AnEconometricMethodforEstimatingPopulationParameters

fromNon-RandomSamples:AnApplicationtoClinicalCaseFinding

ZoëMcLaren,AssistantProfessorSchoolofPublicHealth,UniversityofMichigan

RulofBurger,AssociateProfessorDept.ofEcon,StellenboschUniversity,SouthAfrica

April2017Paperdownloadatzoemclaren.comForthcominginHealthEconomics

Motivation

HowareMDR-TBprevalenceratescurrentlydetermined?

• Surveillancestudy– Accuratebutinfrequent

• Notificationrates– Numberofreportedcaseslikelyunderestimate

• WHOcrudeadjustmenttonotificationrates– Basedonexpertopinion(Glaziouetal.2015)

Ourcontribution

• Developaneweconometricmethodforestimatingpopulationmeansfromaselectedsample– Identifiesunder-detection– Minimaldatarequirements:routinedata– Minimalassumptions– Lowcost,easyreal-worldimplementation

• Usefulformonitoringrareandemergingdiseases• Weestimatethat16to26%ofallmulti-drugresistantTBcasesinSouthAfricawereundiagnosed2004-2011

Foundationformethod

• Methodstoaddresssampleselectiononunobservedcharacteristicsineconomicsliterature– Instrumentalvariables(seeImbensandAngrist1994,Angristand

Imbens1995)– Bivariatenormalstyleselectionmodels(seeHeckman1976)

• HIVlit:adjustingsurveyestimatesforrepresentativeness– Interviewerrandomeffects(McGovernetal.2015)– Heckman-typeselectionmodels(Barnighausenetal.2011,Hoganet

al.2012,ClarkandHoule2014)– Adjustingforsurveynon-responseusingmortalityrates(Nyirendaet

al.2010)

Context:MDR-TB

Multi-drugresistantTB

• Resistanttothetwofirst-lineTBdrugs• Indistinguishablefromdrug-susceptible• Only12%ofnewTBcasestestedforMDRglobally• MDRpatientscomprise:– Lessthan5%ofTBcases– 13%ofTBdeaths– 20%ofTBspending

GuidelinesforMDRtesting• Cliniciansobserveriskfactors– TBhistory–Weakenedimmunesystem– Highriskofexposure:prisoners,miners,healthworkers

• RiskfactorsareimperfectpredictorsofMDR• Cannottesteveryoneforallpossibleformsofdrugresistance

• TesttheproportionofpatientsθwithhighestlikelihoodofMDRbasedonobservedsignalx

TheoreticalModel

Generalmodel

• Supposewehaveapopulationforwhichwewanttoknowthemeanofoutcomey

• Wehavearoutinesamplewithobservationsselectedtomaximizevalueofy

• Characteristicx isobserved• Mappingofx tounobservabley isnotfullyknown• Determiningvalueofy hasassociatedcost

Keyfeaturesofclinicaldecisionmaking

• PatientsmustbetestedbeforeMDRtreatment

• Toofewresourcestotesteverypatient• Clinicianobservesnoisysignalaboutpatient’slikelihoodofMDR-TB

• Testingresourcesdeterminedexogenously:– Testmaterials,labcapacity– Funding– Clinicianawarenessandtraining

Keyfeaturesofclinicaldecisionmaking

• Clinicianwilltestpatientsdeemedmostlikelytohavedrug-resistanceuntilresourcesareexhausted

• WeassumeclinicianbeliefsaboutmappingbetweenriskfactorsandMDR+isconsistentwithintimeperiods

• CliniciansdonotknowactualMDR-TBprevalence

Methods

Identificationstrategy

• Useplausiblyexogenousvariationinthresholdθtodrawinferencesabout– Distributionofyinthepopulation– Samplingmechanism• Clinician’sabilitytopredictMDR+basedonobservablesignalx

