Next-generation sequencing technology will soon allow sequencing the whole genome of large groups of individuals, and thus will make directly testing rare variants possible. Currently, most of existing methods for rare variant association studies are essentially testing the effect of a weighted combination of variants with different weighting schemes. Performance of these methods depends on the weights being used and no optimal weights are available. By putting large weights on rare variants and small weights on common variants, these methods target at rare variants only, although increasing evidence shows that complex diseases are caused by both common and rare variants. In this paper, we analytically derive optimal weights under a certain criterion. Based on the optimal weights, we propose a Variable Weight Test for testing the effect of an Optimally Weighted combination of variants (VW-TOW). VW-TOW aims to test the effects of both rare and common variants. VW-TOW is applicable to both quantitative and qualitative traits, allows covariates, can control for population stratification, and is robust to directions of effects of causal variants. Extensive simulation studies and application to the Genetic Analysis Workshop 17 (GAW17) data show that VW-TOW is more powerful than existing ones either for testing effects of both rare and common variants or for testing effects of rare variants only.

Transmission/disequilibrium tests have attracted much attention in genetic studies of complex traits because (a) their power to detect genes having small to moderate effects may be greater than that of other linkage methods and (b) they are robust against population stratification. Highly polymorphic markers have become available throughout the human genome, and many such markers can be studied within short physical distances. Studies using multiple tightly linked markers are more informative than those using single markers. However, such information has not been fully utilized by existing statistical methods, resulting in possibly substantial loss of information in the identification of genes underlying complex traits. In this article, we propose novel statistical methods to analyze multiple tightly linked markers. Simulation studies comparing our methods versus existing methods suggest that our methods are more powerful. Finally, we apply the proposed methods to study genetic linkage between the dopamine D2 receptor locus and alcoholism.

Studies using haplotypes of multiple tightly linked markers are more informative than those using a single marker. However, studies based on multimarker haplotypes have some difficulties. First, if we consider each haplotype as an allele and use the conventional single-marker transmission/disequilibrium test (TDT), then the rapid increase in the degrees of freedom with an increasing number of markers means that the statistical power of the conventional tests will be low. Second, the parental haplotypes cannot always be unambiguously reconstructed. In the present article, we propose a haplotype-sharing TDT (HS-TDT) for linkage or association between a disease-susceptibility locus and a chromosome region in which several tightly linked markers have been typed. This method is applicable to both quantitative traits and qualitative traits. It is applicable to any size of nuclear family, with or without ambiguous phase information, and it is applicable to any number of alleles at each of the markers. The degrees of freedom (in a broad sense) of the test increase linearly as the number of markers considered increases but do not increase as the number of alleles at the markers increases. Our simulation results show that the HS-TDT has the correct type I error rate in structured populations and that, in most cases, the power of HS-TDT is higher than the power of the existing single-marker TDTs and haplotype-based TDTs.

Although genetic association studies using unrelated individuals may be subject to bias caused by population stratification, alternative methods that are robust to population stratification such as family-based association designs may be less powerful. Recently, various statistical methods robust to population stratification were proposed for association studies, using unrelated individuals to identify associations between candidate markers and traits of interest (both qualitative and quantitative). Here, we propose a semiparametric test for association (SPTA). SPTA controls for population stratification through a set of genomic markers by first deriving a genetic background variable for each sampled individual through his/her genotypes at a series of independent markers, and then modeling the relationship between trait values, genotypic scores at the candidate marker, and genetic background variables through a semiparametric model. We assume that the exact form of relationship between the trait value and the genetic background variable is unknown and estimated through smoothing techniques. We evaluate the performance of SPTA through simulations both with discrete subpopulation models and with continuous admixture population models. The simulation results suggest that our procedure has a correct type I error rate in the presence of population stratification and is more powerful than statistical association tests for family-based association designs in all the cases considered. Moreover, SPTA is more powerful than the Quantitative Similarity-Based Association Test (QSAT) developed by us under continuous admixture populations, and the number of independent markers needed by SPTA to control for population stratification is substantially fewer than that required by QSAT.