Statistical models for haplotyping complex human diseases with a family-based design

It has long been recognized that many human diseases involve the action of multiple genes and nongenetic factors and also show strong correlation among relatives. Because of this complexity, genetic mapping with a family-based design (including parents and offspring) is particularly needed for identifying genes and their inheritance involved in human diseases. In this dissertation, I explore several fundamental aspects of family data in constructing the linkage disequilibrium map of the human genome and fine mapping disease genes. A library of statistical models has been derived to estimate and test the pattern of gene segregation in a natural population and genetic effects of haplotypes on complex diseases. Because genetic information of interest to population and biomedical genetic studies cannot be observed, a series of mixture models proven powerful for solving missing data problems have been built within the family design. These models generate a number of testable hypotheses about the genetic control of complex diseases. Specifically, this dissertation presents various solutions into genetic and statistical problems in the following ways: (1) Construct a multilocus population and multilocus quantitative genetic model with SNP data: The models proposed allow the test of high-order disequilibria on the diversity of a natural population and of crossover interference on the transmission of genes during meiosis. By tracing the path of gene transmission from different parents, the models provide a way of quantitatively testing genetic imprinting effects on human diseases. (2) Develop a new approach for estimating linkage disequilibria at the zygote level: The family design has a capacity of separating the diplotypes that form the same heterozygote and, thereby, estimating gametic and non-gametic disequilibria and trigenic and quadrigenic disequilibria. The new approach relaxes the Hardy-Weinberg equilibrium for a population and extends the concept of linkage disequilibrium mapping to any nonequilibrium populations. (3) Derive a series of closed forms for the EM algorithm: These algorithms are shown to be robust for estimating population genetic parameters (including haplotype frequencies and linkage disequilibria of various orders), gene transmission parameters (including the recombination fractions and crossover interference), and quantitative genetic parameters (including additive, dominant, and imprinting effects of haplotypes). The accuracy and precision of parameter estimates are investigated through simulation studies.;The dissertation provides a handful of state-of-art technologies for genetic mapping of human diseases with commonly used family-based designs. These technologies, coupled with empirical and laboratory studies, will help to predict the occurrence and progression of a disease using the information about its underlying genes and biological pathways.