Advances in Pedigree Analysis: Hardy-Weinberg Equilibrium, Strain Imputation, and Maternal Effects

Genetic studies usually gather participants in one of the three ways: random samples, cases and controls, and pedigrees. Pedigree analysis is computationally demanding and, with the passing of HIPAA, pedigrees are difficult to collect. For these reasons researchers currently favor cases and controls and random samples over pedigrees. However, pedigrees take advantage of familial relationships and vertical inheritance patterns that can avoid some of the confounding and variance inflation that arise when population substructure is present. Pedigree analysis can also test for both linkage and association. In this dissertation I propose to expand the utility of pedigree analysis in three ways: (a) Hardy-Weinberg testing for pedigrees, (b) association testing using imputed strain origins in animals crosses with inbred strains, and (c) testing for prenatal effects using variance component models.;Typically Hardy-Weinberg equilibrium is tested in unrelated individuals using a chi² goodness-of-fit test that compares expected and observed numbers of across genotypes. In this dissertation, a likelihood ratio test for Hardy-Weinberg equilibrium that accommodates a mixture of pedigree and random sample data is proposed. The heterozygous-homozygous test accommodates markers with dominant and recessive alleles and handles the phase ambiguities encountered in combining several linked SNPs (single nucleotide polymorphisms) into a single supermarker. My experience analyzing real and simulated data suggests that the heterozygous-homozygous test has good power and type-one error rates.;Mapping quantitative traits in inbred strains is often simpler than mapping the analogous traits in humans. One of the drawbacks of standard inbred crosses is their reduced genetic diversity. Multiple crosses circumvent these difficulties, but raise substantial computational difficulties. I present a good method for locally imputing the strain origins of each genotyped organism along its genome. Pedigree structure if available can guide imputation. Imputed origins then serve as mean effects in a multivariate Gaussian model for testing association between trait levels and local genomic variation. A dynamic programming algorithm solves the strain imputation process in one quick pass through the genome of a progeny. Imputation accuracy exceeds 99% in practical examples and leads to high-resolution mapping in simulated and real data.;Maternally inherited effects, prenatal effects, and postnatal effects are confounded in traditional family studies. It turns out that these effects can be disentangled by studying families containing children conceived by assisted reproductive technologies (ART). I develop a variance component model to capture these effects. This model is flexible enough to allow any number of family members and degrees of relationship; thus researchers can use both small and extended families simultaneously. Simulations demonstrate that the method has appropriate statistical properties and is robust to model misspecification and missing data.