Sequential Imputation and Linkage Analysis

Multilocus calculations using all available information on all pedigree members are important for linkage analysis. Exact calculation methods in linkage analysis are limited in either the number of loci or the number of pedigree members they can handle. In this thesis, we propose a Monte Carlo method for linkage analysis based on sequential imputation. Unlike exact methods, sequential imputation can handle both a moderate number of loci and a large number of pedigree members. Sequential imputation does not have the problem of slow mixing encountered by Markov chain Monte Carlo methods because of high correlation between samples from pedigree data. This Monte Carlo method is an application of importance sampling in which we sequentially impute ordered genotypes locus by locus and then impute inheritance vectors conditioned on these genotypes. The resulting inheritance vectors together with the importance sampling weights are used to derive a consistent estimator of any linkage statistic of interest. The linkage statistic can be parametric or nonparametric; we focus on nonparametric linkage statistics. We showed that sequential imputation can produce accurate estimates within reasonable computing time. Then we performed a simulation study to illustrate the potential gain in power using our method for multilocus linkage analysis with large pedigrees. We also showed how sequential imputation can be used in haplotype reconstruction, an important step in genetic mapping. In all