ORIGINAL RESEARCH 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 chal-lenges. The permutation test can be used to avoid some of the statistical challenges, but it substantially adds to the computational burden. Utilizing the distributional depen-dencies between p ̂ (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 p ̂ for a sample of relatives at locus x is estimated as a weighted mixture of p ̂ drawn from a pool of ‘representative ’ p ̂ distributions observed at other loci. This weighting scheme is then used to sample from the distri-bution of the permutation tests at the representative loci to obtain an empirical P-value at locus x (which is asymp-totically 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 com-putationally intensive linkage analyses. In addition, because the distribution of p ̂ is a property of the genotypic data for a given sample and is independent of the pheno-typic 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