We propose a new Monte Carlo approach to the problem of calculating the conditional probability of inheritance patterns given sibship genotype data in multipoint linkage analysis. By limiting the study to sibships, we hope to have a linkage analysis method that can incorporate general crossover process model and can be used to examine the issue of genetic interference in the context of linkage studies. This thesis is separated into three parts. In Part I, we introduce the new Monte Carlo approach of multipoint linkage analysis. Our approach is mainly an application of importance sampling method. The crossover distribution used in this approach is estimated from the CEPH and Icelandic family genotype data. Estimation of this crossover distribution is described in Part III. To make the computation efficient, we show that the calculation of the probability of legal ordered parental genotype given sibship genotype and inheritance patterns can be carried out quickly by a straight-forward classification of inheritance patterns. To evaluate the performance of our method, we compare the performance of our method with that of GENEHUNTER in terms of the accuracy in calculating the conditional probability of IBD sharing for sib-pairs in CEPH families given the sibship genotype on chromosome 19. In Part II, we deal with the set of legal inheritance vectors for a sibship at one marker. We classify the sibships according to the genotype of the sibs into 9 classes, and list explicitly the set of legal inheritance vectors for each class. Because an inheritance pattern is legal at several markers if it is legal at everyone of these markers, results in Part II can be extended directly to the set of legal inheritance patterns for many markers. We use the result to reduce the time and memory needed in our Monte Carlo approach in Part I. In Part III, we provide a nonparametric estimate of the crossover distribution on the basis of the CEPH family genotype data, the Icelandic family genotype data, and the order of the markers where genotype data are taken. The only assumption employed in this approach is that, in one meiosis, there is at most one crossover point between markers close enough to each other. This estimated crossover distribution can be used in multipoint linkage analysis without the assumption of no interference.
