Adaptive ridge regression for rare variant detection

Longitudinal data analysis for rare variants detection with penalized quadratic inference function

Longitudinal genetic data provide more information regarding genetic effects over time compared with cross-sectional data. Coupled with next-generation sequencing technologies, it becomes reality to identify important genes containing both rare and common variants in a longitudinal design. In this work, we adopted a weighted sum statistic (WSS) to collapse multiple variants in a gene region to form a gene score. When multiple genes in a pathway were considered together, a penalized longitudinal model under the quadratic inference function (QIF) framework was applied for efficient gene selection. We evaluated the estimation accuracy and model selection performance under different model settings, then applied the method to a real dataset from the Genetic Analysis Workshop 18 (GAW18). Compared with the unpenalized QIF method, the penalized QIF (pQIF) method achieved better estimation accuracy and higher selection efficiency. The pQIF remained optimal even when the working correlation structure was mis-specified. The real data analysis identified one important gene, angiotensin II receptor type 1 (AGTR1), in the Ca2+/AT-IIR/α-AR signaling pathway. The estimated effect implied that AGTR1 may have a protective effect for hypertension. Our pQIF method provides a general tool for longitudinal sequencing studies involving large numbers of genetic variants.

An Adaptive Ridge Procedure for L0 Regularization

Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional data is difficult due to the non-convex optimization problem induced by L0 penalties. In this paper we introduce an adaptive ridge procedure (AR), where iteratively weighted ridge problems are solved whose weights are updated in such a way that the procedure converges towards selection with L0 penalties. After introducing AR its specific shrinkage properties are studied in the particular case of orthogonal linear regression. Based on extensive simulations for the non-orthogonal case as well as for Poisson regression the performance of AR is studied and compared with SCAD and adaptive LASSO. Furthermore an efficient implementation of AR in the context of least-squares segmentation is presented. The paper ends with an illustrative example of applying AR to analyze GWAS data.

Comparison of significant single nucleotide polymorphisms selections in GWAS for complex traits

The goal of this study was to compare significant SNP selection approaches in the context of complex traits based on SNP estimates obtained by models: a model fitting a single SNP (M1), a model fitting a single SNP and a random polygenic effect (M2), the nonparametric CAR score (M3), a SNP-BLUP model with random effects of all SNPs fitted simultaneously (M4). There were 46,267 SNPs tested in a population of 2601 Holstein Friesian bulls, four traits (milk and fat yields, somatic cell score, non-return rate for heifers) were considered. The numbers of SNPs selected as significant differed among models. M1 selected a very large number of SNPs, except for a NRH in which no SNPs were significant. M2 and M3 both selected similar and low number of SNPs for each trait. M4 selected more SNPs than M2 and M3. Considering linkage disequilibrium between SNPs, for MY M2 and M3 selected SNPs more highly correlated with each other than in the case of M4, while for FY M3 selection contained more correlated SNPs than M2 and M4. In conclusion, if the research interest is to identify SNPs not only with strong, but also with moderate effects on a complex trait a multiple-SNP model is recommended. Such models are capable of accounting for at least a part of linkage disequilibrium between SNPs through the design matrix of SNP effects. Functional annotation of SNPs significant in M4 reveals good correspondence between selected polymorphisms and functional information as well as with QTL mapping results.

Likelihood ratio tests in rare variant detection for continuous phenotypes

It is believed that rare variants play an important role in human phenotypes; however, the detection of rare variants is extremely challenging due to their very low minor allele frequency. In this paper, the likelihood ratio test (LRT) and restricted likelihood ratio test (ReLRT) are proposed to test the association of rare variants based on the linear mixed effects model, where a group of rare variants are treated as random effects. Like the sequence kernel association test (SKAT), a state-of-the-art method for rare variant detection, LRT and ReLRT can effectively overcome the problem of directionality of effect inherent in the burden test in practice. By taking full advantage of the spectral decomposition, exact finite sample null distributions for LRT and ReLRT are obtained by simulation. We perform extensive numerical studies to evaluate the performance of LRT and ReLRT, and compare to the burden test, SKAT and SKAT-O. The simulations have shown that LRT and ReLRT can correctly control the type I error, and the controls are robust to the weights chosen and the number of rare variants under study. LRT and ReLRT behave similarly to the burden test when all the causal rare variants share the same direction of effect, and outperform SKAT across various situations. When both positive and negative effects exist, LRT and ReLRT suffer from few power reductions compared to the other two competing methods; under this case, an additional finding from our simulations is that SKAT-O is no longer the optimal test, and its power is even lower than that of SKAT. The exome sequencing SNP data from Genetic Analysis Workshop 17 were employed to illustrate the proposed methods, and interesting results are described.

Rare variants detection with kernel machine learning based on likelihood ratio test

This paper mainly utilizes likelihood-based tests to detect rare variants associated with a continuous phenotype under the framework of kernel machine learning. Both the likelihood ratio test (LRT) and the restricted likelihood ratio test (ReLRT) are investigated. The relationship between the kernel machine learning and the mixed effects model is discussed. By using the eigenvalue representation of LRT and ReLRT, their exact finite sample distributions are obtained in a simulation manner. Numerical studies are performed to evaluate the performance of the proposed approaches under the contexts of standard mixed effects model and kernel machine learning. The results have shown that the LRT and ReLRT can control the type I error correctly at the given α level. The LRT and ReLRT consistently outperform the SKAT, regardless of the sample size and the proportion of the negative causal rare variants, and suffer from fewer power reductions compared to the SKAT when both positive and negative effects of rare variants are present. The LRT and ReLRT performed under the context of kernel machine learning have slightly higher powers than those performed under the context of standard mixed effects model. We use the Genetic Analysis Workshop 17 exome sequencing SNP data as an illustrative example. Some interesting results are observed from the analysis. Finally, we give the discussion.