Identifying ‘‘longevity’’ alleles

To identify ‘‘longevity’’ alleles, we applied six different statistical procedures to selecting individual SNP alleles for their positive effect on life span, using 550K SNP data and the FHS original cohort genotyped sample. These procedures use N regression , the GEE approach, MM, C regression, L regression, and GF method. Because the use of the different procedures is likely to result in different sets of ‘‘longevity’’ alleles, we will distinguish them using the notions of GEE- alleles, MM-alleles, N-alleles, C-alleles, L-alleles, and GF- alleles, meaning that the selection procedure used general estimation equation, mixed model, normal, Cox, logistic re- gressions, or the gene frequency method, respectively. In case of the N-, GEE, MM-, and C- models, life span was considered as a dependent variable. In the L-model, the in- dicator of the event that life span exceeded the age of 90 years, I(LS > 90), was considered as a dependent variable. We use 90 years as the cutoff age for longevity to have enough individuals who survived the cutoff age. This also allowed us to compare the results of our analyses with those of other studies6 in which the same cutoff age has been used. In all five regression models, selection was performed controlling for gender, birth year, and smoking status (ever or never smoked).

The GEE method

The GEE procedure for selecting longevity alleles (with p£ 10-7) was applied to 1,173 members of the original FHS cohort, taking into account sib relationships among indi- viduals. The implementation of this procedure resulted in 1217 GEE-longevity alleles.

Mixed model

The MM regression procedure for selecting longevity al- leles (with p£ 10-7) was applied to the data on 1,173 mem- bers of the original FHS cohort, taking into account sib relationships among individuals. In this model, the observed covariates, including SNP genotypes, were considered as fixed-effects components, and the random effect was mod- eled as a random variable having the multivariate normal distribution with zero mean and covariance matrix defined as Rr, where R is the relationship matrix and r is the additive genetic variance due to polygenic relationships among re- lated individuals. The implementation of this procedure re- sulted in 1,202 MM-longevity alleles.

Seven sets of ‘‘longevity’’ alleles

The six sets of ‘‘longevity’’ alleles identified using six dif- ferent statistical procedures may consist of different numbers of such alleles. To be sure that our results were independent from the method of alleles selection, we also considered the set of SNP alleles at the intersection (I) of the six sets. Each allele in this set was thus selected using all of the six statis- tical procedures. We call such alleles ‘‘I-longevity alleles,’’ meaning ‘‘I’’ for ‘‘intersection.’’ Thus, altogether we obtained seven sets of longevity alleles.

Cox regression

The C regression procedure for selecting longevity alleles was applied to 1,441 members of the original FHS cohort who passed the QC procedure. This number is larger than that used in normal regression because Cox regression al- lows for dealing with individuals which life spans are cen- sored (e.g., some study participants are alive). The procedure selected SNP variants for which the estimate of the regres- sion parameter was negative and significant with p£ 10-7. This procedure resulted in selection of 3,683 C-longevity alleles.

Evaluating additive (polygenic) genetic effects on life span

For each genotyped individual in the original FHS cohort, and for each of the seven sets of longevity alleles, we cal- culated the value of polygenic score index—the number of genetic variants contained in a person’s genome (genetic dose). Then we estimated parameters of seven linear re- gression models, considering life span as a dependent and the polygenic score as an independent variables.10

Logistic regression

The L regression procedure for selecting longevity alleles considered survival to the age of 90 years as longevity phe- notype. The procedure was applied to 1,331 individuals. This number differs from the two methods above because

individuals censored before the age 90 were excluded from the analyses (e.g., alive individuals, whose age did not ex- ceed 90 years). Similar to other regressions, this procedure also controlled for the same observed covariates. It is im- portant to note that the use of the selection threshold p£10-7 (as in four procedures above) did not produce any longev- ity alleles. An increase of this threshold up to p£10-4 resulted in selection of 97 L-longevity alleles.

gether we obtained seven sets of longevity SNP alleles: Six model-specific sets and one intersection set.

The results of evaluating polygenic influence on life span obtained by applying linear regression without observed covariates to the life span data in the original FHS cohort are shown in Table 2 for each of seven sets of selected genetic variants. One can see that each relationship explains a sub- stantial portion of the phenotypic variance. In all cases, the values of the slope (as well as the intercept) associated with polygenic effects were highly statistically significant (p£10-15). We repeated these analyses controlling for observed covariates, including gender, birth cohort, and smoking status (ever, or never smoking). In all cases, the polygenic effects were highly statistically significant.

Gene frequency method