ajhg00048-0172

ajhg00048-0172 - 564 Lettersto theEditor ,thisrandom cance...

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Unformatted text preview: 564 Lettersto theEditor ingtheprobabilityandthecriticalvalue,thisrandom- izedtestcanhaveexactlyanydesiredlevelofsignifi- cance. Two thousandreplicationswereusedineachcase, bothtodeterminethecriticalvaluesandthentocom- putethepower.A 5% significancelevelwasusedhere, althoughcomparableresultswereobtainedforsmaller levels.Thenumbersappearinginthetablearetheesti- matedpowersoftestsundervariouscombinationsof theparameters.Thenumberofreplicationsmeansthat thethirddigitmay notbeaccurateinthetables,but sincethesamerandomlygenerateddatawereusedfor eachtest,thestandarderrorofthedifferenceinpower isnegligible. Intable1we seethatthereisverylittledifference betweenthetwotests.Forsomevaluesoftheparame- ters,theAtestismorepowerful,butinotherstheCtest wins.Intable2,withadifferentfamilysize,thesame conclusionshold. Inthe"phaseunknown"case,thetwotestsareeven closer.Foracollectionoffamilieswithsame sibship size,the two tests have essentially the same power. Closerexaminationofthegeneratedteststatisticsre- vealedarankcorrelationverycloseto1,whichexplains thesimilarityinperformance.Whenavarietyofsibship sizesareconsidered,asintable3,ameasurablediffer- enceoccurs,buteventhisisnotsubstantial.Varying thesignificancelevelorintroducingincompletepene- tranceyieldedsimilarresults. Thereisverylittledifferenceinpowerbetweenthe twotests,soothercriteriamustbeusedtochoosebe- tweenthem.TheC testismaybesomewhatlesscostly incomputationalterms,butwithamoderncomputer, neithertesttakesverylongtoexecute,sothisshould notbeaconsideration.ThecomputationoftheA test Table 2 Phase Known, Two FamiliesofSize I0 POWER AT 0 = .25 .1 .0 a = .25: A test . . . . . . . . .198 .377 .460 C test . . . . . . . . .202 .388 .460 a = .5: A test ........ .375 .644 .756 C test ........ .382 .659 .757 a = .75: A test ........ .536 .855 .942 C test ........ .540 .865 .942 Table 3 Phase Unknown, 2 Families ofSize 10and 10Families of Size2 POWER AT 0 = .25 .1 .0 a = .25: A test ........ .165 .360 .513 C test ........ .168 .383 .514 a = .5: A test ........ .289 .668 .835 C test ........ .286 .687 .832 a = .75: A test ........ .426 .889 .980 C test ........ .426 .894 .976 producesestimatesof0and,asaby-product,themix- ingfractiona.Itisalsopossibletocomputeconfidence intervalsforthesevalues.TheC testdoesnotprovide anestimateof0orofa.Therefore,intheabsenceof anyadditionalinformationabouttheparameters,Irec- ommend theA test. JULIANJ.FARAWAY Department of Statistics University ofMichigan Ann Arbor References FarawayJJ(1993)Distributionoftheadmixture testforthe detectionoflinkageunderheterogeneity.GenetEpidemiol 10:75-83 MacLeanCJ,Ploughman LM, DiehlSR,KendlerKS(1992)A newtestforlinkageinthepresenceoflocusheterogeneity. Am JHum Genet50:1259-1266 © 1994 byThe AmericanSocietyofHuman Genetics.Allrightsreserved....
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This note was uploaded on 11/08/2010 for the course CSE 689 taught by Professor Ken during the Spring '10 term at TAMU Kingsville.

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ajhg00048-0172 - 564 Lettersto theEditor ,thisrandom cance...

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