To control for population stratification in the FAD analysis in this article using the cross-sectional data of centenarians and middle-age controls, we have restricted our analysis to a single ethnic group (Han Chinese) residing in Southern China, and classified the samples by gender as well. The standard method of survival analysis using cohort follow-up data is limited because it requires prospective tracking of the mortality of study participants, with a follow-up period for estimating long-term survival probabilities that may be prohibitively expensive and time-consuming (26). The FAD method circumvents this major limitation of standard survival analysis because it does not require expensive follow-up mortality data of study participants, and it can be applied to both cohort and cross-sectional datasets if the basic assumption of no serious problems of population stratification is met. However, the FAD method has a major limitation: it permits an analysis to ascertain the de facto association of a fixed attribute (including genes) or the combination of gene-fixed exposure on longevity while usually controlling for age and sex. In theory, we can further control for other covariates by extending the FAD method through cross-tabulations of the study participants by confounding factors that are also fixed attributes and meet the assumption of no substantial problem of population stratification, but this may cause problems with small sample sizes of the subgroups. Thus, we applied both FAD methods and multivariate statistical modeling approaches whenever possible to complement each other and to maximize the utility of the available data sources.

Note that the statistically significant estimates of the proportional hazard models analysis represent the significant gene-environment correlations (rGE) and gene-gene correlations. Significant gene-environment effects with a continuous environmental variable discovered in the Cox for differences in means of continuous environmental factors between the gene carriers and non-carriers. For all significant gene-environment synergistic effects with discrete environmental variable and for all significant gene hazards models analysis, we use the chi-squared test to assess the genotype frequency difference across the environmental test. We will need to conduct path analysis employing multivariate regression analysis or structural equation modeling, adjusted for various confounding factors, to significant genotype effects that work through environmental factors and the significantModels as Covariates in a Forward Stepwise Analysis

Results based on the sequential models are presented to show how the effects of genotypes on survival may be mediated by different confounders. We also tried to estimate the effects of all possible gene-environment interactions (GE) and gene-gene interactions (GG) terms in the Cox proportional hazards models.

Results

General Effects of the Genotypes of FOXO1A and FOXO3A on Long-term Survival Probability From Middle Age to Age 100+

The probability of survival from middle age to age 100+, regardless of carrying the minor allele of any other four SNPs of FOXO1A FOXO3A. The results show that, as compared with non-carriers, the probability of survival from middle age to age 100+ for women who are carriers of the minor alleles of the 1A-209 and 1A-213 are 30% and 29% lower than those who are non-carriers, and the estimates are statistically significant. Those men who carry the minor alleles of 1A-209 and 1A-213 may have 27% and 35% lower probability of survival from middle age to age 100+, but the estimate for 1A-209 is not statistically significant and the estimate for 1A-213 is moderately significant (p = .025) (Table 1). As compared with non-carriers, the OR of survival for women and men who carry the minor alleles of 3A-310, 3A-292, and 3A-936 are 1.62-1.67 (p = .0002~.0004) and 1.61-1.73 (p = .001~.005), respectively. These estimates of the general effects imply that, on average, middle-aged women and men who carry the minor allele of any one of the three SNPs of FOXO3A may have 62%-67% and 61%-73% higher probability of survival from middle age to age 100+, and all of the estimates are highly statistically significant.

The negative and independent effects of carrying the minor allele of 1A-209 on survival in women are all highly significant (p < .001), and the independent effects of 1A-213 in women are moderately (p = .029-.043) or marginally (p = .052-.066) significant. The estimates of the independent effects for men who carry the minor allele of 1A-209 or 1A-213 are not significant. The estimates of the joint effects show that carriers of both the minor allele of 1A-213 and non-carriers of the minor allele of the 3A-292 are not significant, and non-carriers of the minor allele of the 1A-213 and carriers of the minor allele of the 3A-936 is only marginally significant (p = .052-.066). These estimates of the independent and joint effects are consistent with those reported in the previous publication (6).

The Independent and Joint Effects of the Genotypes of FOXO1A and FOXO3A on Long-term Survival From Middle Age to Age 100+

The analyses concerning FOXO1A presented in Table 1, employing Formula (1) of the FAD method and in previous relevant studies following the conventional genetic and statistical approach (6), are based on comparing the frequencies of carrying the minor allele of the SNPs of FOXO1A (regardless of whether carrying the minor allele of the SNPs of FOXO3A) between centenarians and younger controls. So are the analyses concerning FOXO3A presented in Table 1 and in the previous studies (27). Although they are useful in exploring the general impacts of one genotype on longevity regardless of carrying or not-carrying the other relevant genotype, these analyses cannot reveal the independent, joint, and interactive effects of the genotypes of FOXO3A and FOXO1A, which influences survival in opposite directions.