Efficient Calculation of Empirical P-values for Genome-Wide Linkage Analysis Through Weighted Permutation

Abstract

Linkage analysis in multivariate or longitudinal context presents both statistical and computational challenges. The permutation test can be used to avoid some of the statistical challenges, but it substantially adds to the computational burden. Utilizing the distributional dependencies between $\hat{\pi}$ (defined as the proportion of alleles at a locus that are identical by descent (IBD) for a pairs of relatives, at a given locus) and the permutation test we report a new method of efficient permutation. In summary, the distribution of $\hat{\pi }$ for a sample of relatives at locus x is estimated as a weighted mixture of $\hat{\pi }$ drawn from a pool of ‘representative’ $\hat{\pi }$ distributions observed at other loci. This weighting scheme is then used to sample from the distribution of the permutation tests at the representative loci to obtain an empirical P-value at locus x (which is asymptotically distributed as the permutation test at loci x). This weighted mixture approach greatly reduces the number of permutation tests required for genome-wide scanning, making it suitable for use in multivariate and other computationally intensive linkage analyses. In addition, because the distribution of $\hat{\pi }$ is a property of the genotypic data for a given sample and is independent of the phenotypic data, the weighting scheme can be applied to any phenotype (or combination of phenotypes) collected from that sample. We demonstrate the validity of this approach through simulation.