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The Diversity of Concentrated Prescribing Behavior: an Application to Antipsychotics

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Physicians prescribing drugs for patients with schizophrenia and related conditions are remarkably concentrated in their choice among antipsychotic drugs. In 2007 the single antipsychotic drug prescribed by a physician accounted for 66% of all antipsychotic prescriptions written by that physician. Which particular branded antipsychotic was the prescriber's "favorite" varied widely across physicians, i.e. physician prescribing concentration patterns are diverse. Building on Frank and Zeckhauser's [2007] characterization of physician treatments varying from "custom made" to "ready-to-wear", we construct a model of physician learning that generates a number of hypotheses. Using 2007 annual antipsychotic prescribing behavior on 17,652 physicians from IMS Health, we evaluate these predictions empirically. While physician prescribing behavior is generally quite concentrated, prescribers having greater volumes, those with training in psychiatry, male prescribers, and those not approaching retirement age tend to have less concentrated prescribing patterns.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.
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NBER WORKING PAPER SERIES
THE DIVERSITY OF CONCENTRATED PRESCRIBING BEHAVIOR:
AN APPLICATION TO ANTIPSYCHOTICS
Anna A. Levine Taub
Anton Kolotilin
Robert S. Gibbons
Ernst R. Berndt
Working Paper 16823
http://www.nber.org/papers/w16823
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
February 2011
This research has benefited enormously from the IMS Health Services Research Network that has
provided data and data assistance. Special thanks are due Stu Feldman, Randolph Frankel, Cindy
Halas, Robert Hunkler and Linda Matusiak at IMS Her any of its affiliated or subsidary ealth. The
statements, findings, conclusions, views and opinions contained and expressed here are based in part
on 1996-2008 data obtained under license from IMS Health Incorporated: National Prescription Audit,
Xponent and American Medical Association Masterfile. All rights reserved. Such statements, findings,
conclusions, views and opinions are not necessarily those of IMS Health of its affiliated or subsidiary
entitites. This research has not been sponsored. The views expressed herein are those of the authors
and do not necessarily reflect the views of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peer-
reviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2011 by Anna A. Levine Taub, Anton Kolotilin, Robert S. Gibbons, and Ernst R. Berndt. All rights
reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission
provided that full credit, including © notice, is given to the source.
The Diversity of Concentrated Prescribing Behavior: An Application to Antipsychotics
Anna A. Levine Taub, Anton Kolotilin, Robert S. Gibbons, and Ernst R. Berndt
NBER Working Paper No. 16823
February 2011
JEL No. D83,I10,L25,O33
ABSTRACT
Physicians prescribing drugs for patients with schizophrenia and related conditions are remarkably
concentrated in their choice among antipsychotic drugs. In 2007 the single antipsychotic drug prescribed
by a physician accounted for 66% of all antipsychotic prescriptions written by that physician. Which
particular branded antipsychotic was the prescriber's "favorite" varied widely across physicians, i.e.
physician prescribing concentration patterns are diverse. Building on Frank and Zeckhauser's [2007]
characterization of physician treatments varying from "custom made" to "ready-to-wear", we construct
a model of physician learning that generates a number of hypotheses. Using 2007 annual antipsychotic
prescribing behavior on 17,652 physicians from IMS Health, we evaluate these predictions empirically.
While physician prescribing behavior is generally quite concentrated, prescribers having greater volumes,
those with training in psychiatry, male prescribers, and those not approaching retirement age tend
to have less concentrated prescribing patterns.
Anna A. Levine Taub
Washington University
Olin School of Business
One Brookings Drive, Campus Box 1133
St. Louis, MO 63130
aalevine@wustl.edu
Anton Kolotilin
Massachusetts Institute of Technology
Department of Economics
50 Memorial Drive, E52
Cambridge, MA 02142
akol@mit.edu
Robert S. Gibbons
MIT Sloan School of Management
100 Main Street, E62-524
Cambridge, MA 02142
and NBER
rgibbons@mit.edu
Ernst R. Berndt
MIT Sloan School of Management
100 Main Street, E62-518
Cambridge, MA 02142
and NBER
eberndt@mit.edu
I. INTRODUCTION
Consideraphysicianseeingapatientwithaconfirmeddiagnosisforwhichanumberof
alternativepharmaceuticaltreatmentsareavailable.Patientresponsetothevarioustreatmentsis
idiosyncraticandunpredictableinterm sofbothefficacyandsideeffects,andthereislittleclinical
evidentiaryliteratureuponwhichthephysiciancanbaseanexan
techoi
ceamongthealternativedrug
treatments.Whattreatmentalgorithmsmightthephysicianemploytogatherevidenceandlearn
regardingtheefficacyandtolerabilityofthevarietyofpossibledrugtherapiesforthepatient?
Giventhisuncertaintyandimperfectinformation,onepossibilityisforthephysicianto
concen
trateprescribingbehavioronasingledrug.Inthiswaythephysicianengagesinlearningby
doing,observesresponsestothatdrug,adjustsdosagestrength aswarranted,andtherebyexploits
his/heraccumulatingknowledgeandexperience.Simultaneouslythephysicia ncouldalsocounselthe
patientontheefficacyandsideeffectresponseshe/s
hemightexperience,therebyimprovingpatient
adherenceandoutcomes,andengagingthepatienttohelpmaintainsymptomremission.
Alternatively,thephysicianmightdiversifyprescribingacrossseveraldrugsinanattemptto
personalizethetreatmentandfindthebestmatchbetweenthepatientandthedrug.Specifically,
basedoninformationfromthepati
ent’shistory,limi
tedexperiencewithseveralotherdrugs,the
existingscientificandclinicalliterature,conversationswithfellowmedicalprofessionalsinthelocaland
largergeographicalcommunity,andperhapsinteractionswithpharmaceuticalsalesrepresentatives,the
physicianmightselectthetherapythataprioriappearstobethebestmatchwiththeparticular
patien
t’scharacteristics.
Thephysiciancanlearnfromeitherexploitingorexploring,concentratingordiversifying,
prescribing“readytowear“vs.“custommade”treatments.
1
Physicianscontinuallyfacethistradeoffas
theytreatpatientsandinvestinlearningaboutavailabletreatments.Howdoesthechoicealongthis
treatmentdiversitycontinuum varybythephysician’sspecialty,volumeofpatientstreated,ageand
DiverseConcentration
2
training?Ifphysiciansconcentratetheirprescribing,isthereaconvergenceandrelativeunanimityon
theirchoiceofafavoritedrug,orisconcentrationnonuniform?Aretherepersistentgeographic
differencesinphysicianprescribingbehavior?Ifthesetofprescribeddrugsisdiverse,dothephysician’s
drugutilizationsharesmi
micre
gionalornationalshares?Thesearetheissuesweaddressinthis
research,withanapplicationtoaparticulartherapeuticclassofdrugsknownasantipsychotics.The
issuesareimportant,forunderstandinghowphysiciansrespondtonewproductlaunches,novel
scientificandcomparativeeffectivenessinformation,theirownexperience,and safetymessagesfrom
theU.S.FoodandDrugAdministrationiscriti
caltomanagingthediffusionofmedicalinformation,and
hassignificantclinicaladoptionandpublichealthimplicationsaswell.
Thatphysicianprescribingbehaviorisrelativelyconcentratedhasbeendocumentedby,among
others,FrankandZeckhauser[2007].
2
Theyreportthatamong1372primarycarephysicianssurveyedin
2004,thefractionofprescriptionsaccountedforbythemostprescribedmedicationusedbythe
physicianwasgenerallyquitehighacrossfouracuteandfivechronicconditions(averaging60%),but
wasabout13percentagepointslowerforchronicthanacuteconditions.Mor
egenerally,whileinsome
casespatientdemographicfactorsaffectedphysiciantreatmentvariability,patientclinicalfactorsplayed
astartlinglyminorrole.Physician“readtowear”treatmentnormsinsomecasescouldbeperceivedas
“assensibleresponsetocomplexdecisionmaking”,butinothercasescouldbeviewedas“disturbing”
and“basedonidiosyncra
ti
cphysicianspecificpreferencesorseverebiasesintheapplicationof
heuristics.”
3
Ourresearchextendstheiranalysisinseveralways.
4
Wefocusonantipsychotics‐‐
medicinestreatingprimarilychronicconditions,andexamineprescriberbehavioracrossamuchlarger
numberandvarietyofspecialties.WealsoputforwardatheoreticalframeworkbasedontheBayesian
learningmodelthatenablesustoconstructandexamineseveraladditionalhypothesesem pirically.
However,unlikeFrankandZeckhauser,weonlyobservephysicians,andnotth
epatie
ntstheytreat.
DiverseConcentration
3
Weproceedasfollows.Wefirstprovideabriefbackgroundonseveralgenerationsof
antipsychoticdrugsandtheillnessestheytreat.Wethenreportpreliminaryevidenceonconcentrated
vs.diversifiedprescribingbehavior,andutilizeourinitialfindingson“diverseconcentration”toput
forwardatheoreticalframeworkthate
nablesustoconstructseveralhypothese
s.Afterdiscussingthe
dataandeconometricframework,wepresentasubstantialsetofempiricalfindings.Weconcludeby
relatingourfindingstothegeographicalvariationliterature,andsuggestdirectionsforfutureresearch.
II. ANTIPSYCHOTICSFORTHETREATMENTOFSCHIZOPHRENIAANDRELATEDCONDITIONS
Schizophreniaisanincura
blemen
talillness.Itischaracterizedby“grossdistortionsofreality,
disturbancesoflanguageandcommunications,withdrawalfromsocialinteraction,anddisorganization
andfragmentationofthought,perceptionandemotionalreaction”.
5
Symptomsarebothpositive
(hallucinations,delusions,voices)andnegative(depression,lackofemotion).Theprevalenceof
schizophreniais12%,withgeneticfactors atplaybutotherwiseunknownetiology.Theillnesstendsto
strikemalesinlateteensandearlytwenties,andfemalesfiveorsoyearslater.Astheillnesscontinue
s,
personswithschizophreniafrequentlyexperienceunemployment,losecontactwiththeirfamily,and
becomehomeless;asubstantialproportionexperienceperiodsofincarceration.
6

