Research article Assessing genetic association with human survival at multi-allelic loci Qihua Tan 1, *, G. De Benedictis 2 , A.I. Yashin 3 , L. Bathum 1 , L. Christiansen 1 , J. Dahlgaard 1 , N. Frizner 1 , W. Vach 4 , J.W. Vaupel 3 , K. Christensen 5 & T.A. Kruse 1 1 Department of Clinical Biochemistry and Genetics, KKA, Odense University Hospital, Odense, Denmark; 2 Cell Biology Department, University of Calabria, Rende, Italy; 3 Max-Planck Institute for Demographic Research, Rostock, Germany; 4 Department of Statistics and Demography, University of Southern Denmark; 5 Epidemiology, Institute of Public Health, and Ageing Research Center, University of Southern Denmark- Odense University, Denmark *Author for correspondence (e-mail: qihua.tan@ouh.fyns-amt.dk; fax: +45-6541-1911) Received 6 August 2003; accepted in revised form 15 September 2003 Key words: association study, gene, Hardy–Weinberg equilibrium, longevity, polymorphism Abstract 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. Introduction Maintenance of genetic variation and genetic polymorphism is one of the key issues in evolu- tionary biology. This is because, apart from the contribution of newly arisen mutations, genetic variation per se conveys heterozygous advantages and makes natural selection possible. It has been shown that the genetically polymorphic popula- tion is advantageous for survival in a changing environment (Lee et al. 1998), and that increased homozygosity may affect individual and popula- tion negatively in stressful and fluctuating envi- ronments by disturbing gene expression (Kristensen et al. 2002), reducing individual fitness and survival and increasing the probability of population extinction (Charlesworth and Charlesworth 1987; Dahlgaard and Hoffman 2000; Bijlsma et al. 2000). Genetic polymorphism thus plays an important role both in maintaining the long-term evolutionary potential of populations and in preserving individual fitness and survival. Genetic variations at highly polymorphic loci have been associated with human longevity, for example the HLA-DRB1 (Ivanova et al. 1998), HUMTHO1.STR (tyrosine hydroxylase gene) (De Benedictis et al. 1998a; Tan et al. 2002), CYP2D6 (cytochrome p450 genes) (Bathum et al. 1998), Biogerontology 5: 89–97, 2004. 89 Ó 2004 Kluwer Academic Publishers. Printed in the Netherlands.