Importance sampling for estimating p values in linkage analysis

Importance sampling methods are proposed for estimating the probability that the maximum of a random process exceeds a high threshold, with particular attention to assessing genome-wide significance levels in linkage analysis. The proposed algorithm is applied to computing the conditional significance level, given observed phenotypes, of scan statistics to map quantitative traits in experimental populations and in extended pedigrees of moderate size with partially informative markers, For detecting an additive effect in an intercross, the importance sampling algorithm is roughly 100 times as efficient as direct Monte Carlo simulation when the true significance level is about .05. For pedigrees with partially informative markers, the efficiency varies greatly with intermarker distance, marker polymorphism, sample size, and missing data. In this case the importance sampling algorithm is used to efficiently explore how p values vary with these parameters. Extensions of the algorithm are discussed for the case of multidimensional statistics that arise when considering dominance effects or searching for multiple loci that may involve interactions.