Becauseschizophreniaisachronicillnessaffectingvirtuallyallaspectsoflifeofaffected
persons,thegoalsoftreatmentaretoreduceoreliminatesymptoms,maximizequalityoflifeand
adaptivefunctioning,andtopromoteandmaintainrecoveryfromtheadverseeffectsofillnesstothe
maximumextentpossible.
7
IntheUS,Medicaidisthelargestpayerofmedicalanddrugbenefitsto
peoplewithschizophrenia.
8

From1955upthroughtheearly1990s,themainstaysofpharmacologicaltreatmentof
schizophreniawereconventionalortypicalantipsychotic(alsocalledneuroleptic)drugsthatweremore
effectiveintreatingthepositivethanthenegativesymptoms,butfrequentlyresultedinextrapyramidal
sideeffectssuchastardivedyskinesia(aninvoluntarymovementdisordermostoftencharacterizedby
DiverseConcentration
4
puckeringofthelipsandtongue,orwrithingofthearmsorlegs),thatmaypersistevenafterthedrugis
discontinued,andforwhichcurrentlythereisnoeffectivetreatment.In1989,Clozaril(genericname
clozapine)wasintroducedintotheU.S.asthefirstinanewtherap
euticclassofd
rugscalledatypical
antipsychotics;thisdrughasalsobeendubbedafirstgenerationatypical(FGA).Althoughjudgedby
manystilltobethemosteffectiveamongallantipsychoticdrugs,for12%ofindividualstakingclozapine
apotentiallyfatalconditioncalledagranulocytosisoccurs(dropinthewhitebloodcellcount,leavingth
e
immunesystempotentiallycompromised).Patientstakingclozapinemustthereforehavetheirwhite
bloodcellcountmeasuredbyalaboratorytestonaregularbasis,andsatisfactorylaboratorytestresults
mustbecommunicatedtothepharmacistbeforeaprescriptioncanbedispensed.Forthisreason,
currentlyclozapineisgene
rallyused
onlyforindividualswhodonotrespondtootherantipsychotic
treatments.
9
Between1993and2002,fivesocalledsecondgenerationatypical(“SGA”)antipsychotic
moleculeswereapprovedbytheFDAandlaunchedintheUS,includingRisperd a l(risperidone, 1993),
Zyprexa(olanzapine,1996),Seroquel(quetiapine,1997),Geodon(ziprasidone,2001)andAbilify
(aripiprazole,2002).GuidelinesfromtheAmericanPsychiatricAssociationstatethatalthougheachof
thesefivesecondge
nerati
onatypicalsisapprovedforthetreatmentofschizophrenia(somelater also
receivedFDAapprovalfortreatmentofbipolardisease,majordepressivedisorder,aswellasvarious
pediatric/adolescentpatientsubpopulationapprovals),theyalsonotethat“Inadditiontohaving
therapeuticeffects,bothfirst‐andsecondgenerationantipsychoticagentscancauseabroadspectrum
ofsideeffects.Sideeffects
areacrucialaspectoftreatmentbecausetheyoftendeterminemedication
choiceandareaprimaryreasonformedicationdiscontinuation.”
10

InitiallytheseSGAswereperceivedashavingsimilarefficacyforpositivesymptomsandsuperior
efficacyfornegativesymptomsrelativetoFGAs,butwithouttheFGAextrapyramidaland
agranulocytosissideeffects.However,beginninginabout20012002andcontinuingtothepresent,a
DiverseConcentration
5
literaturehasdevelopedregardingtheassociationofSGAswithweightgainandtheonsetofdiabetes,
alongwithrelatedmetabolicsyndromesideeffects,particularlyassociatedwiththeuseofZyprexaand
clozapineandlesssoforRisperdal.Variousprofessionaltreatmentguidelineshavecounseledclose
scrutinyofindividualspres
cribedZyprexa,clozapinean
dRisperdal.TheFDAhasorderedmanufacturers
toaddboldedandboxedwarningstotheproductlabels,initiallyforallatypicals,andlater,toboth
typicalandatypicalantipsychoticlabels. Thelabelshavebeenaugmentedfurtherwithwarnings
regardingantipsychotictreatmentofelderlypatientshavingdementia, sincethissubpopulatio
nappears
tobeatgreaterriskforstrokeanddeath.
11

Figure1:NumberofTypicalandAtypicalPrescriptions,annually19962007.
Source:Authors’calculationsbasedonIMSHealthIncorporatedXponent™19962007data.
Despitethiscontroversy,asseeninFigure1,basedona10%randomsampleofallantipsychotic
prescribersintheU.S.(moredatadetailsbelow),thenumberofatypicalantipsy
choticprescriptions
dispensedbetween1996and2007increasedaboutsevenfoldfromabout400,000in1996to2,800,000
in2007,evenasthenumberofconventionalortypicalantipsychoticprescriptionsfell45%from
1,100,000in1996toabout500,000in2003,andhasstabilizedatthatlevelsincethen.
12
Asashareof
Total Prescriptions by Year
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Atypical Antipsychotics Typical Antipsychotics
DiverseConcentration
6
allantipsychoticprescripti ons,theatypicalsharemorethantripledfromabout27%in1996to85%in
2007.Itisalsonoteworthythatdespitealltheconcernsaboutthesafetyandefficacyofantipsychotics,
thetotalnumberofantipsychotic prescriptionsdispensedinthis10%randomsamplety
picalplus
atypicalmorethandou
bledbetween1996and2007,fromabout1,500,000toabout3,300,000,an
averageannualgrowthrate(AAGR)of7.4%.
III. PRELIMINARYEVIDENCEONCONCENTRATEDVS.DIVERSIFIEDPRESCRIBINGBEHAVIOR
AlthoughmanufacturersreceivedapprovaltomarketreformulatedversionsofseveralSGAsin
thelastdecade,nonewmajorantipsychoticproduc
tswerelaunchedintheUSduringthefiveyears
leadinguptoour2007sampleperiod.Overthelastfifteenyears,controversyregardingrelative
efficacyandtolerabilityofthesixatypicalshaspersisted,butprescribershavelearnedaboutthesedrugs
byobservinghowtheirpatientsresponded,readingtheclinic
alliterature,andinteractingwithother
professionals.Theseexperienceshaveenabledprescriberstoselectalocationalongthediversification
concentrationprescribingcontinuum.By2007,fiveyearsafterthelaunchofthelastSGA,how
concentratedordiversifiedwastheirprescribingbehavior?Wehavetwostrikinginitialfindings.
First,concentrationappear
stobeth
edominantbehavior.Amongprescriberswhowroteat
leastoneatypicalan tipsychoticprescriptionin2007,theaverageshareofatypicalprescriptionswritten
fortheprescriber’sfavoriteantipsychoticwas66%.Second,ratherthanexhibiting“herding”behavior,
prescribersarequitediverseintheirconcentrationbehavior,choosingdifferentfavoritedrugs ,i.e.,
doing
it“myway”.Tomitigatethepossibleimpactsofverylowvolumeprescribers,welimitthesample
toallprescriberswhoin2007wroteatleast12prescriptionsforanantipsychotic(atleastoneamonth),
atleastoneofwhichwasanatypical.Whenwefurtherlimitthesampletoveryhighlyconcentrated
prescribersthoseforwhomin2007atleast75%oftheatypicalprescriptionswrittenwereforone
drug(n=6,175
),wefind55%(3,379)choseSeroquelastheirfavoritedrug,28%(1,733)concentratedon
Risperdal,13%(775)focusedonZyprexa,3%(173)onAbilify,2%(93)onGeod
on,and0.4%(22)on
DiverseConcentration
7
clozapine.
13
Incidentally,2007nationalmarketsharesofthesixatypicalswereSeroquel36.2%,
Risperdal27.2%,Abilify13.8%,Zyprexa13.1%,Geodon7.3%,andclozapine2.4%.
Weconcludefromthisinitialdataexaminationthatrelativelyconcentratedpr escribing be havior
isthenormforatypicalantipsychotics(apreferenceforonetherapyforalmostallpatients),butthat
thereissubstantialdiversityamongprescribersconce
rningwhatistheirfavoritedrug.Theseinitial
diverseprescriberconcentrationbehaviorfindingsraiseanintriguingissue:Thehighlypublicized
regionalvariationliteraturedocumentsthatwithinregiontreatmentsofselectedconditionsfor
Medicarepatientsarerelativelyhomogeneouscomparedtoverylargebetweenregiondiffe
rencesin
treatme
ntsandcosts.
14
Isthereacorrespondingbetweenregionvariabilityinantipsychoticprescribing
behavior,orismostvariabilityphysicianspecificandareregionsrelativelyhomogeneous? Howdoes
prescribingconcentrationvarywithgeographicalaggregation?Toaddressthisissue,weneedtodefine
alternativeregionalgeographicalaggregates,anddevelopameasureofconcentrationbehavior.
Althoughcounty,stateandnationalaggregatesareobvious,withintheDartmouthAtlasProject
hospitalrefer
ralregions(H
RRs)haveplayedaprominentrole.HRRs representregionalhealthcare
marketsfortertiarymedicalcarethatgenerallyrequiretheservicesofamajorreferralcenter,primarily
formajorcardiovascularsurgeryproceduresandneurosurgery;HRRshavebeendevelopedbyandare
maintainedbytheDartmo
uthAtlasProject.
15
HRRsmaycrossstateandcountybordersbecausethey
aredeterminedsolelybymigrationpatternsofpatients.Torelateourini tialfindingstotheregional
variationliterature,wewillexaminemeanantipsychoticprescriberconcentration(anditsvariability)
alternativelyattheindividualprescriber,county,HRR,stateandnationallevels.
Therearevariouswaysonecanmeasure
theconcentrationbehaviorofprescriberi,C
i
.Within
theeconomicsliterature,awellknownmeasureofindustryconcentrationistheHerfindahlHirschman
Index(HHI).Foragivenindustryormarket,firstrankthej=1,…Jfirmsbysomemeasureofsize(e.g.,
revenues,employment,profits)withthefirstbeingthelargestfirmandthelas tthesmallest.Thenfor
DiverseConcentration
8
eachfirmcomputeitsindustryshares
j
asitssizemeasuredividedbythetotalindustrysizemeasure,
wherethes
j
shareisbetween0and100.Thensquarethesharesandsumupoverthejfirms,yielding
HHI=∑
j
s
j
2
.NotethattheHHIrangesfr omzeroto10,000,withhigherHHIsindicatinggreater
concentration.
16
Inthecurrentcontextofindividualphysicianprescribingbehavior,wewillusethe
numberofprescriptionswrittenforaparticulardrugmoleculedividedbythetotalnumberof
antipsychoticprescriptionswrittenbytheprescriberin2007tocomputesharesandthenconstruct
HHIs.ThereforeahighHHImeansthattheindividualprescriberisusingoneoratmostseveraldrugs
predominately,whilealow
HHIimpliess/heprescribesinamorevariedmanner.
17
Usingthesame
sampleof19,537prescriberswhoprescribedatleast12antipsychoticsin2007,wecomputemeanHHIs
andtheirvariability(bothstandarddeviationsandcoefficientsofvariation)atalternativelevelsof
regionalaggregation.ResultsaregiveninTable1.
Table1:Means,StandardDeviationsandCoefficientsofVariationforAntipsychoticHHIs
AlternativeGeographicalAggregates,2007
GeographicalAggregate
Mean HHIStd.Dev.Coef.Var.N
IndividualPrescriber494624990.50519537
County323417730.5481904
HospitalReferralRegion19893590.180306
State(plusDistrictofColumbia)1859160.02751
Nation1825nana1

