Statistical methods to further the understanding of complex and continuous genetic traits

My research addresses two important issues in the analysis of complex and continuous genetic traits. The first topic is motivated by an association study of cardiovascular disease. We compare the mathematical basis of two methods for detecting higher-order genotype phenotype associations, multifactor-dimensionality reduction (MDR) and patterning and recursive partitioning (PRP), in order to better understand the utility of these methods in data analysis. We show that MDR is a special case of recursive partitioning in which patterns are used as predictors, tree growth is restricted to a, single split, and misclassification error is used as the measure of node impurity. Our finding indicates that the extensive theory developed for recursive partitioning should be considered when applying both MDR and PRP. The second issue is motivated by a linkage study of gene expression phenotypes in extended pedigrees. The study design is novel since families are not selected on the basis of phenotype. As a result, there is potential for the presence of two types of families: segregating and non-segregating. Segregating families have at least one parent heterozygous at the quantitative trait locus. In contrast, non-segregating families have two homozygous parents and are uninformative for linkage. We use latent class methods to extend Haseman-Elston regression to account for heterogeneity and estimate which families exhibit evidence of segregation and linkage. We derive expressions for the parameters in the latent class model in terms of an assumed genetic model using both the squared difference and family mean corrected product as outcome variables. We use maximum likelihood methods to fit the model, assuming independence of sibling pairs within a family, conditional on class. We use Generalized Estimating Equations (GEE) to fit a model that accounts for correlations among sibling pairs, via the Expectation-Solution algorithm. We show the equivalence of the estimating equations based on the maximum likelihood and GEE approaches, assuming conditional independence. A permutation procedure is used to test for linkage in the segregating class. We illustrate the methods on the motivating set of data and perform a simulation study