• Assumeconsistentbeliefsaboutmappingofxtoy

• Regressiondiscontinuityintuition– Relaxconstraintontestingresources

Identificationstrategy

• Samplemeansatobservedthresholdproportiontestedθ0 informativeaboutunobservablex0:

• Withabinaryy,conditionalexpectationsimplifiesto:

whereµ ispopulationprevalence• Rewritingrelationshipbetweenyandxinerrorform:

• Normalize b0 tozero

Estimation

• Rewriteconditionalexpectation:

• Assumeerrortermefollowsstandardnormaldistribution

• Noclosed-form(analytical)solutionsoweusenumericalapproximationtechniques

• Estimateparametervaluesusingmaximumlikelihoodandgeneralizedmethodofmoments

• Gridsearchestofindmostpromisingparameterspace

Policychangesasinstrumentalvariables

• Exogenousdiscontinuouschangesintestingresources(θ)– Timeperiod– XDRpaperpresentedatinternationalconference– Nationalstrategicplanintroduced

• Shouldnotaffectclinician’sunderstandingofriskfactorsortheunderlyingrateofMDR-TB

Data

Data• NationalHealthLaboratoryServicedatabase• Laboratorydatabaseoftestresultsfor~90%ofallsuspectedTBcases– Jan2004– Sept2010(PriortoXpert)– 2,190,780 TB+testresults– 8,647,12 patients– 4,764healthfacilities

AccessingNHLSTBdatabase

Data

• ExamineMDR-TBtestingforthosewhoaretestedforTB,andhaveaTB+result

• Minimaldatarequirements• Extractnumberofpatients:– TB+result– TestedforMDR–MDR+result

Results

FractionofTB+testedforMDR

0%

5%

10%

15%

20%

25%

2004 2005 2006 2007 2008 2009 2010 2011

Testshare

0%

2%

4%

6%

8%

10%

12%

14%

16%

5% 7% 9% 11% 13% 15% 17% 19% 21% 23% 25%

Percento

fsam

pledM

DR-TBpo

sitive

Theta0

MarginalsamplingefficiencyE(y|theta<theta0) E(y|theta0)

Samplingefficiency:percentofMDRtestedwhoareMDR+

PredictedMDR+matchesobservedMDR+overtime

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

2003 2004 2005 2006 2007 2008 2009 2010 2011

ShareofallTB+patientswhoareMDR-TB+

Observed Predicted

Mainresults:robustnesschecksMethod: ML GMM GMM GMM GMM

Instruments: Time Time Policies Policies

(1) (2) (3) (4) (5)Prevalence 0.0305*** 0.0298*** 0.0342*** 0.0305*** 0.0301***

(0.0002) (0.0013) (0.0004) (0.0016) (0.0004)

Signal-to-noise 1.0749*** 1.0891*** 0.9336*** 1.0716*** 1.0846***

(0.0003) (0.0489) (0.0117) (0.057) (0.0142)

Observations 262,845 262,845 262,853 262,850 262,842

Clustering No No Yes No Yes

Pseudo R2 #1 0.694 0.699 0.529 0.691 0.703

Pseudo R2 #2 0.695 0.695 0.694 0.695 0.696

Log likelihood -90646.845

GMM criterion 0.00131 0.01626 0.00044 0.0078

QuadraticMDR-TBtimetrendestimates

0%

1%

2%

3%

4%

5%

6%

7%

2004 2005 2006 2007 2008 2009 2010 2011

MDR

-TBprevalence

Year

ML(constant) GMM:TimeIV(constant) GMM:PolicyIV(constant)

ML(quadratic) GMM:TimeIV(quadratic) GMM:PolicyIV(quadratic)

Conclusions

• Evidencethat“official”MDRratesaretoolow– 16-26%ofMDRcaseswereundiagnosed– Moreresourcesareneeded

• Routinedatacanprovidereal-timetracking– Widelyavailableandunder-used– Valuablewherecannottesteveryoneorwherecompliancewithguidelines<100%

• ClearapplicationsbeyondTB

Thankyou!