Experimental Gerontology 36 (2001) 1303-1315 <www.elsevier.com/locate/expgero> exhibits sex-dependent influence on human longevity. Department of Thrombosis, Research, University of Southern Denmark and Department of Clinical Biochemistry, Ribe County Hospital, Esbjerg, Denmark, Epidemiology, Institute of Public Health, and Aging Research Center, University of Southern Denmark-Odense University, Denmark. Received January 4 -../0; received revised form March % -../0; accepted March * -../ with cardiovascular disease and longevity in the Danish population. A new procedure that combines both demographic and individual genetic information in determining the relative observed genetic variations is applied. The sex-dependent influences can be found by introducing sex-specific population survival and incorporating the gene-sex interaction. Three genetic polymorphisms, angiotensinogen "6(cid:26)-,7(cid:27), blood coagulation factor VII 89(cid:1)(cid:29)(cid:29): (6(cid:25),7), and FVII- ,(cid:4)(cid:7)(cid:8)/.(cid:27), manifest significant influences on survival in males with reduced hazards of death for carriers of the angiotensinogen "-,7) allele, the 9 7 VII (6(cid:25),7) allele, and the J 9(cid:1)(cid:29)(cid:29)(cid:20),-,&/.) allele. The results show that some of these genotypes associated with lower risk of death could also reduce the carriers' death rate and contribute to increased longevity. However, the presence of sex-dependent effects and the fact that major CVD-associated genes failed to impose a detrimental influence on longevity lead us to conclude that the aging process is highly complicated. Elsevier Science Inc. All rights reserved.

Keywords: Gene; Cardiovascular disease; Sex-dependent influence; Longevity; Survival analysis.

Introduction: polymorphisms of a variety of genes have been studied to see if they are associated with increased risk of atherosclerotic cardiovascular disease and longevity. Table 1 revised from Bladbjerg et al. (2001) shows the control group and centenarian group number and frequency for various genes related to haemostasis and regulating genes. Some of these genotypes were associated with lower risk of death and could contribute to increased longevity. However, the aging process is highly complicated.NEED: Studies have shown that some genes are associated not only with the incidence of Alzheimer's disease but also with mortality at old ages. Homozygosity of the APOE allele has been confirmed to have a deleterious effect on mortality at old ages (Heijmans et al., 2002), and significant depletion of the APOE allele has been found in French (Schachter et al., 1994), Finnish (Louhija et al., 1995), and Chinese (Zhang et al., 2003) centenarians. Other genes associated with polymorphisms and longevity include those coding for apolipoprotein A-I (Hegele et al., 1997), apolipoprotein C-1 (Myant et al., 2000), and angiotensin-converting enzyme (ACE) (Galinsky et al., 1997; Nakata et al., 1997; Alvarez et al., 2000). However, no significant associations were reported in a study focusing on polymorphisms of genes involved in regulating blood pressure and blood coagulation in the Danish population (Bladbjerg et al., 2001). In this paper, we apply an approach derived by Vaupel and Yashin, developed in recent articles (Yashin et al., 1999; Yashin et al., 2001; Tan et al., 2003) on previously published data (Bladbjerg et al., 2001) and combine both demographic and individual genetic information sets to determine the relative risks of the observed genetic variations. This strategy can detect polymorphisms that show potential sex-dependent effects. We estimated the relative risks of the observed genes as well as gene-sex interaction and present sex-specific survival. This approach also incorporates important factors such as sex-dependent influences and unobserved frailty heterogeneity, which were previously ignored. Age-specific cohort population survival is calculated from cohort life tables for Danes born between 1900 and 1920, and the survival for each age is taken from the life tables.Cohort life table for people who reached a certain age is analyzed using a strategy to estimate the hazard of death for carriers (Br) compared to non-carriers or the baseline hazard g(x). According to the proportional hazard assumption, the hazard for carriers can be expressed as exp(ar). The corresponding survival function for carriers is Muo(x) while the cumulative hazard at age x is represented by H(x). Although any value of H(x) can be greater than zero, a gene allele with larger frailty increases the hazard of death while an allele with smaller frailty reduces it. Heterogeneity in individuals' unobserved frailty also contributes to survival. The average survival for a group of carriers can be derived as K(x|r) when the unobserved frailty follows a gamma distribution with mean and variance. Accordingly, mean survival for non-carriers is S(x), and for genotype, one can introduce a simple two-point distribution for the gene allele or genotype. The risk of gene-sex interaction (lg(99)) is defined as the risk of male carriers to that of female carriers. The average survival for the mixed population consisting of both carriers and non-carriers is obtained from population statistics. The proportion of carriers at age x in the data containing both male and female individuals can be constructed using Pn, Pm, Pr, Pn. In estimation, single alleles are used to reduce the number of parameters estimated. Parameters that maximize the likelihood function are estimated using Gauss software.