Table4. Relativehazardsofthegenotypes,theG×G(gene–gene),andthesignificantG×E(gene–environment)interactionsonsurvival likelihoodatveryadvancedages

IncludingG×Gof1A-209and IncludingG×Gof1A-213and oneofthreeSNPsofFOXO3A, oneofthreeSNPsofFOXO3A, ExcludingG×GandG×E andsign.G×E andsign.G×E Models I II III IV V VI VII VIII IX X DemographicandbasicSES  Male(female) 1.15 1.21* 1.21 1.34** 1.33** 1.33** 1.33** 1.34** 1.34** 1.33**  Age 1.07*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06***  Urban(rural) 1.05 1.08 1.09 1.02 1.02 1.03 1.02 1.02 1.02 1.02  1+yearofschooling(0) 0.97 1.05 1.05 1.05 1.06 1.06 1.07 1.05 1.05 1.06  Economicindependence(no) 0.71 0.77 0.81 0.74 0.73 0.73 0.71 0.72 0.73 0.71 Familyandsocialsupport  Currentlymarried(no) 0.87 0.88 0.89 0.92 0.92 0.94 0.93 0.92 0.94  Livingalone(no) 0.99 1.02 1.01 1.03 1.03 1.03 1.03 1.02 1.02  Closeproximitytochild(no) 0.95 0.94 0.97 0.97 0.97 0.97 0.97 0.97 0.97  Familymemberascaregiver(no) 0.97 0.96 1.04 1.00 1.01 0.99 1.02 1.02 1.00  Leisureactivitiesscore 0.91** 0.92** 0.99 0.99 0.99 0.99 0.99 0.99 0.98  Theresiliencescore 0.93*** 0.94*** 0.99 1.00 1.00 1.00 0.99 0.99 0.99 Healthpractice  Regularexercise(no) 0.82* 0.92 1.11 1.11 1.10 0.93 0.93 0.93  Smokinginrecent5years(no) 1.06 1.06 1.07 1.07 1.07 1.06 1.06 1.07  Currentheavyalcoholdrinker(no) 1.08 1.12 1.14 1.14 1.14 1.12 1.11 1.11  DI 19.47*** 20.56*** 20.71*** 20.08*** 18.75*** 18.43*** 18.26*** MaineffectsoftheSNPs  3A-310(noncarrieroftheminorallele) 0.84** 0.84** 0.85** 0.86** 0.76*** 0.83  3A-292(noncarrieroftheminorallele) 0.76*** 0.84  3A-936(noncarrieroftheminorallele) 0.77*** 0.83  1A-209(noncarrieroftheminorallele) 0.86 0.85 0.91  1A-213(noncarrieroftheminorallele) 0.95 0.94 0.99 G×Ginteractions  (1A-209)×(3A-310) 1.33*  (1A-209)×(3A-292) 1.36*  (1A-209)×(3A-936) 1.21  (1A-213)×(3A-310) 1.05  (1A-213)×(3A-292) 1.06  (1A-213)×(3A-936) 0.98 SignificantG×Einteractions  (1A-209)×(regularexercise) 0.68* 0.68* 0.69*  −2Loglikelihood 7866 7838 7833 7762 7752 7752 7751 7759 7759 7756  Numberofobservations 727 727 727 727 727 727 727 727 727 727

