from http://biomedgerontology.oxfordjournals.org/ at Northern Arizona University on May 23, 2015

allelearecodedasNo(noncarrier)(ie,mm,Mm =1,MM thefrequencydistributionofthegenotypesdefinedbycar- oroneofthethreeSNPSofFOXO3Abasedonthedomi- nantmodel,forthemaleandfemalecentenariansandmid- dle-age controls. Tables 2 and 3 present the ofFOXO3Aandwhethercarryingtheminoralleleof1A- andfemalecentenariansandmiddle-agecontrols.

The Extended Fixed Attribute Dynamics Method

tothefamilyofmethodsofcase–controlpopulationas- Yashin and colleagues (21) required knowledge cohort age-specific mortality rates. The FAD extended by Zeng and Vaupel (22) does not these rates, which are not available in many applications.

TheORofsurvivalfromagextox + n(RS)forthose withthefixedattribute(eg,agenotype)tothosewithoutthe attributecanbeestimatedas:

To conduct a novel biodemographic analysis, we also combinethegenotypicdatawiththecorresponding10-year follow-upcohortphenotypicdatafrom760individualswho wereatleast92yearsoldintheCLHLS1998baselinesur- vey,whereas750ofthemdiedafter1998atages100+and 10stillsurvivedinthe2008wave.Thecohortfollow-up dataonsurvivalanddeath,socioeconomics,lifestyle,psycho- logicalcharacteristics,andheathstatus,etc.ofthepartici- pantsusedinthemultivariatestatisticalsurvivalanalysisin thisarticlearefromtheCLHLSconductedin1998,2000, 2002,2005,and2008usingquestionnairesthatfollowed theinternationalstandardsadaptedtotheChinesecultural context(19).Thecarefulevaluations(suchasreliability coefficientsandfactoranalysis)haveshownthatthedata qualityoftheCLHLSsurveyswasreasonablygood(19). Weusethecentenarians’ageatdeath(oragein2008forthe 10centenarianswhosurvivedinthe2008follow-upsurvey) inourcase-controlanalysis.Themeanageofthemaleand femalecentenarianssampleswere101.9and103.2,respec- tively.Themeanagesofthemaleandfemalecontrolswere 46.0and45.4,respectively.Similartothepreviouslypub- lishedstudiesonassociationbetweentheFOXOgenotypes and longevity (2–8), the centenarians and middle-age controlsofthisstudyareethnically(allHanChinese)and geographically(SouthernChina)compatible,andthusthe

wherep(x)istheproportionofindividualswhoarex yearsoldandhavethefixedattribute.ZengandVaupel(22) derivedFormula(1)andempiricallyjustifiedit.

NotethatFormula(1)providesestimatesofthegeneral impactsofonegeneticvariantonsurvivalfromagexto x + n,regardlessofcarryingornot-carryinganotherrele- vantgeneticvariant.WeextendtheFADmethodhereto provideformulastoestimatetheindependenteffectofa geneticvariantintheabsenceofanotherrelevantgenetic variant,thejointeffectswhenbotharepresentandtheef- fectsofinteractionsbetweenthem.

Let i = 0, 1 represent not-carrying and carrying hereafter;andj as“not-exposed”and“exposed”hereafter.Letp 11 the proportion of x-year-old individuals who are define p (x), p (x),and p 10 01 00 are a carrier and not-exposed, noncarrier and and neither carrier nor exposed. Note that the sum p (x), p (x),p (x)andp 11 10 01 00

ofFOXO3AandWhetherCarryingtheMinorAlleleof1A-209,andtheEstimatesoftheOddsRatiosofSurvivalProbability(RS ij/00 MiddleAgetoAges100+Measuringthe“IndependentandJointEffects”oftheGenotypes

Carrierornoncarrierofthe Noncarrierofminoralleleof1A-209(i=0) Carrierofminoralleleof1A-209(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) 27.8 26.6 1.00 20.2 34.0 0.57(0.39–0.83) 0.002  3A-310,carrier(j=1) 29.9 21.7 1.32(0.89–1.94) 0.148 22.1 17.7 1.19 (0.79–1.81) 0.389  3A-292,noncarrier(j=0) 27.7 26.6 1.00 20.5 33.6 0.58(0.40–0.85) 0.004  3A-292,carrier(j=1) 30.1 21.9 1.31(0.89–1.93) 0.148 21.7 17.9 1.16 (0.76–1.76) 0.462  3A-936,noncarrier(j=0) 28.8 28.2 1.00 21.6 34.6 0.61(0.42–0.88) 0.006  3A-936,carrier(j=1) 28.9 19.9 1.41(0.95–2.10) 0.073 20.7 17.3 1.17 (0.77–1.78) 0.451 Men  3A-310,noncarrier(j=0) 23.3 29.3 1.00 20.6 27.8 0.93(0.55–1.55) 0.755  3A-310,carrier(j=1) 35.0 22.3 1.96(1.23–3.15) 0.003 21.1 20.6 1.28 (0.76–2.16) 0.322  3A-292,noncarrier(j=0) 23.8 29.6 1.00 19.9 27.8 0.89(0.53–1.49) 0.636  3A-292,carrier(j=1) 34.8 22.0 1.96(1.23–3.15) 0.003 21.5 20.6 1.30 (0.77–2.17) 0.292  3A-936,noncarrier(j=0) 26.6 31.6 1.00 21.5 28.3 0.91(0.55–1.49) 0.686  3A-936,carrier(j=1) 32.0 19.9 1.92(1.20–3.06) 0.004 19.9 20.2 1.17 (0.70–1.96) 0.522

Note:(1)ThesamplesizeisthesameasthatlistedinTable1.(2)Theoddsratio1.00referstothereferencegroupwithagenotypewithoutcarryingtheminor alleleofanyofthetwoSNPspairedfortheanalysis;thevaluesinitalicsinthistablepresenttheestimatesofthe“joint”effectsofcarryingtheminorallele ofSNP1A-209andcarryingtheminoralleleofoneofthethreeSNPsofFOXO3A;andtherestpresenttheestimatesofthe“independent”effectsofcarryingthe minoralleleofoneofthethreeSNPsofFOXO3Abutnot-carryingtheminoralleleoftheSNP1A-209,orcarryingtheminoralleleoftheSNP1A-209butnot- carryingtheminoralleleofoneofthethreeSNPsofFOXO3A.CI=confidenceinterval;SNP=single-nucleotidepolymorphisms.

mathematicalanddemographicderivationispresentedin theAppendix1:

pvaluesand95%confidenceintervals(CIs)(23)canbe performedtoassesswhethertheestimatesofanORofsur- vival(RSinFormula(1)andRS inFormula(2))issig- ij/00 nificantlydifferentfrom1.0,usingasimpleprocedurein standard statistical software (eg, STATA, SAS or SPSS). Note that RS  and RS  represent the independent 10/00 01/00 impactofthegeneticvariant(oranotherfixedexposure)on survivalfromagextox + n,intheabsenceofanotherfixed exposure(includinggeneticvariant)andthatRS repre- 11/00 sentsthejointimpactofthegeneticvariantandthefixed exposureonsurvivalfromagextox + nwhenbothofthem present.

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