| The field of Statistical Genetics draws on statistics and computer science to address genetic questions. One aim of genetics is to locate on the genome the gene(s) responsible for an inherited trait. This localization is facilitated by linkage analysis, which uses genetic map, pedigree, and trait model information. However, complicating factors exist. While sex-averaged genetic maps are normally used in analyses, the true male-female maps are of different lengths. This use of sex-averaged maps results in map misspecification. Heterogeneity among pedigrees from different populations is another complicating factor. Finally, the trait may be complex, possessing a genetic component but not a simple mode of inheritance; non-syndromic cleft lip and/or palate (CL+/-P) is one such complex trait. For such traits, linkage analysis may involve exploration of a vast multidimensional parameter space. The posterior probability of linkage, or PPL, is an approach designed to model both sex-specific maps and the trait model complexity represented by the multidimensional parameter space in a mathematically rigorous fashion. It accommodates both inter- and intra-population heterogeneity using Bayesian sequential updating over data subsets. However, it requires evaluation of integrals with no functional form, making it difficult to compute, and thus further test, develop and apply. This thesis addresses some of the issues related to the PPL. First, it presents a new program, the multiprocessor linkage package, or MLIP, which allows the computation of the two-point likelihood in reasonable time by distributing the computation of the parameter space while maintaining flexibility in parameter space definition. Second, it defines the sex-specific multipoint PPL and explores, for multipoint analyses, the impact of using a sex-averaged map as opposed to the correct sex-specific maps on the PPL and other approaches. Third, it presents a simulation study, in order to evaluate alternative sequential updating procedures in application to the complex pedigrees in a large CL+/-P data set. Finally, it applies the PPL to a genome scan of CL+/-P families, drawn from seven distinct populations, with potentially etiologically distinct clefting phenotypes. |