Notes:Samplesize:553womenand174men,allwereaged92+in1998CLHLSbaselinesurveyandsurvivedtoage100+in1998orafollow-upwaveofthe CLHLSsurvey,allofthemwereHanChinesefromSouthernChina;therelativehazards(RH)=exp(B),whereBisthecoefficientofthecategoricalvariableestimated intheCoxproportionalhazardmodels.RHistheratioofthehazardofdeathwhenthevariable=1ascomparedtothereferencegroupindicatedintheparentheses. EachoftheModelsI,II,III,andIVhasfivesubmodels,andeachsubmodelincludesoneofthefiveSNPs(ie,twoSNPsofFOXO1AandthreeSNPsofFOXO3A). TheestimatesoftherelativehazardsofthepotentialconfoundersamongthefivesubmodelswithineachoftheModelsI,II,III,andIVarealmostidentical,withfew minordifferencesuptotheseconddecimalpoint.Inotherwords,theestimatesofthecoefficientsofthepotentialconfoundersinModelsI,II,III,andIVwerenot affectedbywhichSNPwasincludedintothemodel.Thus,wepresentonlyonesetoftheestimatesofthepotentialconfoundersintheModelsI,II,III,andIVcon- cerningtheSNP3A-310inTable4,andtheestimatesoftherelativehazardsofthemaineffectsoftheotherfourSNPs(1A-209,1A-213,3A-292,and3A-936)are listedinTable5.CLHLS=ChineseLongitudinalHealthyLongevitySurvey;DI,deficitsindex;SES,socioeconomicstatus;SNP=single-nucleotidepolymorphism.

interactionterms between 1A-209 and the three SNPs of FOX3Aareaddedintothemodel(ModelsV,VI,andVII), thepositiveeffectsofthethreeSNPsofFOXO3Aevenbe- came stronger—increasing survival likelihood by 23%– 24%(p <.01).TheseestimatesconfirmthatFOXO3Ahas itsownsignificantandpositiveimpactsonsurvivalatad- vancedagesindependentoftheeffectsofotherpotential socialandbehavioralmediatorsorconfounders.Thisfind- ingisingeneralconsistentwiththeresultoftheGerman study(5)showingthattheFOXO3Avariantsweremore frequent in centenarians than in 90-year-olds based on

threeSNPsofFOXO3Aareincluded.

Second,thenegativeeffectsofcarryingtheminoral- lelesoftheSNPs1A-209and1A-213onlong-termsur- vival from middle age to age 100+ discovered by

agesby31%–32%(p VII that included all potentially confounding anyofthethreeSNPsofFOXO3A.

Table5. 1A-213,3A-292,and3A-936intheModelsI,II,III,andIV

Discussion

on the effects of FOXO genes on longevity, the studyhasmadeafewuniquecontributions.First,theex- demographic interpretation to the conventional case– thesameestimatesoftheORsofsurvivalandtheirassoci- by the conventional case–control population analysisonlongevityusingthelogisticregressioncontrol- lingforthesamecovariatesastheFADdoes.Thisfactver- ifies the statistical properties of our FAD method. ofsurvivalfromagextox + nwouldbeincreasedorre- presents ORs expressing the difference of ofsurvival.

SNP=single-nucleotidepolymorphisms.*p<.10;**p<.05;***p<.01.

are no longer statistically significant at very advanced ages,adjustedforthepotentiallyconfoundingfactors(see theestimatesof1A-209and1A-213inModelsItoXin Tables4and5).

Third, the G × G interactions between 1A-209 3A-310 and between 1A-209 and 3A-292 decreasethesurvivallikelihoodby33%–36%(p someofthenonsignificantp

Second,we provideduniqueestimatesoftheindepen- dent, joint, and interactive effects of the genotypes of FOXO1A and FOXO3A on probabilities of survival from middleagetoage100+.Inadditiontotheinterestingfind- ingsoftheindependenteffectsofFOXO1AandFOXO3A, wediscoveredthatthepositiveeffectsofFOXO3Aandneg- ative effects of FOXO1A substantially compensate each otherifonecarriesboth,althoughFOXO3Ahasastronger impact.Thisisasignificantstepforwardascomparedwith theconventionalgeneticanalysisreportedinpreviouspub- licationsontheassociationofFOXO3AorFOXO1Agenes withlongevity(2–7)thatdidnottakeintoaccountthe



Table6. Chi-squareteststoassessrGEandrGGforthesignificantG×EandG×GsynergisticeffectsdiscoveredbytheCoxproportional hazardsmodelanalysis