Several topics in statistical genetics

This thesis presents statistical methods for several problems in statistical genetics. The topics discussed here are (1) family-based association tests with multiple closely linked markers, (2) family-based association tests for half-sibs, and (3) testing for age-of-onset anticipation with affected parent-child pairs.; The first topic is concerned with family-based tests of association between the alleles of multiple closely linked marker loci and traits. An approach is presented for adjusting for bias due to population admixture in family-based association studies. Adjustment for population admixture is carried out by conditioning on the minimal sufficient statistic for the population admixture, sampling plan and genetic model. The adjustment therefore results in correct type I error rates regardless of the population admixture, sampling plan and genetic model. The approach is applicable with any pattern of missing marker genotype and phase information. Since multiple closely linked markers are tested simultaneously, this approach can be more powerful than approaches that test closely linked markers one at a time. Tables of the conditional distributions of patterns of sibship genotypes of two bi-allelic markers given the minimal sufficient statistics are presented for nuclear families. A recursive approach that is capable of computing the conditional distributions given the minimal sufficient statistic with an arbitrary number of markers is also described in detail.; The second topic involves the application of a general approach by Rabinowitz and Laird (1999) that adjusts for population admixture by conditioning on the minimal sufficient statistic for parental marker genotypes, to pedigrees with half-sibs; that is, to two nuclear families sharing one parent in common. The minimal sufficient statistic for population admixture is derived under the null hypothesis for pedigrees with half-sibs. The conditional distributions for pedigree with half-sibs are presented for any pattern of missing parental marker genotype information.; Rabinowitz and Yang (1999) presented a non-parametric approach to testing for age-of-onset anticipation that adjusts for preferential ascertainment of children with early onset. The third topic presents a derivation of the variance estimation for the second statistic of the non-parametric approach based on U-statistic theory. The results of a simulation study that examines the type I error rates and power of the test are presented. The nonparametric approach is also extended to the case where more than one affected parent-child pairs from the same pedigree are included in the test.