An important problem in the final stage of positional cloning is to determine whether associated SNPs can account in part or in full for observed linkage signals. In Chapter 2, I develop a novel statistical approach that quantifies the degree of linkage disequilibrium between a candidate SNP and the putative disease locus through joint modeling of linkage and association using affected sib pairs. The proposed method yields parameter estimates for the disease and SNP allele frequencies and the degree of disease-SNP linkage disequilibrium. These estimates are valuable for estimating the distance between the candidate SNP and the unobserved disease locus, and for selecting additional SNPs that have frequencies close to the predicted disease allele frequency.; For most gene mapping studies, the data collected for follow-up association analysis may contain mixed types of sampling units, such as unrelated affected and unaffected individuals, affected sib pairs, discordant sib pairs, and a variety of other data structures. Efficient use of the data requires a unified statistical framework that allows the joint analysis of all available sampling units. In Chapter 3, I extend the association test in Chapter 2 to sibships of arbitrary size and disease phenotype configuration. This unified statistical framework enables the construction of different association study designs and comparison of their efficiencies. Results from this work will help researchers design association studies more efficiently in terms of power and genotyping resource allocation.; Another important problem in gene mapping studies is to identify genetic variants that influence disease related quantitative traits. Traditional quantitative trait linkage mapping uses the variance-components approach with the key assumption that the analyzed quantitative trait in a family follows a multivariate normal distribution. Violation of this assumption may yield biased results. To accommodate non-normally distributed data, in Chapter 4, I develop a Gaussian copula variance-components method that forms multivariate non-normal distributions by combining given non-normal marginal models with dependence patterns as characterized by genetic components. The Gaussian copula variance-components approach allows the analysis of continuous, discrete, and censored data, and will provide a useful arsenal of tools for linkage analysis of non-normally distributed quantitative traits.
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