Table6. Chi-squareteststoassessrGEandrGGforthesignificantG×EandG×GsynergisticeffectsdiscoveredbytheCoxproportional hazardsmodelanalysis

SignificantSynergisticEffects (1A-209)×(r.exercise) (1A-209)×(3A-310) (1A-209)×(3A-292) (1A-209)×(3A-936) Regularexercise 3A-310 3A-292 3A-936 Yes No Carrier Noncarrier Carrier Noncarrier Carrier %carrying1A-209 40.87 39.83 39.59 40.54 39.44 40.71 40.73 39.35 Pofchi-squaretestofrGEorrGG .917 .937 .917 .913 Conclusion rGEdoesnotexist rGGdoesnotexist rGGdoesnotexist rGGdoesnotexist

Note:rGE=gene–environmentcorrelations;rGG=gene–genecorrelations.

effectsofwhethercarryingtheminoralleleoftheSNPof anotherrelevantgene(FOXO1AorFOXO3A)thataffects longevityinoppositedirections.

betweenFOXO1AandFOXO3Athatarethethemesofthis studybecausetheFOXO3AgenotypicdatafromtheNorth- ernChinasamplesarenotavailable.Wearesofarnotable toinvestigatetheimpactsoftheG×Ginteractionsbetween FOXO1AandFOXO3AaswellastheG×Einteractionon survivalatagesyoungerthan92yearsastheneededgeno- typic data matched with the follow-up survival-death observationsforparticipantsyoungerthanage92arenot available.Wearealsonotabletointerpretwhythenegative effectsofFOXO1Aonlong-termsurvivalfrommiddle-age toage100+foundinthecross-sectionalcase–controlanal- ysisdiminishedatveryadvancedages92–110inthecohort survivalanalysis;itisnotclearwhytherearesubstantial genderdifferencesintheindependenteffectsofthegeno- typesofFOXO1AandFOXO3Aonprobabilitiesofsurvival frommiddleagetoages100+discoveredbyus.Thebio- logical, epigenetic, and environmental mechanisms by whichFOXOgenes’G×Gcombinationsandinteractions andG×Einteractionsmayaffectthehumanlongevityat oldagesarenotinvestigatedinourpresentbiodemographic analysisbutarewarrantedinthefutureinterdisciplinary research(27–30).Forexample,afurtherstudyneedsto investigatehowG×Einteractionbetween1A-209and regular exercise is translated into physiological effects on cellular responses that may significantly increase survivallikelihood at advanced ages. More replication analyses and further biological functional study plus demographic–socialresearchusinggenotypicandlongi- tudinal phenotypic data may provide stronger scientific evidenceandexplanationsforthefindingspresentedin thisarticle.

Third,wepresenteduniqueestimatesofthegeneticinflu- enceofFOXO1AandFOXO3AandtheirG×Ginteractions onsurvivalatveryadvancedages,adjustedforvarious potentially confounding factors, using prospective co- hortdata.WefoundthatthepositiveeffectsofFOXO3A onsurvivalfrommiddleagetoages100+remainstatisti- cally significant at very advanced ages, but the corre- spondingnegativeeffectsofFOXO1Adisappear.Wealso discovered that the interactions between 1A-209 and 3A-310andbetween1A-209and3A-292significantlyde- creasethesurvivallikelihoodatveryadvancedagesby 33%–36%.

Fourth,thisisthefirststudythatinvestigatestheimpacts ofG×EinteractionsbetweentheFOXOgenesandsocial- behavioralfactorsonsurvivalatveryadvancedages.Our newfindingthatG×EinteractionbetweentheSNP1A-209 andregularexercisesignificantlyincreasethesurvivalby 31%–32%(p <.05)atveryadvancedagesmayhaveimpor- tantpolicyandpracticalrelevance.

studyandunansweredquestionsthatneedtobeexplored further.Onelimitationisthat,aswestatedinTheExtended FixedAttribute Dynamics Method section and expressed mathematicallyinFormulasA4andA5intheAppendix1, boththeFADmethodemployedinthisarticletoproduce theestimatesofTables1–3andtheconventionalcase–control statisticalgeneticapproachassumethat(a)theinitialdistri- butionsofthegeneticvariantand(b)theirassociationwith longevitydonotdiffersubstantiallybetweencohortsof long-livedindividualsandyoungercontrols.However,al- thoughrestrictingouranalysistoasingleethnicgroup(Han Chinese) residing in Southern China and classifying the samplesbygenderaswellmayreduceandhopefullymini- mizethebias,weareawareofthattheremaystillbebias becauseofpotentialviolationoftheassumptions(a)and (b);andwedonotknowtowhatdegreetheseassumptions maybeviolatedintherealworld.Thisimpliesthatthere- sultsoftheORofsurvivalprobabilityfrommiddleageto age100+measuringthegeneral,independent,andjointef- fectsoftheFOXOgenotypesbasedondatafromthecases (centenarians)andcontrols(middle-agegroup),presented inTables1–3,maybesubjecttoabiasofunknownmagni- tudebecauseofconfoundingwithbirthcohortsofcentenar- iansandmiddle-ageindividuals.Similarcautionswerealso raised in previous studies following the case–control ap- proach(2–6),andthepotentialbiasneedstobeevaluatedin thefuturewhenmoresophisticatedcohortfollow-updata sourcesbecomeavailable.AlthoughLiandcolleagues(6) havedonethereplicationanalysisonthegeneraleffectsof FOXO1AonlongevityusingfemalesamplesfromSouthern andNorthernChina,wearenotabletoperformthereplica- tionfortheindependent,joint,andG×Ginteractioneffects

Finally,itisworthnotingthat,althoughthegeneticef- fectsofFOXOgenesonlongevityestimatedinthisarticle andtheotherstudies(2–8)arefascinating,wearenotable toestimatetheproportionofvarianceinindividuals’proba- bilitiesofsurvivalfrommiddleagetoage100explainedby theFOXOgenes.Thisisbecausethecohortdataonout- comeofthatwho(amongthemembersofthemiddle-age controlgroup)willsurvivetoage100requiredforsuchvar- ianceanalysisarenotavailable.However,previousstudies onelderlytwinshaveshownthatonlyonefourthofthe differencesinindividuallifespanaredeterminedbyge- neticinherencethatinvolvesmultiplegenesandtheother threefourthsaredeterminedbysocial,behavioral,and environmentalfactors(31).Clearly,knowingwhichgen- otypesapersoncarriesdoesnottellwhetherheorshe maysurvivetoage100.Themostimportantissueisto promotebettersocialandenvironmentalconditionsand healthy behaviors that will affect health and longevity directlyandindirectlythroughinteractionswithgenet- ics.OurnewfindingthatG×Einteractionbetweenthe SNP1A-209andregularexercisesignificantlyincrease survival by 31%–32% at very advanced ages has pro- videdapieceofstrongempiricalevidencetosupportthis understanding.

Funding

Sundaresa

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,etal.Sirt