IMSHealthIncorporatedXponent™2007datageneralprescribersampledata.HHIiscalculatedusing2007antipsychoticmarketshares.
_____________________________________________________________________________________
 Attheindividualprescriberlevel,prescribingbehaviorisveryconcentrated(HHIis almost5000),
butthereisalsosubstantialvariability,withthecoefficientofvariationbeingjustover0.5.However,as
oneaggregatesintolargerregions,notonlyislessconcentratedprescribingobserved,butsotooisless
relativevariability,part
icularlyasonemovesfromthecountytotheHRRgeographicalaggregate.In
particular,95%ofthedifferenceinmeanHHIbetweenindividualprescriber andnationallevelshares
DiverseConcentration
9
disappearsattheHRRlevel,and99%disappearsatthestatelevel.Inhissurveyofregionalvariabilityof
varioussurgicalprocedures,Phelps[1992,pp.2526]categorizescoefficientsofvariationinthe0.1to
0.2rangeasrevealing“lowvariability”,whilethoseat0.4andgreaterareterm
ed“highvari
ability”
procedures.Withinthatclassificationscheme,antipsychoticprescribingbehaviorishighlyvariableat
theindividualprescriberandcountylevel,butislowvariabilitybehaviorattheHRRandlargerregional
aggregates.Weconcludethatwhileprescribingbehaviorisrelativelyconcentratedatthelevelofthe
individualprescriber,andisconsiderablyless
concentratedatthecountylevel,atboththeindividual
prescriberandcountylevel,antipsychoticprescribingbehaviorishighlyvariable.AttheHRRlevelof
aggregation,however,thereisrelativelylittlebetweenregionvariability,andprescriptiondrugshares
closelymimicnationaltrends.
 Thispreliminaryevidenceleadsustofocus onindividualprescri
b
erratherthanHRRvariability,
andtoinquirewhattheoryofindividualprescriberlearningandtreatmentbehaviorcanhelpus
understandthisnonuniformconcentrationbehavior.Isthetheoryalsoabletogeneratesome
predictionsthatcanbeassessedempirically?Tothoseissueswenowturnourattention.
IV. TOWARDSA
THEORYOF PRESCRIBERLEARNINGANDTREATMENTBEHAVIOR
A. ALTERNATIVEEXPLANATIONSFORDIFFERENTIALLYCONCENTRATEDPRESCRIBING
Weobservethatwhenphysiciansseesimilarpatientswithschizophreniathetreatmentsthey
prescribeforthesepatientsvaryrelativelylittlewithinagivenprescriberpractice,butvarygreatly
acrossindividualprescriberpractices.Thisisconsistentwit
hthe“readytowear”vs.“custommade”
primarycarephysicianbehaviorobservedbyFrankandZeckhauser[2007],butisparticularlystriking
herebecauseschizophreniaandrelatedillnessesrequirechronicmaintenanceratherthanacute,
episodictreatment.Theeconomicsandstrategyliteratureoffersmanyexplanationsfordifferentactors
persistentlyr
espondingindiversem
annerswhenfacedwiththesamesituations.Theseexplanations
DiverseConcentration
10
generallyfallintooneofthefollowingfourgroups:perception,motivation,administration,and
inspiration,whichwenowbrieflysummarize.
18

