Multipoint linkage analyses of data collected on related individuals are often performed as a first step in the discovery of disease genes. Through the dependence in inheritance of genes segregating at several linked loci, multipoint linkage analysis detects and localizes chromosomal regions (called trait loci) which contain disease genes. Our ability to correctly detect and position these trait loci is increased with the analysis of data observed on large pedigrees and multiple genetic markers. However, large pedigrees generally contain substantial missing data and exact calculation of the required multipoint likelihoods quickly becomes intractable. In this paper, we present a new Markov chain Monte Carlo approach to multipoint linkage analysis which greatly extends the range of models and data sets for which analysis is practical. Several advances in Markov chain Monte Carlo theory, namely joint updates of latent variables across loci or meioses, integrated proposals, Metropolis--Hastings restarts via sequential imputation and Rao--Blackwellized estimators, are incorporated into a sampling strategy which mixes well and produces accurate results in real time. The methodology is demonstrated through its application to several data sets originating from a study of early-onset Alzheimer's disease in families of Volga-German ethnic origin.
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