Topics in Human Gene Mapping

This thesis is interdisciplinary between Mathematical Statistics, Genetics, and Medicine. It mainly consists of topics in mathematical modelling of the correlation of inheritance of genes and disease in a family, a method called linkage analysis. It is organized as follows. First, a short introduction with the relevant background is given and then four papers are included. The first paper discusses hypothesis testing of linkage of a disease gene to a certain position on the chromosome. The focus is on the choice of lod scores and its relation to p-values. The second paper is a result of collaboration with the research groups in Lund and Denmark in the effort to localize the gene responsible for a malignant melanoma. Here, the theory presented in the first paper is used. The third paper concerns modelling of complex diseases, i.e. diseases governed by genetic contribution from at least two loci. We have studied the contribution of a particular locus to increased risk of relatives compared with population prevalence. Relative risk is modelled as the product of the relative risk at the main locus and the relative risk due to genetic contribution from other loci and shared environmental effects. Additionally, we show how this relative risk is related to probabilities of allele sharing identical by descent at the main locus and the power to detect linkage. The last paper contributes to the development of the algorithms used in the linkage and family based association analysis. One of the most demanding issues in these analyses is how to calculate the inheritance distribution at a certain position on the chromosome. The well established algorithms are based on the assumption that the markers used in the studies are in linkage equilibrium (LE). However, today's marker data have markers in linkage disequilibrium (LD). We develop a novel hidden Markov model algorithm for association and linkage analysis when markers are in LD