The power of two-locus affected sib-pair linkage analysis to detect interacting disease loci

It has been shown that two-locus linkage analysis can, for some two-locus disease models, be used to detect effects at disease loci that do not reach significance in a genome scan. However, few examples exist where two-locus linkage has been successfully used to map genes. We study the possible gain in power of affected sib-pair nonparametric two-locus linkage analysis for two-locus models which fulfil the two-locus triangle constraints. Using a new parameterization of the two-locus joint identity-by-descent sharing probabilities we can, for fixed marginal sharing at both of two unlinked disease loci, derive a two-locus distribution such that the power of a two-locus analysis is maximized. In a simulation study we look at two test statistics, the two-locus maximum liklihood score and the correlation between nonparametric linkage scores, and study power as a function of marginal sharing. We show that in a best-case scenario two-locus linkage can have considerable power to detect pairs of interacting loci if there is a moderate increase in allele sharing at one of the two loci, even if there is a very small increase in allele sharing at the other locus. But we also show that the power to detect interacting loci in a two-locus analysis decreases as the marginal sharing at the two loci decreases and for any distribution with a small increase in allele sharing at both loci the power of a two-locus analysis is always low.