisproportionaltotheabsolutenumberofsimulatedpatientstreatedinthatacuitygroup. Figure3reaffirmsthatthetimelinessofcaredeliveryis highlyacuity-dependent[35].WhereasESI-1andESI2patientsaretreatedefficiently,loweracuitypatients oftenexperiencetremendousdelays.Forexample,ESI-3 patientsintheacademicEDhavean average lengthofstay over6hours(Figure3,rightpanel,rightmostgreencircle). ThisisduetotwopropertiesoftypicalESI-3patients:low prioritization,whichaccountsforlengthydoor-to-bed times,andwidely-rangingcomplexities,whichcontribute tolongdoctor-to-exittimes. InordertounderstandthecausesofEDcrowding, weexamineFigure2.Inthebottomtwopanels,wesee thesimulatedmeanidleresourcesasafunctionoftime ofday.Whilethereareessentiallyzeroidlephysicians fromnoontomidnightinthenationallyaverageED, bedsarethelimitingresourceintheacademicsetting. Theimpactcanbeseeninthemiddletwopanels.Note thesharpincreaseofpatientsinthewaitingroomin theacademicsettingeveryevening.Thisstemsfroma combinationofahighinfluxofpatientarrivals…particularlyhigh-complexityESI-2andESI-3patients(see toptwopanelsofFigure2)…combinedwitharisein thenumberofboardedpatients.Thisdynamicmakes plainwhyaddingbeds(orreducingboardingdelays)can haveasignificantimpactinanaverageacademicenvironment,butlittletonoeffectinanationallyaverage environment.Numericalexperiments Improvementfromresourceadditionissite-specificIdentifyingtheprimarycausesofcrowdinginanEDis acriticalstepinknowinghowtoincreasethroughput. Importantly,ourmodelshowsthatextensive…butpoorlytargeted…resourceadditionscanhaveanegligibleimpact onpatientflow.InFigure4,wedisplaysimulatedmean door-to-eventtimesthatresultfromafewresourcing remedies. Theresponseisdifferentinthetwosettings.Theadditionofonefull-timephysiciansignificantlyreducedmean lengthofstayintheprovider-limitednationalsetting,but hadlittleeffectinthebed-limitedacademicsetting.Conversely,additionalbedsandnursessignificantlyaffected themeanlengthofstayintheacademicsetting,butnot thenationalsetting. WealsoobservethatwhenanEDisprimarilybottleneckedbyasingleresource,addingacombinationof resourcesprovidesnomoreimprovementthanahighly targetedremedy.Thisismanifestedintheleftpanel ofFigure4,wherethedoor-to-eventtimesthatresult fromaddingonedoctor,eightbeds,andtwonursesis nearlyidenticaltotheresultfromaddingonedoctor alone.Furthermore,wenotethatthemodelcanidentifythepointofdiminishingreturns.Forexample,we foundthataddingonedoctorinthenationalsetting reducesmeanlengthofstaybyonehour,butaddingaseconddoctordoesnotfurtherreducemeanlengthofstay (notdepicted).

