Ifthe ORofsurvivalRS ij/00 smaller)than1.0,thei–jcombinationofthegene-fixedex- posureispositively(ornegatively)associatedwithlongev-

FrequencyDistributionoftheGenotypesDefinedbyCombinationsofWhetherCarryingtheMinorAlleleofOneoftheThreeSNPs ofFOXO3AandWhetherCarryingtheMinorAlleleof1A-213,andtheEstimatesoftheOddsRatiosofSurvivalProbability(RS )From ij/00 MiddleAgetoAges100+Measuringthe“independentandjointeffects”ofthegenotypes

Carrierornoncarrierofthe Noncarrierofminoralleleof1A-213(i=0) Carrierofminoralleleof1A-213(i=1) minoralleleoftheSNPsof FOXO3A Cent.%genotype Contr%genotype RS (95%CI) p Cent.%genotype Contr%genotype RS (95%CI) p ij/00 ij/00 Women  3A-310,noncarrier(j=0) 19.2 18.8 1.00 28.7 41.7 0.68(0.45–1.00) 0.043  3A-310,carrier(j=1) 23.0 14.6 1.55(0.97–2.48) 0.052 29.1 24.9 1.15 (0.76–1.75) 0.489  3A-292,noncarrier(j=0) 19.0 18.8 1.00 29.1 41.3 0.70(0.47–1.03) 0.061  3A-292,carrier(j=1) 23.2 14.8 1.55(0.97–2.47) 0.052 28.7 25.1 1.14 (0.74–1.73) 0.534  3A-936,noncarrier(j=0) 20.1 19 1.00 30.3 43.7 0.66(0.45–0.97) 0.029  3A-936,carrier(j=1) 22.1 13.8 1.53(0.95–2.47) 0.066 27.5 23.5 1.12 (0.73–1.71) 0.595 Men  3A-310,noncarrier(j=0) 13.9 17.5 1.00 30.0 39.5 0.96(0.55–1.69) 0.867  3A-310,carrier(j=1) 27.2 14.7 2.34(1.30–4.25) 0.002 28.9 28.3 1.29 (0.74–2.29) 0.352  3A-292,noncarrier(j=0) 14.3 17.7 1.00 29.3 39.7 0.91(0.53–1.59) 0.712  3A-292,carrier(j=1) 27.1 14.5 2.29(1.28–4.14) 0.003 29.3 28.1 1.28 (0.74–2.26) 0.357  3A-936,noncarrier(j=0) 17.2 19.3 1.00 30.9 40.6 0.86(0.51–1.45) 0.538  3A-936,carrier(j=1) 24.3 12.8 2.14(1.21–3.81) 0.005 27.6 27.3 1.14 (0.67–1.96) 0.617

Note:SeefootnotestoTable1andTable2,exceptreplacing1A-209by1A-213.CI=confidenceinterval;SNP=single-nucleotidepolymorphisms.

ThebasicandextendedFADmethodsarebasedonthe fundamentaldemographicinsightthattheprevalenceofa fixed attribute (eg, genetic variant, birth weight, child- hoodconditions,andseriousdisease(s)sufferedearlierin life)andcombinationsoftwofixedattributesinapopula- tioncanchangewithageeventhoughnoindividualcan changehisorhervariant.Therefore,muchcanbelearned abouttheimpactofthefixedattribute(includinggenetic variant)andthecombinationsofthefixedattributeson survival.

InFormula(2),individualsareidentifiedas“carriers”or “noncarriers,”andacarriercouldhave1or2copiesofthe minoralleleoftheSNPsintheapplicationofourpresent study.Henceweareimplicitlyassumingthattheminorallele isdominantratherthanrecessiveoradditive.Amodified versionoftheFADapproachandapplicationisrequiredto analyzerecessiveoradditivemodels.

Gene–environmentinteraction(G×E)isdefinedas“a different effect of an environmental exposure on disease andhealthriskinpersonswithdifferentgenotypes,”or,al- ternatively,“adifferenteffectofagenotypeondiseaseand healthriskinpersonswithdifferentenvironmentalexpo- sures”(24,25).Similarly,gene–geneinteraction(G×G)is definedas“adifferenteffectofagenotypeondiseaseand healthriskinpersonswithandwithoutanothergenotype.” Applyingthestandarddefinitionandmethodforestimating theG×EorG×Ginteractions(25),wepresentinAppen- dix2theproceduresforestimatingtheeffectsofgene-fixed exposureinteractionsonsurvivalfromagextox + n,using theORsofsurvival(RS ,i = 0,1; j = 0,1)derivedby ij/00 Formula(2).

casesandyoungercontrols,theestimatesofthe by the logistic regression not adjusted for mathematical proof and the empirical evidence, regression without controlling for covariates arenotpresentedhereduetospacelimitation,butavail- ableuponrequest.).Thisfactverifiesthestatisticalprop- muchtheprobabilityofsurvivalfromagextox + words, the FAD method provides clearer interpretations and presents meaningful synthesesofthecase–controlgeneticanalysisonlongev- ity.Asthetwoapproachesproduceexactlythesamenu- still uses the conventional approach of logistic regres- FAD method contributes an additional new insight demographic interpretation on the magnitude of approach of logistic regression in case–control analysisonlongevity.

mulas(1)and(2)canbeusedtoanalyzecross-sectional datafromdifferentcohortsoflong-livedcasesandyounger controlsorfollow-updatafromthesamecohort.Inthecase ofanalyzingthecross-sectionaldata,weactuallyconnect theyoungercohortandthelong-livedcohortintowhatthe demographictextbookscall“ahypotheticalcohort,”and estimatetheORofsurvivalbasedonproportionsofthege- neticvariantandfixedexposureamongthelong-livedand youngercohorts(ie,atadvancedandyoungeragesinthe “hypotheticalcohorts”).

Itisimportanttonotethat,ifoneusescross-sectional data,boththeFADmethodexpressedinFormulas(1)and (2)andtheconventionalcase–controlstatisticalgenetic approachassumethattheinitialdistributionsofthege- neticvariant,thefixedexposureandtheircombinations, andtheirassociationwithlongevitydonotdiffersubstan- tially between cohorts of long-lived individuals and youngercontrols,thatis,thereisnosubstantialproblem ofpopulationstratification(seemoredetaileddiscussions inAppendix1onpotentialbiasifthisbasicassumptionis violated).Ifcohortfollow-updataareused,oneneedsto assumethatthelosstofollow-upfromagextox + nis notcorrelatedwithrespondents’combinationofthege- neticvariantandthefixedexposureunderstudy.Serious attentionmustbepaidtothisissueinapplyingeitherthe conventional statistical genetic approach or the FAD methodforidentifyinggeneticcontributionstolongevity. TocontrolforpopulationstratificationintheFADanaly- sisinthisarticleusingthecross-sectionaldataofcente- nariansandmiddle-agecontrols,wehaverestrictedour analysistoasingleethnicgroup(HanChinese)residing inSouthernChina,andclassifiedthesamplesbygender aswell.