In men, the patterns of the independent effects of FOXO1A and FOXO3A are substantially different from those of women. As compared with men who are non-carriers, carriers of the minor allele of one of the two SNPs of FOXO1A and FOXO3A are all non-significant (see the panels for the general effects). Applying our extended FAD method expressed in Formula (2), we found that carriers of the minor allele of one of the three SNPs of FOXO3A, with the reference to non-carriers, have positive independent effects (RS > 1) on survival at very advanced ages (92-110), adjusted for all confounders. The estimates of RS range from .618 to .643. To avoid the problems of multicollinearity, we should not include more than one SNP of FOXOPotentially confounding and how we estimated these 15 potentially confounding factors - FOXO3A genes are not correlated with each other. How- ever, including GG of 1A-209 and one of three SNPs of FOXO3A, or including GG of 1A-213 and one of three SNPs of FOXO3A, or excluding GG and GE, or including both GG and GE with sign.GE, the relative hazards of the genotypes, the GG (gene-gene), and the significant GE (gene-environment) interactions on survival likelihood at very advanced ages are presented in Table 4.

Demographic and basic SES models I II III IV V VI VII VIII IX X 
Male (female) 1.15 1.21* 1.21 1.34** 1.33** 1.33** 1.33** 1.34** 1.34** 1.33** 
Age 1.07*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 1.06*** 
Urban (rural) 1.05 1.08 1.09 1.02 1.02 1.03 1.02 1.02 1.02 1.02 
1+ year of schooling (0) 0.97 1.05 1.05 1.05 1.06 1.06 1.07 1.05 1.05 1.06 
Economic independence (no)  	0 .71  	0 .77  	0 .81  	0 .74  	0 .73  	0 .73  	0 .71  	0 .72  	0 .73  	0 .71 
Family and social support 
Currently married (no) 0.87 0.88 0.89 0.92 0.92 0.94 0.93 0.92 0.94 
Living alone (no) 	0 .99  	1 .02  	1 .01  	1 .03  	1 .03  	1 .03  	1 .03  	1 .02  	1 .02  
Close proximity to child (no) 	0 .95  	0 .94  	0 .97  	0 .97  	0 .97  	0 .97  	0 .97  	0 .97  
Family member as caregiver (no) 	0 .97  	0 .96  	1 .04  	1 .00  	1 .01  	0 .99  	1 .02  	1 .02  
Leisure activities score 0.91** 0.92** 0.99 0.99 0.99 0.99 0.99 0.99 
The resilience score 0.93*** 0.94*** 0.99 1.00 1.00 1.00 0.99 
Health practice 
Regular exercise (no)   	0 .82*   	  	  	  	  	  	  	  	  	  	  
Smoking in recent five years (no)   	  	  	  	  	  	  	  	 	 	 	 	  
Current heavy alcohol drinker (no)   	   	   	   	   	   	   	   	   	  
DI   	   	   	   	   	   	   	    
19.47***   	
20.56***   	
20.71***   	
20.08***   	
18.75***   	
18.43***   	
18.26***   	

Main effects of the SNPs 
3A-310 (non-carrier of the minor allele) 0.84** 0.84** 0.85** 0.86** 0.76*** 0.83 
3A-292 (non-carrier of the minor allele) 0.76*** 0.84 
3A-936 (non-carrier of the minor allele) 0.77*** 0.83 
1A-209 (non-carrier of the minor allele) 0.86 0.85 0.91 
1A-213 (non-carrier of the minor allele) 0.95 0.94 0.99 

GG interactions 
(1A-209)(3A-310) 1.33* 
(1A-209)(3A-292) 1.36* 
(1A-209)(3A-936) 1.21 
(1A-213)(3A-310) 1Survival-death observations for participants younger than age 92 are not available. We are also not able to interpret why the negative effects of FOXO1A on long-term survival from middle-age to age 100+ found in the cross-sectional case-control analysis diminished at very advanced ages (92-110) in the cohort survival analysis; it is not clear why there are substantial gender differences in the independent effects of the genotypes of FOXO1A and FOXO3A on probabilities of survival from middle age to ages 100+ discovered by us. The biological, epigenetic, and environmental mechanisms by which FOXO genes' GG combinations and interactions and GE interactions may affect human longevity at old ages are not investigated in our present biodemographic analysis but are warranted in future interdisciplinary research (27-30). For example, a further study needs to investigate how GE interaction between 1A-209 and regular exercise is translated into physiological effects on cellular responses that may significantly increase survival likelihood at advanced ages. More replication analyses and further biological functional study plus demographic-social research using genotypic and longitudinal phenotypic data may provide stronger scientific evidence and explanations for the findings presented in this article.

Third, we presented unique estimates of the genetic influence of FOXO1A and FOXO3A and their GG interactions on survival at very advanced ages, adjusted for various potentially confounding factors, using prospective cohort data. We found that the positive effects of FOXO3A on survival from middle age to ages 100+ remain statistically significant at very advanced ages, but the corresponding negative effects of FOXO1A disappear. We also discovered that the interactions between 1A-209 and 3A-310 and between 1A-209 and 3A-292 significantly decrease the survival likelihood at very advanced ages by 33%-36%.

Fourth, this is the first study that investigates the impacts of GE interactions between the FOXO genes and social-behavioral factors on survival at very advanced ages. Our new finding that GE interaction between the SNP 1A-209 and regular exercise significantly increases the survival by 31%-32% (p < .05) at very advanced ages may have important policy and practical relevance. There are further areas of study and unanswered questions that need to be explored further.