Multivariate survival models induced by genetic frailties, with application to linkage analysis.

We derive a multivariate survival model for age of onset data of a sibship from an additive genetic gamma frailty model constructed basing on the inheritance vectors, and investigate the properties of this model. Based on this model, we propose a retrospective likelihood approach for genetic linkage analysis using sibship data. This test is an allele-sharing-based test, and does not require specification of genetic models or the penetrance functions. This new approach can incorporate both affected and unaffected sibs, environmental covariates and age of onset or age at censoring information and, therefore, provides a practical solution for mapping genes for complex diseases with variable age of onset. Small simulation study indicates that the proposed method performs better than the commonly used allele-sharing-based methods for linkage analysis, especially when the population disease rate is high. We applied this method to a type 1 diabetes sib pair data set and a small breast cancer data set. Both simulated and real data sets also indicate that the method is relatively robust to the misspecification to the baseline hazard function.