Perception:
Physiciansmaydisagreeaboutthebesttreatmentforaparticularpatient.Forexample,suppose
twomedicalstudiesarrivedatdifferentconclusions.Onephysicianreadsonlyonestudy,whilethe
otherphysicianonlyreadstheother.Inthiscase,bothphysicians arechoosingwhattheybelieveisthe
besttreatmentfortheirpatientsan
dyetstillchoosetotreatthemindifferentways.Physiciansmay
persistinchoosingdifferenttreatmentregimesaslongastheydonotobservetheoutcomesofthe
otherphysician’spatients,orgainaccesstothearticlereadonlybytheotherphysician.
Motivation:
Ifphysiciansinsteadag
reedonthemostappropriatetreatmentbu
tdonothavethemotivation
toprescribetheoptimaltreatmentsfortheirpatients,onemayalsoobserveverydifferentprescribing
decisionsforeachphysician.Ifthereisweakcompetitionamongphysiciansforpatie nts,ifknowledge
concerningwhichphysiciansareobtainingthemostsuccessfuloutcomesfortheirpatientsisdifficultto
obtain,
and/orifphysicians’prescribingbehaviorisreinforcedbycontactswithpharmaceuticalsales
representativesvyingfortheallegianceofeachprescriber,thentotheextentphysiciansales
representativeallianceswereheterogeneous,wewouldexpecttoobservestrongbrandallegiances
amongphysicians,andthattheseallegia
nceswouldbetodifferentmedi
cines.
19
Administration:
Alternatively,itcouldbethatphysicianshavereachedaconsensusregardingwhatisthebest
treatmentregimeforapatient,andtheymayalsowanttogivetheirpatientsthebestcarepossible,but
physiciansfaceadministrativeorfinancialconstraintspreventingthemfromgivingtheirpatientsthe
besttreatment.Forexample,ifthebes
ttreatmentisdrugAbutonlydrugBiscoveredbyaparticular
healthplan’sformulary,onemayobservephysiciansusingdrugAwhenevertheycananddrugBinall
DiverseConcentration
11
othercases.Inthiscontextonewouldobserveverydifferentpres cribingbehavioracrossphysicians
becausetheirpatientshavedifferentinsurancecoverage.Inthecontextofantipsychoticdrugs,
however,Medicaid(thedominantpayerforpatientswithschizophrenia),placedlittleifanyrestrictions
onchoiceamongtheatypicalsduringou
r2007sample
period;MedicarePartDrequiredthatany
privateprescriptiondrugplanofferallbutoneoftheatypicalantipsychoticdrugsonitsformulary,and
manyotherprivateinsurershadsimilarformularyprovisions.
20
Inspiration:
Yetanotheralternativeisthatphysiciansmayhavepriorbeliefsaboutwhatisthebest
treatmentfortheirpatient,buttheymayeitherneedtolearn moreaboutthedrugtouseiteffectively
ortheremaybeconsiderableuncertaintyregardingwhethertheyhavecorrectbeliefsconcerningthe
efficacyandtolerabilityofeachdrug.Ineitherconte
xt,asphysicianstreatmorepatientstheylearn
frompatients’responsestoeachdrug.
Althoughwedonotaprioriruleoutthefirstthree explanationsunderlyingdifferentially
concentratedprescribingbehavior,inthefollowingsectionweoutlineamodelthatformalizesone
versionofth
einspirationin
tuitionandoffersabasicframeworkleadingtooursubsequent more
detailedempiricalanalyses.ItalsobuildsontheFrankandZeckhauser[2007]“sensibleuseofnorms”
hypothesis.
B. AMODELOFPRESCRIBERLEARNINGWITHINCOMPLETEINFORMATION
Assumepatientsarrivesequentiallytobeseenbyaphysicianandareindexedbyp
א
N={1,2,…}.
Anewpatientarrivesataphysician’sofficeatthebeginningofeachtimeintervalw,i.e.patientp
arrivesatthephysician’sofficeatthepointintimepw,wlaterthanpatie ntp1whoarrivedat(p1)w.
Letthecontinuoustimediscountra
tebegivenbyr.A
patientphasthecombinationofsymptoms
observablebythephysiciananddenotedbyswheresisrandomlydrawnfromthesetofallpossible
symptoms,S={1S}.ThesetofavailabledrugsthattreatthesesymptomsconsistsofD={1D}.The
DiverseConcentration
12
maximumpossiblebenefitofdrugdforsymptomsisB
sd
.Thebestdrugtreatme ntforagivensetof
symptomsisindicatedbyd*(s),i.e.B
sd*(s)
>B
sd
foralld≠d*(s).AssumethephysicianknowsB
sd
forall
combinationsofsinSanddinD.
Thetherapyforapatientiscomprisednotonlyofthedrug,d,thatthephysicianprescribes,but
alsoanycomplementaryactions,a,thatthephysicianundertakes,suchasadjustingthedosageofthe
drug(aprocessknownastitrating),oran
yactionsth
ataffectthepatient’sadherenceandoutcomes,
suchascommunicatinginformationonexpectedpossiblesideeffectsandtheirduration.Inorderto
achievethemaximumpotentialbenefitfromadrug,thephysicianmustsimultaneouslyundertakethe
idealcomplementaryactions.Inparticular,therealizedeffectivenessofdrugdprescrib
edforpatientp
withsymptomssis
 b
sdp
=B
sd
[1(ax
dp
)
2
],(1)
whereadenotescomplementaryactionsthephysicianundertak es,and
x
dp
=θ
d
+ε
dp
.(2)
Weassumeθ
d
andε
dp
areindependentnormallydistributedrandomvariablesforalldandp,withmean
zeroandvariancesσ
2
d
andσ
2
ε
,respectively.
Thisformulationimpliesthatthemaximumbenefitofadrugisachievedwhena=x
dp
.As
|a‐x
dp
|increases,therealizedbenefitfromdrugd,b
sdp
,decreases.Giventhesquareddifference,the
decreaseinrealizedbenefitoccursatanincreasingratewiththesizeofthegap.
Afterprescribingdrugdtopatientpandundertakingcomplementaryactionsa, thephysician
observesx
dp
.Thatis,thephysicianobservesthecomplementaryactionthatwouldhavebeenoptimal
forthepatientjusttreated,giventhedrugthatwasprescribedforthatpatient.Notethatthephysician
doesnotobservex
d’p
ford’d(i.e.,theidealactionshadthatpatientbeengivenanotherdrug)orx
dp’
for
p’p(i.e.,theidealactionsforanotherpatientgiventhatdrug).
DiverseConcentration
13
RecallthephysicianknowsthemaximumpotentialbenefitfromeachdrugB
sd
aswellasthe
distributionfromwhichθ
d
andε
dp
aredrawn.Thereforetheonlyuncertaintythephysicianfacesiswha t
complementaryactionswillworkbestforaparticulardrugandaparticularpatient.Jovanovicand
Nyarko(1996)haveasimilarfeatureintheirmodel.Thismodeldiffersfromthemultiarmedbandit
modelinwhichtheeffectivenessofeachdrugB
sd
wouldbeunknownandtherewouldbeno
complementaryactions.
Itisusefultodiscusstheintuitionunderlyingthismodel.Herethephysicianlea rnsbytaking
differentcomplementaryactionsawhenprescribingdrugdando bservingafterwardstheimpacton
thatpatient,x
dp
.Thefactthatthephysiciandoesnotobserveθ
d
impliesthats/hetypicallycannotlearn
everythings/heneedstoknowaboutadrugfromtreatingasinglepatient.Notethatforsimplicitywe
assumethatthebestactionthatthephysiciancanpotentiallylearntomake,θ
d
,dependsonlyonthe
drugprescribedbutnotonthesymptoms.Symptomsinturnde terminewhichdrughasthehighest
potentialforgivingapatientthebestoutcomes,d*(s).Wehavealsoassumedthatthespeedof
learningthecomplementaryactionθ
d
foreachdrugddependsononlyhowoftenthephysician
prescribesdrugd,notonthepatientspresentingwithsymptomsforwhoms/heprescribesthisdrug.
Denotethephysician’sprescriptionandoutcomehistorythroughpatientpbyh
p
=
(h
1,p
,h
2,p
,…,
h
d,p,
…,h
D,p
)whereh
d,p,
isdeterminedr ecursivelyby:
h
d,p
=emptyifp=0;
=h
d,p1
ifd
p
(s
p
,h
p1
) dandp>0;and
=(h
d,p1
,x
dp
)ifd
p
(s
p
,h
p1
)=dandp>0.(3)
Thephysician’spolicyistochooseadrug,d
p
(s,h
p1
),andcomplementaryactions,a
p
(d,h
p1
),foreach
patientpwithsymptomsandeachhistoryh
p1
.Sincecomplementaryactionsadonotaffectlearning
aboutθ
d
,theoptimalcomplementaryactionsaandphysician’sexpectedperpatientpayofffrompatient
paregivenby:
DiverseConcentration
14
a
p
(h
p1
