The results show no significant risk for the single gene allele, which is consistent with Bladbjerg et al.'s findings. However, three polymorphic variations (angiotensinogen "6"-7", FVII (6)-7,(10)) display significant sex-dependent effects that reduce hazards of death for male carriers by factors + and -. The highest likelihood was achieved when there was no significant risk for any gene allele. The significance levels for relative risks for genes and gene-sex interaction are determined by testing the statistical differences between the estimated risks and one with null hypothesis 0. The p-values for frequency parameters are obtained by testing Z.Fibrinogen-A, D/1--F/D in females is set to one, as Mw and Peereference. The result indicates that some polymorphisms that reduce the hazard of 3 are also favourable for male longevity but not for female longevity. In Fig. 1, sex-specific survivals for carriers and non-carriers of the angiotensinogen allele are plotted. Male carriers have better survival than non-carriers, but for females, it is the opposite, although the difference in survival between female carriers and non-carriers is very small. The observed and estimated proportions of carriers of the angiotensinogen allele by age for males and females are plotted in Fig. 2. While the frequency of carriers of the M-allele goes up with age in males, it tends to decline in females due to the sex-dependent influence of the gene frequencies for carriers of the gene alleles.

The p-values for the estimated initial frequencies are not shown since they are all significantly different from zero. Proportions of carriers of the three alleles are estimated as 7E7/E7, and respectively.

Incorporation of gene-sex interaction in the analysis produces results that were missed in the original analysis using the gene frequency method. The gene frequency method ignores gene-sex interactions when comparing gene frequency differences between control groups and centenarians. This could be attributed to the lack of efficiency of the gene frequency method when applied to small samples.

In the new model, the risk of gene-sex interaction is defined as an extra risk for female carriers compared to male carriers. Information from both sexes is used to determine the parameter of interaction. However, one important non-traditional epidemiologic approach, the case-only design, which was originally derived for analysing gene-environment interaction in disease prevalence can be introduced here to detect gene-sex interaction in human longevity when treating centenarians as cases.

Although this conclusion is compatible with our result, the case-only approach does not allow for evaluation of the independent effect of the allele but merely involves a departure from multiplicative effects. The relative risk model exploited in this paper is of primary interest as it not only tests for the gene-sex interaction but also evaluates the risk of the allele genotype as well as its initial frequency. In addition, it can also estimate the genotype-specific survival distribution.

Nevertheless, the easily applicable case-only approach is a useful tool for measuring gene-sex interaction in human longevity as it avoids the troubles originated from ordinary case-control design.