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page7of11 http://www.biomedcentral.com/1472-6947/14/50 Figure3 Simulateddoor-to-eventtimes. Theradiusofeachdotcorrespondstothenumberofpatientsinthatdemographicandthesizesare comparableacrossplots.Thetimelinessofcaredeliveryislargelyaffectedbypatientacuity.Fasttrackmechanismscanhelpallpatientsin provider-limitedsettingsDuetoprioritization,low-acuity(ESI-4andESI-5) patientscanoftenwaithoursforwhatwillbequicktreatmentanddischargefromtheED.Toexpeditecarefor thesepatients,manyEDshaveimplementedaFastTrack (FT)mechanism…aseparatebaystaffedwithmidlevel providersequippedtotreatlow-acuitypatients.Often timestosaveoncapitalcosts,bedsandstaffarerepurposedfromtheMTA,leavingfewerresourcesavailablefor MTApatients.Ourmodelcanquantifythistradeoff. WemeasuredtheeffectofvariousFTmechanismson lengthofstayandLWBS.ThenumberofbedsrepurposedforeachFTwerechosensothattherelativesizes wereroughlyequivalentbetweenthenationalandacademicsettings.Forexample,a4-BedFTinthe32-bed nationalsettingutilizes12.5%oftotalbedcapacity,and a6-BedFTinthe47-bedacademicsettingutilizes12.8% oftotalbedcapacity.InaccordancewiththeESIImplementationHandbook[27],ESI-4andESI-5patientswere eligibletousethefasttrack,andthesepatientswere assignedtoeithertheMTAorFTbasedonbedavailability.Patientscouldnotswitchtreatmentareasonce assigned,andprovidersonlytreatedpatientsintheareato whichtheproviderswereassigned(otherconfigurations arepossible). Themodeldemonstratesthattherearesettingswhere resourcescanbedivertedtotheFTwithoutcompromisingcareforhigheracuitypatientsintheMTA.Forexample,intheprovider-limitednationalsetting,the8-BedFT mostefficientlyachievesthisgoal(leftpanelofFigure5). Becauselow-acuitypatientswererapidlytreatedintheFT, Figure4 Effectofadditionalresourcesonpatientflow. Simulatedmeandoor-to-eventtimeswithadditionalresourcesforeachED environment.Inbothsettings,asuiteofresourcesisnomoreeffectivethanasingle,well-targetedresource.

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page8of11 http://www.biomedcentral.com/1472-6947/14/50 Figure5 Effectoffasttrackmechanismsonpatientflow. SimulatedeffectofFastTrackmechanismsinthenationallyaverageandaverage academicenvironments. Bold valuesarethestandardsettingsforeachenvironment.FTmechanismsinthebed-limitedacademicsettingarea cleartradeoffbetweenlow-acuityandESI-3throughput.theytendednottooccupyMTAbeds,wheretheirtreatmentwassignificantlydelayedduetoprioritization.This freedmorebedsforESI-3patients,reducingtheirmean lengthofstay.High-acuity(ESI-1andESI-2)patientswere notaffected. ObservethatdivertingtoomanyresourcestotheFT adverselyaffectsESI-3patientsmeanlengthofstay.In fact,thereexistsettingswhereanydiversionofresources totheFTcompromisescareforpatientsintheMTA. Inourmodel,ESI-3patientsintheacademicsetting experienceanincreasedmeanlengthofstayforallFT mechanisms(rightpanelofFigure5).Reducingboardingtimescanhelpallpatientsinbed-limited settingsPatientsdispositionedtoadmitareboardedintheEDif ahospitalbedisnotavailable.Thesepatientsdecrease EDcapacitybyeffectivelyblockingabedandoccupying staff.Weexaminedtheeffectofvaryingboardingtimeson throughputinbothEDsettings. Figure6showsthesensitivityofthemeanlengthof stayforadmits,discharges,andoverallLWBSrateto meanboardingtimeineachsetting.Asexpected,we seethatthemeanboardingtimedirectlyaffectsthe meanlengthofstayforadmitsinbothsettings.However,inthenationalsetting,themeanlengthofstay fordischargesandtheoverallLWBSrateisnotlargely affectedbychangingboardingtimes.ThisisbecausedischargesandLWBSpatients(whotendtobelow-acuity) areaffectedbythenumberofblockedbeds,whichis