) =E[θ
d
|h
d,p1
],and
E[b
sdp
|h
d,p1
] =B
sd
(1‐Var(θ
d
|h
d,p1
)‐σ
ε
2
).(4)
Fromtheseequationsweseethatthemoretimesaphysicianhasuseddrugd,theclosers/hewill
expecttobetoachievingthesecondbestbenefitsofthedrugdonapatientwithsymptomss,
B
sd
(1‐σ
ε
2
).
Ifthephysicianismyopic(i.e.,s/heonlycaresaboutthecurrentpatient’soutcomeandnot
aboutanyfuturepatients’outcomes),thentheoptimalprescribingdecisionissimply
d
p,
(
s
p,
,
h
p1
)=
sdp 1
[|]
argmax
p
d
Eb h
. (5)
Ifth
ephysicia
nisnotmyopic(i.e.,s/hecares about maximizingtheexpecteddiscountedpatientbenefit
ofallpatientss/heexpectstoseeovertime),thenthephysician’soptimizationproblemis
sdp 1
1
()
max
([|])
rwp
p
p
d
p
EeEbh . (6)
Wenowconsidertheempiricalpredictionsemanatingfromthislearningmodel.
C.
PREDICTIONSOFTHEMODEL
Supposefirstthatwislarge(i.e.,thephysicianisalowvolumeprescriber).Inthiscase,over
timethephysicianwillconcentra teonasubsetofdrugs.Moreover,thissubse tofdrugswilldependon
theinitialhistoryofidiosyncraticpatients’symptomspresentedtothephysician.Boththenumberof
drugsandtheide
ntityofthedrugsforwhichthephysicianconcentratesdependontheinitialhistoryof
symptompresentationtothephysician.Theintuitionbehindthisisasfollows.Ifthephysicianobserves
asequenceofpatientswithagivensymptomsets,thens/hechoosesanappropriatedrug,sayd,for
them
.Thephysicianwilllearnagreatdealaboutthisdrugdandwillbeunwillingtoswitchtoanother
drugd’whens/heseesapatientwithspecificsymptomsets’(evenifd’wouldbemoreappropriatefor
s’ifthephysi
cianhadthesameknowledgeaboutdrugsdan
dd’).
DiverseConcentration
15
Moreformally,consideraphysician’schoiceforapatientwithsymptomss’betweentwodrugs
d’andd.Ifthephysicianismyopicthenhis/herexpectedutilityfromusingdrugsd’anddisgivenby
B
s’d’
(1‐Var(θ
d’
|h
d’,p1
)‐σ
ε
2
),(7)
B
s’d
(1‐Var(θ
d
|h
d,p1
)‐σ
ε
2
).(8)
Therefore,themyopicphysicianistradingoffthedifferencebetweenB
s’d’
andB
s’d
againstthedifference
betweenVar(θ
d’
|h
d’,p1
)andVar(θ
d
|h
d,p1
).Ifthemaximumpotentialbenefitfromdrugd’,B
s’d’
,is
greaterthanthatofdrugd,B
s’d
,butthephysicianprescribeddrugdmoreoftenthandrugd’inthepast
sothatVar(θ
d
|h
d,p1
)<Var(θ
d’
|h
d’,p1
),thens/hemayprefertochoosedrugd.Notealsothatbecause
thecomplementaryactionsofaphysicianarenotobservedbyotherphysicians,thereisnospillover
learning.Inparticular,learningthemarketsharesofthedrugsthatotherphysiciansareprescribingis
nohelpinlearningadrug’sidealcomple
mentaryactions.
Aswisdecreased(i.e.,thevolumeofpatientsseenbythephysicianincreases),themodel
impliesthatphysicianshavealargerincentivetoinvestinlearninghowtousenewordifferentdrugs
effectively.Thereforewewouldexpecttoseemorediverseprescribingwithincreasesinpatient
volume,cet
erisparibus.Thesetofdrugsaphysicianuseswillstilldependontheinitialhistoryof
symptomsofthepatientsthephysicianhasseen,butthisdependencewillbeweaker.
Finally,aswdecreasestozero(i.e.,thephysicianseespatientsalmostcontinuously),thesetof
drugsthatphysicianswillpresc
rib
emaybeequaltotheuniverseofdrugs,D.Moreformally,ifwe
assumethattherearesufficientlymanydifferentsymptomssuchthateachdrugdin
Disoptimalfor
somesymptomssin
S,d*(s)=d,thenaveryhighvolumephysicianwilleventuallylearnagreatdeal
aboutoptimalcomplementaryactionsθ
d
foreachdrugdinDandprescribed*(s)foreverys.
Anticipatingourempiricalcontext,wenotethatphysicianspecialtiesthatarelikelytosee
particularlylargenumbersofpatientswithsymptomsetscanbeexpectedtohavegreaterincentivesto
investinlearningaboutdifferentdrugsthanthosespecialtiesrarelyencounteringsuchpatients.Tothe
DiverseConcentration
16
extentthesymptomsetspresentedtothephysicianisheterogeneous,givenpatientvolume,sotoowill
betherangeofdrugsprescribed.
Thisframeworkimpliesthatwewouldexpectlowvolumephysicianstoconcentratemorethan
highvolumephysicians.Inadditionwewouldexpectthetreatmentregimesamonglow
volume
physicianstovaryagreatdealmorethanamonghighvolumephysicians,sincethetreatmentdecisions
oflowvolumephysiciansdependmuchmoreontheiridiosyncraticrandompatienthistorythando
thoseofhighvolumephysicians.
Similarlytodifferencesinpatientarrivalrate,w,physicianswithhigh
erdis
countrates,r,would
belesslikelytoexperimentwithmoredrugs.Therefore,allelseequal,wewouldexpectphysicianswith
higherdiscountratestohavemoreconcentratedprescribing.Ifonebelievesolderphysicians
approachingretirementdiscountthedistantfuturemoreheavilythanyoungerphysicians,then
conditionalonhistoriesoftheirpatients
,wewouldexpectolderphysiciansnearingretirementto
experimentlessandtoconcentratemore.
Toillustratethesecomparativestaticresults(andthelogicofthemodelmoregenerally),
considerthefollowingsimpleexample.Therearetwodrugsd
1
andd
2
,andtwosymptomss
1
ands
2
.
Beforeseeinganypatients,thephysicianhasthesameuncertaintyabouttheidealcomplementary
actionforeachdrug,θ
d
;thatis,σ
d
2
=σ
2
.Suppose,however,thatthephysicianlearnstheideal
complementaryactionpreciselyafterasingleprescription;thatis,σ
ε
2
=0.Tomaketheanalysis
interestingweassumethatd
i
*
(s
i
)=s
i
fori
{1,2}whichisequivalenttoB
11
>B
12
andB
22
>B
21
.Notethatwe
donotassumethatthebenefitsaresymmetric,becauseasymmetriesgenerateadditionalinteresting
insights.Finally,weassumethatsymptomss
1
ands
2
areequallylikely.
First,supposethatthephysicianismyopic.Clearly,inthefirstperiodthephysicianprescribes
thebestdrug.Therearethreecasesconcerningwhathappensnext:
DiverseConcentration
17
1.
Thephysicianalwaysprescribesthedrugthatsheprescribedinthefirstperiod.This
caseisrealizediffB
12
>B
11
(1‐σ
2
)andB
21
>B
22
(1‐σ
2
).
2.
Ifthephysicianprescribedd
1
inthefirstperiod,thensheprescribesd
1
thereafter.If
thephysicianprescribedd
2
inthefirstperiod,thensheprescribesthebestdrug
d
i
*
(s
i
)thereafter.ThiscaseisrealizediffB
12
>B
11
(1‐σ
2
)andB
21
<B
22
(1‐σ
2
).
3.
Thephysicianalwaysprescribesthebestdrugd
i
*
(s
i
).ThiscaseisrealizediffB
12
<
B
11
(1‐σ
2
)andB
21
<B
22
(1‐σ
2
).
Second,supposethatthephysicianisnotmyopic.Tomaketheanalysis interesting,weassume
thatCase1isrealizedifthephysicianismyopic:B
12
>B
11
(1‐σ
2
)andB
21
>B
22
(1‐σ
2
).Finally,for
definitenessweassumethatthephysicianismoretemptedtoconcentrateond
1
ratherthand
2
,inthe
sensethat
2122
2
2221
1211
2
1112
11
BB
BB
BB
BB
.
Thislastassumptionguaranteesthatthetwocriticalvaluesofδsatisfyδ
L
<δ
H
below.Dependingonthe
discountfactorδ=e
rw
,weagainhavethreecases:
1.
Thephysicianalwaysprescribesthedrugthatsheprescribedinthefirstperiod.This
caseisrealizedifthephysicianissufficientlyimpatient(or,equivalently,low
volume)thatδ<δ
L
.
2.
Ifthephysicianprescribedd
1
inthefirstperiod,thensheprescribesd
1
thereafter.If
thephysicianprescribedd
2
inthefirstperiod,thensheprescribesthebestdrug
d
i
*
(s
i
)thereafter.Thiscaseisrealizedifthephysicianismoderatelypatient(or,
equivalently,moderatevolume)suchthatδ
L
<δ<δ
H
.
3.
Thephysicianalwaysprescribesthebestdrugd
i
*
(s
i
).Thiscaseisrealizedifthe
physicianissufficientlypatient(or,equivalently,highvolume)thatδ>δ
H
.
DiverseConcentration
18
Thecriticalvaluesδ
L
andδ
H
aregivenby:
H
/2
1
H
/2
B
12
B
11
1
2

