Generalized Cochran-Mantel-Haenszel Test Statistics for Correlated ...

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statisticsbutmodiedtohandlecorrelatedoutcomes.Twoofthesestatisticsareasymptot- RCtables.TheyaresimilarinformtothestandardgeneralizedCochran-Mantel-Haenszel Threenewteststatisticsareintroducedforcorrelatedcategoricaldatainstratied ABSTRACTS strata.Thislatterstatisticisalsoappropriatewhenstrataareassumedtoberandom. Keywords:correlatedcategoricaldata,generalizedCochran-Mantel-Haenszelstatistics, oneisdesignedspecicallyforthemany-stratacasebutisvalidevenwithasmallnumberof sparsedata. icallyvalidinbothmany-strata(sparsedata)andlarge-stratalimitingmodels.Thethird
asstagesofdiseaseseverityorlevelsofimprovementfollowinganintervention.Inaddition, thecategoricalresponsesmaybecorrelatedbecauseofrepeatedormultiplemeasurementson Inmulticenterclinicaltrials,theresponsesareoftenrecordedonadiscretescale,such 1INTRODUCTION primaryobjectiveofthetrialsistostudythetreatmenteect. twoormoretreatmentgroupssuchasthedierentdosesofanactiveingredient,andone correlatedcategoricaldata.Moreover,thesubjectsinthetrialsareusuallyrandomizedto eachindividualorsubsamplingfromclusterssuchasfamilyunits.Suchdataareoftencalled thedataanalysiswhenadjustmentforotherprognosticfactorsisnecessary.Underthe situationoccursforexamplewhenenrollmentoflargenumberofpatientsisnotpossible ateachindividualcenter.Furthermore,thesparsesituationwillbecomemoreseriousin islarge,butthenumberofpatientsinmanycentersissmall.Thismany-strata(sparsedata) Sometimesthedatafromtheabovetypetrialsaresparse,i.e.,thenumberofcenters(q) many-strata(sparsedata)situation,sincethetotalsamplesizeincreaseswiththenumber ofnuisanceparameters(hereduetocentereectsandprognosticfactors),thestandard generalizedestimatingequations(GEE)approachandthestandardlikelihoodmethodfor Similarlythegeneralweightedleastsquares(WLS)method(Koch,etal.,1977)foranalysis correlatedcategoricaldatawillfail;seeLiangandZeger(1995)forfurtherexplanation. ofcorrelatedcategoricaldatawillbeinvalidinthemany-strata(sparsedata)situation. ateachtimepoint,combiningtheresultsateachoccasiontogetanoverallconclusionis responses.AlthoughdatacansometimesbeanalyzedbyusingCMHstatisticsseparately multiplehypergeometricdistributionisnotsatisedwhentherearecorrelatedcategorical statisticsarerobusttothesparsesituation.However,theassumptionofanunderlying Incontrasttotheaboveapproaches,generalizedCochran-Mantel-Haenszel(CMH) dicult.Furthermore,whenthereareirregulartimepointsfordierentsubjectsorthedata arefromsubsamplingfromclusters,thisapproachisnotavailable. buttheasymptoticvaliditydependsonthenumberofstrataq!1.ZhangandBoos (1995)proposedtwoscoretestsforcorrelatedbinarydatathatareasymptoticallyvalidin bothmany-strata(sparsedata,q!1)andlarge-stratalimitingmodels(Robins,Breslow Liang(1985)proposedonescoretestwhichhandlesthesparsecorrelatedbinarydata, 1
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