| Linkage and association analysis are both tools for mapping the locations of genes responsible for human traits. A common approach for quantitative trait linkage analysis in human pedigrees involves the use of variance component models. In the first part of this dissertation, I extended the variance-component method to allow for genetic and/or environmental variance components as functions of measured covariates. I show that our method can provide large gains in power when there is heterogeneity in heritability of the quantitative trait locus due to covariates, such as age and/or sex.;The recent availability of a high-density reference panel has allowed for the imputation of genotypes at single nucleotide polymorphism markers that were untyped in a cohort or case-control study but that have been characterized in the reference panel. In the second part of this dissertation, I compared the performance of three different strategies to take account of the uncertainty of these imputed genotypes in the imputation-based association studies for quantitative traits. I found that for most realistic settings of genome-wide association studies (GWAS), the strategy of regressing the phenotype on the genetic dosages provided a good compromise between power and computational efficiency.;Although researchers have noticed the phenomenon of gene-environment interactions in disease etiology, it still remains uncertain how to trace the disease susceptibility loci by considering the role of environment and its potential to interact with genes, especially in GWAS. In the third part of this dissertation, I proposed a new likelihood-based method to identify genes involved in a gene-environment interaction, exploiting gene-environment independence at the population level. I compared its performance with the existing methods under different settings of parameters and by different criteria. The new likelihood-based approach shows merit in various settings, especially when the disease is not very rare. The simulation studies also showed that the empirical power of the new method was still great when the violation of the assumption was realistically modest. |