B
11
B
12
,
L
/2
1
L
/2
B
21
B
22
1
2

B
22
B
21
.
D. LIMITATIONSOFTHEMODEL
Althoughthismodelhasseveralclearpredictions,itislimitedina numberofways.First,inthis
modelphysiciansfullyknowthebasic“quality”B
sd
ofeachdrug,i.e.,itsmaximumpotentialbenefit;they
onlydonotknowwhatcomplementaryactionsshouldbetakenwitheachparticulardrug.Inparticular
thisimpliesthatphysicianknowledgeofthenationalorlocalmarketshareofeachdrugshouldnot
affectthephysician’sdecisions.Thisisincontrasttosimplemodelsof“herding
behavior,forinour
frameworkdifferencesinbehaviorpersistevenwhenprescribersobservenationwidemarketshares.
21

Second,andrelated,thephysicianlearnsonlyfromher/hisownexperience.Arichermodel
wouldincorporatelearningovertimefromcolleaguesandmarket/scientificreportsaboutdrugsand
optimumcomplementaryactions.
Third,inthismodelevenifaphysician’spayoffsareminimallyrelatedtopatients’payoffs,since
thephysician’sobjectiveisproportionaltothepatients’payoffs(e
veniftheproportionalconstantis
small),thephysicians’prescribingdecisionsaresociallyoptimal.Forexample,ifthephysician’spayoffis
1%ofapatient’sutility,thenthephysician’sprescriptiondecisionsareasifs/heincorporatedthefull
valueofthedecision.Inotherwords,theproblemdo
esnotchangeifonerescalesB
sd
.Thisobservation
impliesthattheonlyrolethesocialplannercanplayinthismodelifs/hehasthesamediscountingas
thephysicianistoprovidethephysicianwithinformationfromotherphysicians.Amorerealisticmodel
wouldincludecostsandbenefitsoflearningaboutadrugfromothersources.
Wenowdescribethedatautilizedinouranalysis,andthenwewillevaluatetheexte
nttowhich
thepredictionsofthismodelareconsistentwithprescribingbehaviorobservedinourdata.
DiverseConcentration
19
V.
PRESCRIBINGBEHAVIORDATA
OurprescriberbehaviordataaretakenfromtheIMSXponentdatasourcethattracks
prescribingbehaviorbylinkingindividualretailandmailorderdispensedpharmacyprescriptionstothe
prescriberidentificationnumber.A10%randomsampleofallprescriberswhowroteatleastone
antipsychoticprescriptionin1996wasdrawn
,and
theseprescribersarefollowedonamonthlybasis
fromJanuary1996throughSeptember2008.Eachyearafter1996thesampleisrefreshedbyaddinga
10%sampleofnewantipsychoticprescribers.Theseprescribersare“new”inthesensethattheyare
newtothesample;theymayhavebeenprescribin
gantipsychoticsformanyyears.
Weaggregatevariousspecialtiesintofivegroups.Primarycarephysicians(“PCPs”)include
internalmedicine,familymedicineandpractice,pediatrics,andgeneralpracticeprescribers.Another
groupofprescribersispsychiatrists(“PSY”),whichnotonlyincludesgeneralpsychiatrybutalsochild‐
adolescentandgeriatricpsychiatry.Theneurologistgroup(“NEU”)includesthosein
generalneurology,
aswellasgeriatricandchildneurologists.Afourthgroupofprescribersencompassesnonphysicians
(“NPs”),primarilynursepractitionersandphysicianassistants.
22
Manystateshavelicensed nurse
practitionersandcertainphysicianassistantstowriteprescriptions,undervaryingphysiciansupervision
provisions.Inonesurveyofnursepractitioners,almostonethirdofpatientstheytreatedwereseenfor
mentalhealthproblems.
23
Wedesignateallotherprescribersasother(“OTH”).
AsseeninTable2,althoughPCPscompriseabout50%ofoursampleof19,737prescribers,in
2007theyandtherelativelypopulousOTHgroupofprescriberswroterelativelyfewantipsychoticand
atypicalprescriptions,averaginglessthansixpermonth.Incontrast,PSYsaveragedmorethan600
antipsychotic(550
atyical)prescriptionsannually,severaltimesthesecondleadingprescribersNPs,
withabout175antipsychotic(155atypical)prescriptionsannually.NEUprescriberswriteonaverage
almost100antipsychoticprescriptionsannually,about80ofwhichareforatypicals.
DiverseConcentration
20
____________________________________________________________________________________
Table2:MeanValuesofCharacteristics of2007PrescriberSample,byPrescriberSpecialty
AntipsychoticAtypicalNo.DistinctNo.DistinctAntipsy‐Atypical
Specialty
NumberAnnualRx’sAnnualRx’sAntipsychoticsAtypicalschoticHHIHHI
NEU72897.6482.303.602.335,6577,025
PCP9,54468.0352.824.312.734,6125,915
PSY3,463609.56551.377.464.713,2453,661
NP1,641174.85155.304.292.885,1815,633
OTH4,16154.2429.532.761.656,9127,081
Notes:NEUgeneral,geriatricandchildne
urologists;PCP
primarycarephysicians,internalmedicine,
familymedicineandpractice,pediatrics,andgeneralpractice;PSYgeneral,childadolescentand
geriatricpsychiatry;NPnonphysicianprescribers,nursepractitionersandphysicianassistants;OTH
allotherprescribers.
AllvaluescalculatedusingIMSHealthIncorporatedXponent™generalprescribersample2
007datafor
prescriberswritingatleast12antipsychoticprescriptions.
____________________________________________________________________________________
Intermsofconcentrationofprescribingbehavior,whilePSYsarethehighestvolume
prescribers,theytreatwithonaveragethelargestdistinctnumberofantipsychotics(7.46)andatypicals
(4.71),andexhibittheleastconcentratedantipsychotic(atypical)prescribingbehavior,havingon
averageanHH
Iof3,245(3
,661);incontrast,OTHphysiciansarethelowestannualvolumeprescribers,
usethesmallestnumberofdistinctantipsychotic(2.76)andatypical(1.65)molecules,andarethemost
concentratedantipsychoticandatypicalprescribers,havingHHIsof6,912and7,081,respectively.While
NPsarethesecondonlytoPSYsinterm
sofannualprescribervolume,intermsofboththevarietyof
drugstheyuseandtheirconcentration,theirbehaviorisquitesimilartothatoftherelativelylow
volumePCPs.
WelinktheprescriberidentifiersintheIMSXponentdatabasetotheAmericanMedical
Association(“AMA”)directoryofphysicians.Nota
bly
,whiletheAMAMasterfileDirectoryhas
education,training,specialtycertificationanddemographicdataonmostphysiciansandtypeofpractice
DiverseConcentration
21
asof2008,thereisnocomparabledataavailableonNPnursepractitionersorphysicianassistantsand
thereforeforoursubsequentempiricalanalysesweexcludeallNPs.
24

Severalfeaturesofthephysiciandatasetareworthnoting.First,wehavedataononly
physicians/NPsandtheirprescribingbehavior,notonthepatients theysee.Second,IMSkeepstrackof
prescribersthataredeceasedorretire,usinglookbackwindowswithnoprescribingactivityforone
yearforwardandoneyearbackward.Th
ird
,because1996antipsychoticprescribersarefollowed
throughSeptember2008(unlesstheydieorretire),asthesampletimeframebecomesmorerecent,the
setofprescribersinthesampleislikelyolderthanwouldbeobservedinanentirelynewrandomsample
drawnin,say,2007.
25

VI.
EMPIRICALFRAMEWORK
WhiletheconventionalHHIdescribedearliermeasuresconcentration,itcannotdistinguishwell
betweendifferentpatternsofconcentration.Inaduopoly,forexample,withfirmsAandB,oneobtains
thesameHHIiffirmAhas80%marketshareandfirmBhas20%aswiththereversesituationinwhichA
has20%mar
ketshareandBhas80%.Ourtheoreticalframeworksuggestswefocusnotonlyon
concentration,butalsoonthediversityofconcentration.Thissuggestsanalternativemeasureof
concentrationthatfocusesonthedeviationofconcentrationfromnationaltrends.Considerphysiciani
prescribingdrugjing
eographicalre
gionr,anddenotetheshareofprescriptionswrittenbythis
physicianfordrugjass
ijr
.Lettheoverallmarketshareofdrugjinregionrbem
jr
,whereboths
ijr
andm
jr
arebetweenzeroand100.Asameasureofthedevianceofphysiciani’sprescribingbehaviorfromthat
oftheaggregateregionalphysicians’marketshare,wecalculate
D
ijr
=∑
j
(s
ijr
‐m
jr
)
2
.(9)
Ifeveryphysicianinregionrhadthesameprescribingshare,D
ijr
wouldequalzero.Asphysician
prescribingbehaviorheterogeneity(homogeneity)withinregionrincreases,D
ijr
increases(decreases).
26
DiverseConcentration
22
Theregressionspecificationwewilltaketothedataisofthefollowinggeneralform:
iiiii
XVoluneAgeC
(10)
whereXisavectorofcovariatesdescribedbelow.Asseveralofourmeasuresofconcentrationwillby
constructiontakeonvaluesonlywithinagiveninterval(forexampleHHIwillbebetween0and10,000,
andiscensoredabove10,000),wetakeaccountofthisinouranalysisbyempl
oyingapprop
riate
econometricestimationmethods.Insomeregressionswespecifyinteractionvariables,particularly
amongmeasuresofvolumeandphysicianspecialty.
Regardingcovariates,theageoftheprescribingphysicianistakenfromtheAMAMasterfile
Directory.Inourempiricalanalysisweuseagequartilesasindicatorvariableregressorsinsteadof
merelytherawageofthephysician.Thisallowsustoevaluatewh
etheryoungphysiciansorthosenear
retirementusetechnologyinsimilarordifferentways,perhapsnonlinearinage.
Whilewedonothaveanyinformationaboutpatients,severalphysicianpracticesetting
variableswillhelpuspartiallytocontrolforthepatie
ntmixseenbyagivenphy
sician.Inparticular,we
observethespecialtyofthephysicianaswellaswhetherthephysicianishospitalorofficebased,and
thecounty/regioninwhichthepracticeislocated.
27
Weexpect,asTable2reports,thatspecialtyisalso
correlatedwithantipsychoticprescribingvolume.
Intermsofdifferentiallearningcosts,wemightexpectthelearningcostsforphysicianstovary
dependingontheirtrainingand/orcurrentpracticeenvironment.Inparticularinouranalysiswewill
controlforwhetherthephysicianpracticesinagrouporhasasolopractice,thesizeofthecountyin
whichth
ephysicianpractices,andwhetherofthephysicianhasanMDorDOdegree.
28

Finallywemightexpectwomenandmentousetechnologyinsomewhatdifferentways.
Therefore,inouranalysiswecontrolforthegenderofthephysician.Inadditionsomephysiciansask
thattheirprescribingdatanotbesharedwithpharmaceuticalorotherforprofitorganizations.Wewill
DiverseConcentration
23
examinewhetherthesephysiciansappeartodifferfromotherphysiciansintheirconcentrat ionand
deviationprescribingbehavior.
InTable3belowweprovidesummarystatisticalinformationforboththedependentand
explanatoryvariablesweuseinouranalysis.
Table3:SummaryStatistics
Variable Obs Mean Std.Dev.
Minimu
m
Maximu
m
DeviationofPhysician'sAntipsychoticprescribingfromHRRShares 17,652 2,660 2,441 5 10,321
DeviationofPhysician'sAntipsychoticprescribingfromNationalMarket
Shares 17,652 2,735 2,499 30 10,051
HHIofIndividualPhysician'sAntipsychoticPrescribing 17,652 4,920 2,484 1,196 10,000
HHIofIndividualPhysician'sAtypicalPrescribing 16,262 5,708 2,498 1,701 10,000
%ofPrescriptionsforAntipsychoticsthatwereforAtypicals 17,652 71.46 32.60 0 100
NumberofDiffe
rent
AntipsychoticsPrescribed 17,652 4.54 2.70 1 17
NumberofDifferentAtypicalsPrescribed 17,652 2.85 1.64 0 6
TotalYearlyAntipsychoticPrescriptions 17,652 171.80 431.35 12 7,186
TotalYearlyAtypicalAntipsychoticPrescriptions 17,652 145.92 388.51 0 6,780
PrescriberAge 17,652 50.37 10.80 26 92
PCP 17,652 0.54 0.50 0 1
PSY 17,
6
52 0.19 0.40 0 1
NEU 17,652 0.04 0.20 0 1
OTH 17,652 0.23 0.42 0 1
SoloPractice 17,652 0.20 0.40 0 1
Population(county) 17,652 1,065,738 1,810,008 1,299 9,734,701
Female 17,652 0.26 0.44 0 1
HospitalBasedPhysician 17,652 0.08 0.27 0 1
DOFlag 17,652 0.09 0.
28 0 1
Ph
ysicianOptOut 17,652 0.03 0.18 0 1
AllvaluescalculatedusingIMSHealthIncorporatedXponent™generalprescribersample2007data.
Thereferencegroupinallourregressionsisayoung(underage43)physician,practicingina
countywithlessthan150,000residents,whohasanMDdegree,isnothospitalbased,didnotrequest
thathis/herprescribinginformationbewithheldforcompaniesinterestedinitformarketingpurposes,
andwhosespecialtyisonethattypicallydoesnotprescribemanya
ntipsychotics(OTH).Allcoefficient
DiverseConcentration
24
estimatesthereforecomparehowtheprescribingbehaviorofaparticularphysicianhavingdifferent
characteristicscomparestophysiciansintheexcludedreferencegroup.
VII. RESULTS
Webeginourempiricalanalysisbyexaminingwhichphysiciansuseawidervarietyofdrug
molecules.Weemploytwomeasuresofvariety.Thefirstmeas
ureisthenu
mberofdistinct
antipsychoticdrugmoleculesprescribedin2007,whilethesecondistheHHIoftheirprescriptionsin
2007.Weexaminethesebothacrossallantipsychoticprescribingaswellasjustatypicalprescribing.
A.
UseofDiverseTechnology:NumberofDistinctDrugMoleculesPrescribed
29

