Tests for covariate-associated heterogeneity in IBD allele sharing of affected relatives

Linkage studies that aim to map susceptibility genes for complex diseases commonly test for excess allele sharing among affected relatives. Conventional methods based on identical-by-descent IBD allele sharing do not allow for possible differences among families, such as arise in the case of locus heterogeneity, and thus have reduced ability to detect linkage in the presence of such heterogeneity. We investigated two approaches to test for heterogeneity in allele sharing, using a family-level covariate that may be associated with different disease mechanisms leading to differences in allele sharing. Likelihood ratio tests for heterogeneity were formulated based on an extension of the linear and exponential likelihood models developed by Kong and Cox. Alternatively, we examined the asymptotic and permutation distributions of T-tests for differences between mean allele-sharing linkage scores from two covariate-defined family subgroups, assuming exchangeability. The size and power of heterogeneity tests were evaluated for S(all) and S(pairs) allele-sharing scoring functions using data sets of families with affected sibling and cousin pairs, generated under a model of locus heterogeneity. In certain simulation scenarios, the likelihood ratio test statistics did not follow the expected asymptotic distributions. The type I error estimates for the T-statistics conformed to nominal 5 and 1% levels in all scenarios considered, and corresponding power was comparable to that of the likelihood ratio tests. Application of these tests for heterogeneity detected significant differences in allele sharing between subgroups of families with inflammatory bowel disease.