Finally, it is worth noting that, although the genetic effects of FOXO genes on longevity estimated in this article and the other studies (28) are fascinating, we are not able to estimate the proportion of variance in individuals' probabilities of survival from middle age to age 100+ explained by the FOXO genes. This is because the cohort data on outcome of that who (among the members of the middle-age control group) will survive to age 100 required for such variance analysis are not available. However, previous studies on elderly twins have shown that only one-fourth of the differences in individual lifespan are determined by genetic inheritance that involves multiple genes, and the other three-fourths are determined by social, behavioral, and environmental factors (31). Clearly, knowing which genotypes a person carries does not tell whether he or she may survive to age 100. The most important issue is to promote better social and environmental conditions and healthy behaviors thatE. 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Hum Genet. Andersson T, Alfredsson L, Källberg H. Calculating measures of Biological Interaction. Eur J Epidemiol. Cameron C, Trived K. Microeconometrics: Methods and Applications.; Cambridge: Cambridge University Press; This study is part of the project funded by National Institute of the Chinese Ministry of Science and Technology (973 grant 2007CB512100 to X.L.T.). Acknowledgments Jianxin Li for their contributions in the Chinese Longitudinal Healthy Longevity Survey and the DNA samples collection, and we thank all inter-Fengyu Zhang, Qiushi Feng and Jessica Sautter. Competing Interests: The authors have declared that no competing interests exist. Human Participation Protection: The Research Ethics Committees of Duke University and Peking University granted approval for the Protection of Human Subjects for each wave of the Chinese Longitudinal Healthy Longevity Survey, which is the data source of this study. The survey respondents gave informed consent before participating. Collection and data analysis, and wrote the paper; L.C. and H.C. analyzed data; X.L.T. and H.Q.C. led the laboratory work of DNA extraction and genotyping, Y.L. and Z.X. performed data and article. Of immune homeostasis: molecules to die for? J Immunol.  associated with human longevity. Proc Natl Acad Sci U S A. Anselmi CV, Malovini A, Roncarati R, et al. Association of FOXO A locus with extreme longevity in a southern Italian centenarian study. Rejuvenation Res. longevity. Aging Cell. Proc Natl Acad Sci U S A. FOXO A with longevity trait in Chinese populations. Hum Mol Genet. longevity and selected age-related phenotypes: a genome-wide association study in the Framingham Study. BMC Med Genet. Kuninga, Mg, Westendor GJ, et al. Haplotypes in the human genome associated with aging.Eur J Hum Genet.Kenyon J.The genetics of aging.Nature.Transcription Factor, FOXO a, accelerates cellular senescence human dermal fibroblasts.J Gerontol A Biol Sci Med Sci.Oxidative aging and insulin receptor signaling.J Gerontol A Biol Sci Med Sci.In this case, we connect the younger cohort and the long-lived individuals (denoted as p1 ij) controls (denoted as p2 ij), then compare the observed p2 (x+n) of the long-lived individuals (cases) and the observed p2 ij a hypothetical cohort and derive the estimate of RS ij/00 long-lived individuals (as cases) and younger namely assuming that there is no substantial problem population stratification. We further explore in the following resilience among community-dwelling older women. J Psychiatr Res. longevity in China. Curr Gerontol Geriatr Res. to death in the elderly than phenotypic frailty: Lessons from the cardiovascular health study. J Am Geriatr Soc. G, Dupre E, Sautter, Zh, Li, Zen Frailty and mortality among Chinese at advanced ages. J Gerontol Soc Sci. The definition of pij(x) is given in the text of The Extended Fixed Attribute Dynamics Method section. Let s(x), s(x), s(x), and s(x) denote the conditional 11 10 01 00 survival probability from age x to x + n for those who are both carrier and exposed, carrier and not-exposed, non-carrier and exposed, and neither carrier nor exposed, respectively (the terms carrier, non-carrier, exposed, and not-exposed are defined in The Extended Fixed Attribute Dynamics Method section in theA careful literature search, we believe that a bootstrap simulation was used to estimate the intervals and P-values of ISm and ISa (32, 33). 

Appendix 3. Potentially Confounding Factors Included in the Cox Hazards Regression Models: We chose the following variables as relevant covariates based on reviews of previous studies in this field and our understanding of the Chinese social context. Demographic and socioeconomic variables include age, gender, residence (rural vs urban), education (no schooling vs 1 year of schooling; note that two-thirds of the Chinese oldest old aged 80+ reported no schooling), and economic independence (having his or her own retirement wage and/or earnings vs no income).