WefirstestimateaPoissonspecificationrelatingthenumberofdistinctantipsychoticdrugsa
physicianprescribesin2007toahostofexplanatoryvariablesandthenusingasimilarspecificationwe
estimatethenumberofdifferentatypicaldrugsaphysicianprescribesduringthatyear;theformer
involvesamaximumof17antipsychotics,and
thelattersixatypicals.AsseeninTables4and5,the
estimatesrevealthat,holdingotherfactorsfixed,PSYsprescribethelargestnumberofdistinctdrugs
(forallantipsychotics,andonlyatypicals),followedbyPCPs,NEUs,andOTH(theexcludedgroup).In
addition,estimatesonthephysicianspecialtyvolumeinteractionvariablesindi
catethatwhil
eforall
specialtieshighervolumephysiciansemployalargernumberofdistinctmolecules(bothatypicalsand
antipsychotics),volumemattersmostforphysicianspecialistswhoarerelativelylowvolume
prescribers,OTHsandPCPs.Acrossspecialties,trainingandpatientvolume/experienceappeartobe
substitutes.Inadditionastheyage,older
physiciansusemoreantipsychoticsoverall,howeverthis
trendabatesasphysiciansapproachretirementage;weobservetheoldestquartileofphysiciansusing
onlyslightlymoredistinctantipsychoticsthantheyoungestquar tile(borderlinestatisticalsignificance). 
Whenexaminingphysicians’useofatypicals,however,weobservetheonlysignificantagecoefficientis
thatontheoldestquartile(59+),whopr
escribe
fewerdistinctatypicals.Forphysicians approaching
retirement,thedifferenceinprescriberageeffectsfortheoverallantipsychoticversusatypicalonly
DiverseConcentration
25
suggeststhattheoldestphysiciansaredisproportionateusersofdistinctolderconventional
antipsychotics.
_____________________________________________________________________________________
Table4:PoissonRegressiononNumberofDistinctAntipsychoticDrugMoleculesPrescribedin2007

Coefficient
Standard
Error P>|z|
TotalYearlyAntipsychoticPrescriptions
0.001039 0.000048 <.001
PCP*TotalYearlyAntipsychoticPrescriptions
0.000366 0.000051 <.001
PSY*TotalYearlyAntipsychoticPrescriptions
0.000792 0.000049 <.001
NEU*TotalYearlyAntipsychoticPrescriptions
0.000472 0.000071 <.001
AgeQuartile4350*
0.0374 0.0102 <.001
AgeQuartile5158*
0.0513 0.0101 <.001
AgeQuartile59+*
0.0186 0.0107 0.081
PCP*
0.4520 0.0115 <.001
PSY*
0.8965 0.0129 <.001
NEU*
0.2608 0.0233 <.001
Female*
0.0899 0.0084 <.001
Population150,000500,000(county)*
0.0357 0.0099 <.001
Population500,0001,000,000(county)*
0.0742 0.0105 <.001
Populationmorethan1,000,000(county)*
0.0692 0.0101 <.001
SoloPractice*
0.0019 0.0091 0.831
HospitalBasedPhysician*
0.0085 0.0125 0.497
DOFlag*
0.0334 0.0129 0.010
PhysicianOptOut*
0.0120 0.0190 0.530
Constant
0.9876 0.0141 <.001
NumberofObservations=17,652

PseudoR
2
=0.145

*Indicatesdummyvariable.AllvaluescalculatedusingIMSHealthIncorporatedXponent™generalprescribersample2007data,andpopulation
estimatesfromtheUSCensusBureau.
_____________________________________________________________________________________
Physiciansinlargercountiesusesomewhatfewerdistinctantipsychoticandatypicalmolecules,
howeverthesizeofthecountyseemstomatterlesswhencomparingcountieswithmorethan500,000
residents.Forallantipsychoticsandforonlyatypicals,femaleprescribersuselessvarietyrelativeto
maleprescribers,butthiseffectissignificantonlyforallantipsy
c
hotics.Prescribingvarietyisunrelated
toofficepracticetype,whether hospitalaffiliated,andwhetherthephysicianrestrictsuseofprescribing
DiverseConcentration
26
data.FinallyweobservethatphysicianswithaDOinsteadofaMDdegreeuseawidervarietyofdrug
molecules.
_____________________________________________________________________________________
Table5:PoissonRegressiononNumberofDistinctAtypicalMoleculesPrescribedin2007

Coefficient
Standard
Error P>|z|
TotalYearlyAntipsychoticPrescriptions
0.001059 0.000061 <.001
PCP*TotalYearlyAntipsychoticPrescriptions
0.000405 0.000066 <.001
PSY*TotalYearlyAntipsychoticPrescriptions
0.000937 0.000062 <.001
NEU*TotalYearlyAntipsychoticPrescriptions
0.000478 0.000089 <.001
AgeQuartile4350*
0.0113 0.0127 0.375
AgeQuartile5158*
0.0152 0.0126 0.230
AgeQuartile59+*
0.0423 0.0134 0.002
PCP*
0.5093 0.0148 <.001
PSY*
1.0558 0.0166 <.001
NEU*
0.3502 0.0292 <.001
Female*
0.0308 0.0105 0.003
Population150,000500,000(county)*
0.0460 0.0126 <.001
Population500,0001,000,000(county)*
0.0900 0.0132 <.001
Populationmorethan1,000,000(county)*
0.0868 0.0127 <.001
SoloPractice*
0.0086 0.0115 0.452
HospitalBasedPhysician*
0.0124 0.0160 0.437
DOFlag*
0.0518 0.0161 0.001
PhysicianOptOut*
0.0348 0.0238 0.144
Constant
0.4958 0.0179 <.001
NumberofObservations=17,652

PseudoR
2
=0.1045

*Indicatesdummyvariable.AllvaluescalculatedusingIMSHealthIncorporatedXponent™generalprescribersample2007data,and
populationestimatesfromtheUSCensusBureau.
_____________________________________________________________________________________
B.
Newvs.OldDrugs
Insteadoffocusingonabsolutenumbersofdistinctdrugsprescribed,wenextexaminethe
shareofaphysician’santipsychoticprescriptionsthatarewrittenforatypicals.Sincethepercentof
atypicalscanatmostbe100,weemployaTobitregressiontoestimatehowvariouscharacteristicsof
DiverseConcentration
27
thephysicianaffecttheshareofantipsychoticprescriptionswrittenforatypicals.ResultsofthisTobit
regressionarepresentedinTable6.
_____________________________________________________________________________________
Table6:TobitRegression(MarginalEffectsEstimatedatVariableMeans)on
PercentofAllAntipsychoticPrescriptionswrittenforAtypicalsin2007

dy/dx
Standard
Error
P>|z|
Mean
Value
TotalYearlyAntipsychoticPrescriptions
0.0108 0.0061 0.074 171.80
PCP*TotalYearlyAntipsychoticPrescriptions
0.0154 0.0070 0.028 36.44
PSY*TotalYearlyAntipsychoticPrescriptions
0.0155 0.0061 0.011 118.84
NEU*TotalYearlyAntipsychoticPrescriptions
0.0032 0.0094 0.737 3.99
AgeQuartile4350*
1.77 0.760 0.020 0.252
AgeQuartile5158*
1.42 0.761 0.063 0.262
AgeQuartile59+*
2.00 0.810 0.014 0.222
PCP*
17.02 0.793 <.001 0.536
PSY*
44.72 1.035 <.001 0.194
NEU*
27.66 1.660 <.001 0.041
Female*
6.68 0.640 <.001 0.263
Population150,000500,000(county)*
3.55 0.760 <.001 0.262
Population500,0001,000,000(county)*
5.65 0.796 <.001 0.225
Populationmorethan1,000,000(county)*
7.30 0.769 <.001 0.264
SoloPractice*
0.310 0.682 0.650 0.199
HospitalBasedPhysician*
2.67 0.995 0.007 0.081
DOFlag*
0.103 0.970 0.915 0.086
PhysicianOptOut*
2.74 1.486 0.065 0.034
NumberofObservations=17,652

