Assessing genetic association with human survival at multi-allelic loci

Genetic variation plays an important role in natural selection and population evolution. However, it also presents geneticists interested in aging research with problems in data analysis because of the large number of alleles and their various modes of action. Recently, a new statistical method based on survival analysis ( the relative risk model or the RR model) has been introduced to assess gene-longevity associations [ Yashin et al. ( 1999) Am J Hum Genet 65: 1178-1193] which outperforms the traditional gene frequency method. Here we extend the model to deal with polymorphic genes or gene markers. Assuming the Hardy-Weinberg equilibrium at birth, we first introduce an allele-based parameterization on gene frequency which helps to cut down the number of frequency parameters to be estimated. We then propose both the genotype and allele-based parameterizations on risk parameters to estimate genotype and allelic relative risks ( the GRR and ARR models). While the GRR model allows us to investigate whether the alleles are recessive, dominant or codominant, the ARR model further minimizes the number of parameters to be estimated. As an example, we apply the methods to empirical data on Renin gene polymorphism and longevity. We show that our models can serve as useful tools in searching for important genetic variations implicated in human aging and longevity.