Robust multipoint identical-by-descent mapping for affected relative pairs

The genetic mapping of complex traits has been challenging and has required new statistical methods that are robust to misspecified models. Liang et al. proposed a robust multipoint method that can be used to simultaneously estimate, on the basis of sib-pair linkage data, both the position of a trait locus on a chromosome and its effect on disease status. The advantage of their method is that it does not require specification of an underlying genetic model, so estimation of the position of a trait locus on a specified chromosome and of its standard error is robust to a wide variety of genetic mechanisms. If multiple loci influence the trait, the method models the marginal effect of a locus on a specified chromosome. The main critical assumption is that there is only one trait locus on the chromosome of interest. We extend this method to different types of affected relative pairs (ARPs) by two approaches. One approach is to estimate the position of a trait locus yet allow unconstrained trait-locus effects across different types of ARPs. This robust approach allows for differences in sharing alleles identical-by-descent across different types of ARPs. Some examples for which an unconstrained model would apply are differences due to secular changes in diagnostic methods that can change the frequency of phenocopies among different types of relative pairs, environmental factors that modify the genetic effect, epistasis, and variation in marker-information content. However, this unconstrained model requires a parameter for each type of relative pair. To reduce the number of parameters, we propose a second approach that models the marginal effect of a susceptibility locus. This constrained model is robust for a trait caused by either a single locus or by multiple loci without epistasis. To evaluate the adequacy of the constrained model, we developed a robust score statistic. These methods are applied to a prostate cancer-linkage study, which emphasizes their potential advantages and limitations.