Multivariate survival analysis methods for mapping genes for complex diseases

Many complex human diseases are due to multiple disease genes and both genetic and environmental risk factors. These diseases often also show variable age of disease onset. In order to incorporate both covariates and age of onset information into genetic analysis, we define an additive genetic gamma frailty model constructed based on the inheritance vectors. Within this modeling framework, we derive retrospective likelihood ratio tests for linkage and a score test for testing genetic association in the linked region using sibships data. Such tests can incorporate both affected and unaffected sibs, environmental covariates and age at disease onset or censoring information, and therefore provide a practical solution to mapping genes for complex diseases with variable age of onset. Simulation studies indicate that the proposed methods have correct type 1 error rates and perform better than the commonly used methods for linkage or association analysis. We demonstrate the methods using a type 1 diabetes data set, a breast cancer data set, a real data set of affected sib pairs of prostate cancer, and the simulated data sets from the Genetic Analysis Workshop 12 (GAW12).; We also consider age-matched case-control design for testing genetic association in which subjects developing disease are matched to one or more subjects without disease at the same point in time or age. Based on a conditional retrospective likelihood proposed by Prentice and Breslow (1978), we derive a score test of association for the age-matched case-control studies. Based on the idea of Genomic Control, a population-based association method proposed by Devlin and Roeder (1999), which automatically accounts for nonindependence caused by population stratification and cryptic relatedness in a case control sample, we derive and estimate the degree of overdispersion generated by population substructure and modify the score test to correct for population stratification. The application to the simulated family data provided by the Genetic Analysis Workshop 12 gives desirable results.