Rare variants are believed to play an important role in disease etiology. Recent advances in high-throughput sequencing technology enable investigators to systematically characterize the genetic effects of both common and rare variants. We introduce several approaches that simultaneously test the effects of common and rare variants within a single-nucleotide polymorphism (SNP) set based on logistic regression models and logistic kernel machine models. Gene-environment interactions and SNP-SNP interactions are also considered in some of these models. We illustrate the performance of these methods using the unrelated individuals data from Genetic Analysis Workshop 17. Three true disease genes (FLT1, PIK3C3, and KDR) were consistently selected using the proposed methods. In addition, compared to logistic regression models, the logistic kernel machine models were more powerful, presumably because they reduced the effective number of parameters through regularization. Our results also suggest that a screening step is effective in decreasing the number of false-positive findings, which is often a big concern for association studies.

In this paper, we propose a computationally efficient approach —space(Sparse PArtial Correlation Estimation)— for selecting non-zero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both non-zero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer data set and identify a set of hub genes which may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.

While high-throughput genotyping technologies are becoming readily available, the merit of using these technologies to perform genome-wide association studies has not been established. One major concern is that for studies of complex diseases and traits, the whole-genome approach requires such large sample sizes that both recruitment and genotyping pose considerable challenge. Here we propose a novel statistical method that boosts the effective sample size by combining data obtained from several studies. Specifically, we consider a situation in which various studies have genotyped non-overlapping subjects at largely non-overlapping sets of markers. Our approach, which exploits the local linkage disequilibrium structure without assuming an explicit population model, opens up the possibility of improving statistical power by incorporating existing data into future association studies.

In the fast-developing field of expression quantitative traits loci (eQTL) studies, much interest has been concentrated on detecting genomic regions containing transcriptional regulators that influence multiple expression phenotypes (trans-hubs). In this paper, we develop statistical methods for eQTL mapping and propose a new procedure for investigating candidate trans-hubs. We use data from the Genetic Analysis Workshop 15 to illustrate our methods. After correlations among expressions were accounted for, the previously detected trans-hubs are no longer significant. Our results suggest that conclusions regarding regulation hot spots should be treated with great caution.