Simple, robust linkage tests for affected sibs

Parametric-linkage analysis applied to large pedigrees with many affected individuals has helped in the identification of highly penetrant genes; but, for diseases lacking a clear Mendelian inheritance pattern or caused by several genes of low to moderate penetrance, a more robust strategy is nonparametric analysis applied to small sets of affected relatives, such as affected sib pairs. Here we show that the robustness of affected-sib-pair tests is related to the shape of the constraint set for the sibs' identity-by-descent (IBD) probabilities. We also derive a set of constraints for the IBD probabilities of affected sib triples and use common features of the shapes of the two constraint sets to introduce new nonparametric tests (called "minmax" tests) that are more robust than those in current use. Asymptotic-power computations support the robustness of the proposed minmax tests.