Regression models for linkage heterogeneity applied to familial prostate cancer

Linkage heterogeneity frequently occurs for complex genetic diseases, and statistical methods must account for it to avoid severe loss in power to discover susceptibility genes. A common method to allow for only a fraction of linked pedigrees is to fit a mixture likelihood and then to test for linkage homogeneity, given linkage (admixture test), or to test for linkage while allowing for heterogeneity, using the heterogeneity LOD (HLOD) score. Furthermore, features of the families, such as mean age at diagnosis, may help to discriminate families that demonstrate linkage from those that do not. Pedigree features are often used to create homogeneous subsets, and LOD or HLOD scores are then computed within the subsets. However, this practice introduces several problems, including reduced power (which results from multiple testing and small sample sizes within subsets) and difficulty in interpretation of results. To address some of these limitations, we present a regression-based extension of the mixture likelihood for which pedigree features are used as covariates that determine the probability that a family is the linked type. Some advantages of this approach are that multiple covariates can be used (including quantitative covariates), covariates can be adjusted for each other, and interactions among covariates can be assessed. This new regression method is applied to linkage data for familial prostate cancer and provides new insights into the understanding of prostate cancer linkage heterogeneity.