The standard method of survival analysis using cohort follow-up data is limited because it requires prospective trackingofthemortalityofstudyparticipants,withafol- low-upperiodforestimatinglong-termsurvivalprobabil- itiesthatmaybeprohibitivelyexpensiveandtimeconsuming (26).TheFADmethodcircumventsthismajorlimitationof standardsurvivalanalysisbecauseitdoesnotrequireex- pensivefollow-upmortalitydataofstudyparticipantsandit canbeappliedtobothcohortandcross-sectionaldatasetsif thebasicassumptionofnoseriousproblemsofpopulation

stratificationismet.However,theFADmethodhasamajor limitation:itpermitsananalysistoascertainthe“defacto” associationofafixedattribute(includinggenes)orthecom- binationofgene-fixedexposureonlongevitywhileusually controllingforageandsex.Intheory,wecanfurthercontrol forothercovariatesbyextendingtheFADmethodthrough cross-tabulationsofthestudyparticipantsbyconfounding factorsthatarealsofixedattributesandmeettheassump- tionofnosubstantialproblemsofpopulationstratification, butthismaycauseproblemswithsmallsamplesizesofthe subgroups.Thus,weappliedbothFADmethodsandmulti- variatestatisticalmodelingapproacheswheneverpossible tocomplementeachotherandtomaximizetheutilityofthe availabledatasources.

Notethatthestatisticallysignificantestimatesofthein- proportionalhazardmodelsanalysisrepresentthesignifi- gene–environmentcorrelations(rGE)andgene–genecorre- significantgene–environmenteffectswithacontinuousen- vironmental variable discovered in the Cox fordifferencesinmeansofcontinuousenvironmentalfac- torsbetweenthegenecarriersandnoncarriers.Forallsig- nificant gene–environment synergistic effects with discreteenvironmentalvariableandforallsignificantgene hazardsmodelsanalysis,weusethechi-squaredtesttoas- sessthegenotypefrequencydifferenceacrosstheenviron- test,wewillneedtoconductpathanalysisemployingmul- tivariateregressionanalysisorstructuralequationmodel- ing, adjusted for various confounding factors, to significantgenotypeeffectsthatworkthroughenvironmen- andthesignificantgene–environmentinteractionorgene– geneinteractioneffectsonsurvivallikelihood.

Multivariate Hazards Model for Survival Analysis

The effects of the genotypes of the FOXO1A and FOXO3A,theirG×GandG×Einteractionsonsurvival likelihoodatveryadvancedages92–110areexaminedbased onCoxproportionalhazardmodelsusingtheavailable genotypicandlongitudinaldatafrom727interviewees(553 womenand174men;thesamplesizeusedinourCoxpro- portional hazards model analysis is slightly smaller than thatusedintheFADanalysisbecauseaverysmallnumber of cases who were interviewed and contributed DNA in 1998werelosttofollow-upandwehadtodropthemfrom theregression.Empiricaltestinghasshownthatdropping thesefewloss-to-follow-upcasesdoesnotaffecttheesti- mates)whowereaged92+andcontributedDNAintheCL- HLS1998baselinesurveyandsurvivedtoage100+either inthebaselineorinoneofthesubsequentfollow-upsur- veysconductedin2000,2002,2005,and2008,butalmost allofthemdiedbefore2008.Theassumptionofproportion- alityofthehazardswasassessedandmettherequirement forallofthemodelsanalyzed.Survivaltimeisenteredas daysbetweenthelastinterviewdateanddateofdeathfor thosewhodied(ordateat2008interviewforthe10indi- vidualswhostillsurvivedin2008follow-upsurvey),while usingtheexactageatlastinterviewasacovariate(survival analysisinpopulationagingstudiesusuallydoesnotuse ageatdeathorcensoringassurvivaltimebecauseitcould noteasilyidentifytheageeffectonthemortalityriskifthe ageisusedasthesurvivaltime).Demographiccharacteris- tics(includingexactageat1998baselinesurvey,gender andrural-urbanresidence,etc.),socialconnections,family support,healthpractices,theresiliencescore,andcurrent healthstatus(seeAppendix3)areincludedinthehazards modelsascovariatesinaforwardstepwiseanalysis.Results basedonthesequentialmodelsarepresentedtoshowhow theeffectsofgenotypesonsurvivalmaybemediatedby differentconfounders.Wealsotriedtoestimatetheeffects ofallpossiblegene–environmentinteraction(G×E)and gene–geneinteraction(G× G)termsintheCoxpropor- tionalhazardsmodels.

Results

General Effects of the Genotypes of FOXO1A and FOXO3A on Long-term Survival Probability From Middle Age to Age 100+

probabilityfrommiddleagetoage100+,regardlessofcar- Dynamics Method subsection. The genotypes presented minor allele of any other four SNPs of FOXO1A FOXO3A.Theresultsshowthat,ascomparedwithnoncar- 1A-213are0.70(p=.0073)and0.71(p=.0152),respec-

doneinthepreviouspublication(6).

theprobabilityofsurvivalfrommiddleagetoage100+for womenwhoareacarrieroftheminorallelesofthe1A-209 and1A-213are30%and29%lowerthanthosewhoare noncarriers,andtheestimatesarestatisticallysignificant; thosemenwhocarrytheminorallelesof1A-209and1A- 213mayhave27%and35%lowerprobabilityofsurvival frommiddleagetoage100+,buttheestimatefor1A-209is notstatisticallysignificantandtheestimatefor1A-213is moderatelysignificant(p =.025)(Table1).Ascompared withnoncarriers,the ORofsurvivalforwomenandmen whocarrytheminorallelesof3A-310,3A-292,and3A-936 are 1.62–1.67 (p = .0002~–.0004) and 1.61–1.73 (p = .001~–.005),respectively.Theseestimatesofthegeneral effectsimplythat,onaverage,middle-agewomenandmen whocarrytheminoralleleofanyoneofthethreeSNPsof FOXO3Amayhave62%–67%and61%–73%higherprob- abilityofsurvivalfrommiddleagetoage100+,andallof theestimatesarehighlystatisticallysignificant.

negativeandindependenteffectsofcarryingtheminoral- leleof1A-209onsurvivalinwomenareallhighlysignifi- cant(p andindependenteffectsof1A-213inwomenaremoder- ately(p =.029–.043)ormarginally(p andmagnitudeoftheORsbutwithlowerlevelofsignifi- and noncarriers of the minor allele of the 3A-292are notsignificant, 3A-936isonlymarginallysignificant(p = minoralleleofthe1A-213andnoncarriersoftheminoral- significant(p = .052–.066).Theseestimatesoftheindepen- the carrying or not-carrying the minor allele of the (Table1)andtheconventionalgeneticanalysis(2–7).

The Independent and Joint Effects of the Genotypes of FOXO1A and FOXO3A on Long-term Survival From Middle Age to Age 100+