Abstract

The thesis is going to explore two problems in statistical genetics. One arises in the mapping of individual QTL using extended human pedigrees and the other arises in mapping multiple interacting QTL, using experimental crosses.

In Chapter 2, we derive a robust score statistic for extended human pedigrees based on a variance component model. Then we completely characterize the test process when markers are fully informative by deriving explicit formulas for the Fisher's information, the skewness of marginal distribution and the average recombination rate. These results make us capable of approximating the genome-wide significance level and the power without simulations. Theoretical power analysis reveals the relative contributions to the power from each relative pair and also suggests the best way of splitting a pedigree too large to be analyzed by computer. When markers are partially informative, large scale simulations are run to explore how the power depends on the effect size, pedigree structure and marker information content. In Chapter 3, we propose an importance sampling algorithm that provides an efficient, unbiased estimation to the genome-wide significance level in various situations.

In the second part, we use model selection to map multiple interacting QTL for experimental crosses. We discuss three model selection criteria that take the model pattern into account: the p-value criterion, a modified BIC based on multivariate regression analysis and a modified BIC based on change point detection. A new search strategy based on the Cross-Entropy method is proposed to search for the optimal model under each criterion. Large scale simulations demonstrate that: (1) the p-value can serve as a model selection criterion for detecting a complex model; (2) all methods have comparable performance when considering only main effect models; (3) for complex models with interactions, our modified BIC based on multivariate regression analysis has the largest power and a reasonable false positive rate. In addition, the p-value criterion inspires the theoretical work in Chapter 5, where we derive a unified p-value approximation for a model with any interaction pattern.