PseudoR
2
=0.017

LeftCensored=0RightCensored=3,353

*dy/dxforadumyvariablerepresentseffectofadiscre techangefrom0to1.AllvaluescalculatedusingIMSHealthIncorporatedXponent™
generalprescribersample2007data,andpopulationestimatesfromtheUScensusBureau.
_____________________________________________________________________________________
AsseeninTable6,otherthingsequal,olderphysiciansusealowerpercentageofthesenewer
drugsthandothoseintheyoungestquartile(underage43),particularlytheoldestquartileof
physicians,althoughthe2.00percentagepointmagnitudeeffectismodest.Bycomparison,otherthings
equal,theatypicalshareisalmostsevenper
c
entagepointsgreaterforfemalethanmaleprescribers.
DiverseConcentration
28
Conditionalonoverallvolume,PSYprescriberswritethelargestshareofatypicalprescriptions,followed
byNEU,PCPs,andfinallyOTH.However,asvolumeincreases,highvolumePCPsandhighvolume
physiciansinspecialtiesthatdonottypicallyprescribeantipsychotics(OTH)usealargershareof
atypicals,whereashighvolumePSYsincreasinglyuseoldergene
rationtypicalantipsychoticsastheir
prescriptionvolumeincreases.Interestingly,theshareofatypicalprescriptionsdecreaseswithcounty
populationsize.Togetherthesefindingsconcerninggreateruseofolderantipsychoticsinmore
populousareas,particularlybyhighvolumeprescribingPSYs,couldreflectgreaterspecializationbyPSYs
inmoreurba
nareas,servingmorehe
terogeneouspatientpopu lations.
Inaddition,wefindthatphysicianswhodonotwanttheirprescribingbehaviorinformation
usedforpharmaceuticalmarketingprescribealargerpercentageofatypicals(butthiseffectisonly
marginallysignificant),whereashospitalbasedphysiciansusealowerpercentageofatypicals.Practice
typeandformofmedic
aldegreearestatisticallyinsignificantfactors.
C. PhysicianPrescribingHHI
Nextweexaminethecon centrationofphysicianprescribingasmeasuredbytheHHIofthe
physician’sprescriptionsofallantipsychotics,andtheirHHIamongtheatypicals.Initialvisualdata
inspectionsuggestedalognormaldistributionofHHIs,censoredfr
omaboveat10,000.Wetherefore
estimateTobitmodelswherethedependentvariableisalternativelylogofoverallantipsychotic
physicianHHIorlogofatypicalphysicianHHI.Bothregressionsgenerateasimilarpatternoffindings,
asisseeninTables7and8.Inparticular,consistentwiththepredictionsfromourtheoretical
model,
otherthingsequal,highervolumephysicianshavelessconcentratedprescribingbehavior.Wealso
observethatvolumemattersmoreforphysiciansthatareeitherPCPsorthoseinOTH,againsuggesting
thatexperienceandmedicalspecialtytrainingaresubstitutes;inparticular,thepositivecoefficient
estimateonthePSYvolumeinteractiontermalmostentirelyoffsetsthene
gativ
eestimateonthe
(implicit)OTHvolumeinteractionvariable.Moreover,whileolderphysicianshavelessconcentrated
DiverseConcentration
29
overallantipsychoticandinsignificantlydifferentatypicalprescribingbehaviorcomparedtothe
youngestphysicianquartile,theoneexceptionisthattheoldestquartileofphysiciansexhibitmore
concentratedatypicalprescribing,thatistheyutilizeasmallervarietyofatypicalsthandoallyounger
____________________________________________________________________________________
Table7:TobitRegression(Margin
a
lEffectsEvaluatedatVariableMeans)
onLog(AntipsychoticPrescriptionHHIfor2007)

dy/dx
Standard
Error
P>|z|
Mean
Value
TotalYearlyAntipsychoticPrescriptions
0.000821 0.000080 <.001 171.80
PCP*TotalYearlyAntipsychoticPrescriptions
0.000149 0.000090 0.089 36.44
PSY*TotalYearlyAntipsychoticPrescriptions
0.000626 0.000080 <.001 118.84
NEU*TotalYearlyAntipsychoticPrescriptions
0.000359 0.000120 0.002 3.99
AgeQuartile4350*
0.029 0.010 0.002 0.252
AgeQuartile5158*
0.039 0.010 <.001 0.262
AgeQuartile59+*
0.019 0.010 0.067 0.222
PCP*
0.435 0.010 <.001 0.536
PSY*
0.761 0.013 <.001 0.194
NEU*
0.238 0.021 <.001 0.041
Female*
0.057 0.008 <.001 0.263
Population150,000500,000(county)*
0.020 0.010 0.037 0.262
Population500,0001,000,000(county)*
0.040 0.010 <.001 0.225
Populationmorethan1,000,000(county)*
0.032 0.010 0.001 0.264
SoloPractice*
0.005 0.009 0.582 0.199
HospitalBasedPhysician*
0.019 0.013 0.119 0.081
DOFlag*
0.023 0.012 0.056 0.086
PhysicianOptOut*
0.035 0.019 0.056 0.034
NumberofObservations=17,652

PseudoR
2
=0.218

LeftCensored=0RightCensored=1,571

*dy/dxforadummyvariablerepresentseffectofadiscretechangefrom0to1.AllvaluescalculatedusingIMSHealthIncorporated
Xponent™generalprescribersample2007data,andpopulationestimatesfromtheUSCensusBureau.
_____________________________________________________________________________________
physicianquartiles.Restatedinanotherway,theoldestphysicianquartileisnodifferentfromyounger
quartilesinitsconcentrateduseofantipsychoticdrugs,butitsprescribingofnewgenerationatypical
drugsismoreconcentratedandlessdiverse.Thiscouldreflectgreaterfamiliaritywithuseofolderfirst
generationantipsychoticsfromexperie
ncesearli
erintheirprescribingcareers.
DiverseConcentration
30
Amongspecialties,holdingvolumesfixed,relativetoOTHprescriberswhohavethemost
concentratedoverallantipsychoticprescribingbehavior(theomittedgroup),PSYareleast
concentrated,followedbyPCPs,andNEUs;whenconfinedtojusttheatypicalsweobserveasimilar
pattern.
_____________________________________________________________________________________
Table8:TobitRegression(MarginalEffectsEvaluatedatVariableMeans
)on
Log(A
typicalAntipsychoticPrescriptionHHIfor2007)

dy/dx
Standard
Error
P>|z|
Mean
Value
TotalYearlyAntipsychoticPrescriptions
0.001026 0.000080 <.001 182.67
PCP*TotalYearlyAntipsychoticPrescriptions
0.000051 0.000090 0.557 39.04
PSY*TotalYearlyAntipsychoticPrescriptions
0.000859 0.000080 <.001 128.99
NEU*TotalYearlyAntipsychoticPrescriptions
0.000384 0.000110 0.001 4.30
AgeQuartile4350*
0.002 0.009 0.869 0.252
AgeQuartile5158*
0.008 0.009 0.424 0.262
AgeQuartile59+*
0.055 0.010 <.001 0.223
PCP*
0.206 0.011 <.001 0.563
PSY*
0.708 0.013 <.001 0.210
NEU*
0.011 0.021 0.592 0.043
Female*
0.034 0.008 <.001 0.267
Population150,000500,000(county)*
0.013 0.009 0.159 0.261
Population500,0001,000,000(county)*
0.052 0.010 <.001 0.225
Populationmorethan1,000,000(county)*
0.047 0.010 <.001 0.262
SoloPractice*
0.017 0.009 0.046 0.201
HospitalBasedPhysician*
0.003 0.013 0.805 0.079
DOFlag*
0.029 0.012 0.014 0.088
PhysicianOptOut*
0.037 0.018 0.043 0.035
NumberofObservations=16,262

PseudoR
2
=0.22

LeftCensored=0RightCensored=2,606

*dy/dxfordummyvariablesrepresentseffectofadiscretechangefrom0to1.AllvaluescalculatedusingIMSHealthIncorporatedXponent™
generalprescribersample2007data,andpopulationestimatesfromtheUSCensusBureau.
_____________________________________________________________________________________
Inbothregressions,concentrationisgreater,otherthingsequal,aspopulationincreases.
Howeverasintheearliernumberofdistinctmoleculesprescribedregressions,inallcountieswith
DiverseConcentration
31
greaterthan500,000populationphysiciansseemtoexhibitsimilarlevelsofconcentration.Female
prescribershavemoreconcentratedprescribing.Concentrationisunaffectedbypracticesizeforoverall
antipsychoticprescriptions,howeversolopractitionershavemoreconcentratedatypicalantipsychotic
use.DOshavelessconcentratedprescribing.Hospitalbasedphysiciansarenodifferentfromother
physiciansintheirprescribingconcen
trationbehavior.Finallyweobservethatprescribersthatplace
restrictionsontheuseofprescribingdataforpharmaceuticalmarketingpurposeshaveless
concentratedprescribing;howeverthiseffectisonlymarginallysignificant.
D.
PhysicianDeviantPrescribingBehavior
Finallyweexaminethedeviationofanyindividualphysician’sprescribingbehaviorfromnational
marketshares,andfromaggregatedrugmoleculesharesintheirHRR;