afunctionofbothboardingtimes andadmitrate .The nationalsettingisnotprimarilybed-limitedandhas arelativelylowadmitrateof12.8%.Thus,systematicallyreducingboardingtimesunblocksasmallnumberofbedsinasettingwherebedsarenotscarceto beginwith. Intheacademicsetting,ontheotherhand,weobservea well-knownphenomenon[22,23,26,36]thatlongerboardingtimesincreaseEDcrowding.Therightpanelof Figure6quantifieshowmuchthemeanlengthofstayfor dischargesandoverallLWBSratedecreaseasboarding timesarereduced.Thisisbecausetheacademicsetting hasarelativelyhighadmitrateof25.8%andisbedlimited.Thus,loweringboardingtimesunblocksasignificantnumberofbedsinanenvironmentwherecrowding isprimarilycausedbybedavailability.Thissuggeststhat

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page9of11 http://www.biomedcentral.com/1472-6947/14/50 Admirate = 12.8%Admit rate = 25.8% t Figure6 Effectofreducingboardingtimesonpatientflow. SimulatedeffectofboardingtimesonlengthofstayandLWBSinthenationally averageandaverageacademicEDsettings.Thedottedverticallinemarksthestandardmeanboardingtimeforeachsetting.Thebed-limited academicsettinghasahigheradmitrateandshowsgreatersensitivitytoboardingtimes.inthissetting,systematicallyreducingboardingtimescan beeffectiveinimprovingEDthroughput. Thedynamicsofhospitalcapacitythroughouttheday largelydetermineEDboardingtimes.Thisphenomenon maybeaffectedbythetimingofhospitaldischargesand canbequantifiedbythismodel.Duetoalackofavailable data,wedonotpresentthishere.DiscussionEmergencyDepartmentcrowdingisacomplexproblem affectingmorethan130millionpatientvisitsperyearin theU.S.[36].Althoughemergencydepartmentsplaya vitalroleinprovidingunscheduledaccesstohealthcare, financialstrainandlimitedresourceschallengehospitals toprovidetimelyandeffectivecare.Computersimulation ofEDpatientflowcancapturetheinherentcomplexityof thissystemandelucidateitsunderlyingdynamics.With thisgoalinmind,wehavedevelopedaflexiblemodelof EDpatientflow.Inthespanofminutes(onapersonallaptop),wecanaccuratelysimulateEDthroughputacrossa widevarietyofsettings.Themodelgeneratesaminute-byminutecensusofpatientsintheED(Figure2,bottompanels),andcalculatestraditionalthroughputmetricsbroken downbybothacuity(Figure3)anddisposition(Figure6). Asexpected,whenthemodelisequippedwithrealistic parameters,weseepervasiveEDcrowding.Inthecurrentworldofscarceresourcesandlittlemarginforerror, itisessentialtorigorouslyidentifythespecificcausesof crowding,sothattargetedmanagementinterventionscan havemaximaleffect.OurmodelcanpredictandquantifyhowaparticularEDwillrespondtoagivenwhatifŽ scenario. Withourabilitytogeneratenon-traditionalpatientflow statistics,suchasaminute-by-minuteaccountofidle resources(Figure2,middlepanels),wecanweightthevariousfactorsthatcausecrowdingonasite-to-sitebasis. Oneoftherecurringobservationsinourinvestigationis thateachsimulatedenvironmenthasitsowndominant resourcebottleneck.Furtherhighlightingtheimportance ofquantifiedpredictions,wefoundthataddingasuite ofresourcesisnomoreeffectivethanaddingasingle, well-targetedresource(Figure4). Todemonstratethisphenomenon,weconstructedand theninvestigatedtwoqualitativelydistinctEDenvironments:onecreatedfromstatisticsaveragedoverallU.S. emergencydepartments,andanotherfromstatisticsaveragedoveracohortofU.S. academic emergencydepartments(Figure1).Wefoundthatashortageofproviders dictatedcrowdinginthenationallyaveragesetting,but ashortageofbedswastheprimarycauseofdelaysin theaverageacademicenvironment(Figure2).Asaresult, solutionsthataimtoincreasebedcapacity…suchassystematicallyreducingboardingtimes…areeffectiveinthe