Multiple phenotype association tests based on sliced inverse regression.

BACKGROUND: Joint analysis of multiple phenotypes in studies of biological systems such as Genome-Wide Association Studies is critical to revealing the functional interactions between various traits and genetic variants, but growth of data in dimensionality has become a very challenging problem in the widespread use of joint analysis. To handle the excessiveness of variables, we consider the sliced inverse regression (SIR) method. Specifically, we propose a novel SIR-based association test that is robust and powerful in testing the association between multiple predictors and multiple outcomes. RESULTS: We conduct simulation studies in both low- and high-dimensional settings with various numbers of Single-Nucleotide Polymorphisms and consider the correlation structure of traits. Simulation results show that the proposed method outperforms the existing methods. We also successfully apply our method to the genetic association study of ADNI dataset. Both the simulation studies and real data analysis show that the SIR-based association test is valid and achieves a higher efficiency compared with its competitors. CONCLUSION: Several scenarios with low- and high-dimensional responses and genotypes are considered in this paper. Our SIR-based method controls the estimated type I error at the pre-specified level α .

Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors.

The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We use the framework of the alternating direction method of multipliers to design an efficient minimization algorithm for the proposed model. Since the objective function is the sum of the non-quadratic log-likelihood and nonconvex nondifferentiable regularizer, we propose to solve the intractable subproblems by the majorization-minimization (MM) method and the iteratively reweighted least squares (IRLS) algorithm, respectively. Numerical experiments show the efficiency of the proposed method for Poissonian image restoration including denoising and deblurring.

A novel association test for rare variants based on algebraic statistics.

With the rapid growth of next-generation sequencing technology, more and more rare variants are available in the human genome. In recent years, the point of study has already changed direction to rare variants in genome-wide association studies (GWAS). Although a variety of approaches have been proposed to test associations between rare variants and phenotypes of interest, it is far from the end of this problem, and it is worth exploring new statistical methods based on special features of rare variants. As we all know, the most direct way is to evaluate the association in a two-way contingency table if the phenotype is a discrete variable. The numbers of observations are very close or equal to 0s for most of cells in the contingency table due to the extremely low mutation rates of rare variants. In this paper, we propose a novel association test for rare variants based on a generalization of Fisher's exact test, and the p-value of this exact test can be computed under the multivariate hypergeometric distribution in the framework of algebraic statistics. Simulation results show that our proposed method outperforms the existing methods, despite there is heterogeneity among causal variants. We also successfully apply our method into the genetic association study of coronary artery disease and hypertension from the Wellcome Trust Case Control Consortium.