averageacademicenvironment,butlimitedinthenationallyaveragesetting(Figure6).FastTrackmechanismshad theconverseeffect(Figure5). Inthisway,simulationofEDsdoesmorethanconfirmmanagementintuitions.Havingacomprehensive viewofpatientflowcanhelpconstructasystem-wide understandingofwhatgivenmanagementinterventions actuallyaccomplish.Forexample,theobservationthatthe responsetomanagementinterventionsishighlysensitivetolocalresourcelimitationsisperhapsundervalued insomedata-drivenassessmentsofEDperformance.A 2008reportfromtheAmericanCollegeofEmergency Physicians(ACEP)concludedthat,theclearestcauseof crowding[intheED]istheboardingofadmittedpatientsŽ, andwarnedthatseparatefasttrackmechanisms,will

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Hurwitz etal.BMCMedicalInformaticsandDecisionMaking 2014, 14 :50 Page10of11 http://www.biomedcentral.com/1472-6947/14/50createsilosandobstaclestopatientflowŽ[37].However,a 2011surveyreportfromtheNationalAssociationofPublicHospitals(NAPH)liststheimplementationorexpansionofafasttrackmechanismasahighperformance strategyŽtoimproveEDthroughput[38].Moreover,the NAPHrecommendsexpandingEDbedspace…astrategyKhareetal.,whosesimulationparametersproduceda provider-limitedsetting,foundtobeineffective[18].We notethattheNAPHsurveysampledfromitsmembership,whichfeaturesalargenumberofcommunityand safety-nethospitalsthatresembleournationallyaverage ED.Itisthenconsistentthattheywouldfindfasttrack mechanismstobeuseful.Ontheotherhand,itisnot clearwhichhospitalscontributedtotheconclusionsfrom ACEP.Ifthesampleisskewedtowardlargehospitalswith amoreacutepatientmix,itwouldhelpexplainthese contradictingrecommendations.ConclusionWehaveconstructed,andmadepubliclyavailable athttp://spark.rstudio.com/klopiano/EDsimulation/,an efficientmodelofEDpatientflowwhichcapturesthe complexitiesofEDprocessofcare.Withtheflexibility ofnumerousinputparameters,ourmodelcanaccurately simulateawidevarietyofenvironments.Weinvestigated twoqualitativelydistinctEDenvironmentsandfound thatsimilarchangestoprocessofcare…suchasadding resources,implementingfasttrackmechanisms,orsystematicallyreducingboardingtimes…hadverydifferent effectsonpatientflow.Accuratelypredictingtheeffects ofthesechangesisoftendifficult,whichsuggeststheusefulnessofmoregranularsimulationsinunderstanding EDdynamics.Moreover,ourmodelsabilitytoaccurately quantifythesedynamicsprovidesameanstoidentify specificbottlenecksandtesttheeffectsofproposedoperationalchanges.ThiscanallowEDandhospitalmanagers toformulatecost-effective,hospital-specificsolutionsto EDcrowding.Competinginterests Theauthorsdeclarethattheyhavenocompetinginterests. Authorscontributions JKandJATconceivedthestudy.JEH,JL,andSAMdesignedandwrotethe preliminarysimulationcode.JEHwrotethefinalsimulationcode.JEHandJL researchedpubliclyavailabledata,andestimatedinputparameters.JEH,JL, andSAMdesignedandanalyzedpreliminarynumericalexperiments.JEH performedthefinalnumericalexperiments.SAM,JK,andJATprovidedexpert adviceonstudydesignandoversawtheproject.JEH,SAM,andJATdrafted themanuscript,andallauthorscontributedtoitsrevision.JEHandKKL adaptedthesimulationcodetotheonlineplatform.JEHtakesresponsibility forthepaperasawhole.Allauthorsreadandapprovedthefinalmanuscript. Acknowledgements KKLwassupportedbyNationalScienceFoundationGrantNumberDMS 1127914.SAMwassupportedbySimonsFoundationGrantNumber245653. Authordetails1DepartmentofMathematics,UniversityofFlorida,GainesvilleFL,USA.2StatisticalandAppliedMathematicalSciencesInstitute,ResearchTriangle ParkNC,USA.3DepartmentofEmergencyMedicine,UniversityofFlorida, GainesvilleFL,USA. 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