Penalized regression approaches to testing for quantitative trait-rare variant association

In statistical data analysis, penalized regression is considered an attractive approach for its ability of simultaneous variable selection and parameter estimation. Although penalized regression methods have shown many advantages in variable selection and outcome prediction over other approaches for high-dimensional data, there is a relative paucity of the literature on their applications to hypothesis testing, e.g., in genetic association analysis. In this study, we apply several new penalized regression methods with a novel penalty, called Truncated L1 -penalty (TLP) (Shen et al., 2012), for either variable selection, or both variable selection and parameter grouping, in a data-adaptive way to test for association between a quantitative trait and a group of rare variants. The performance of the new methods are compared with some existing tests, including some recently proposed global tests and penalized regression-based methods, via simulations and an application to the real sequence data of the Genetic Analysis Workshop 17 (GAW17). Although our proposed penalized methods can improve over some existing penalized methods, often they do not outperform some existing global association tests. Some possible problems with utilizing penalized regression methods in genetic hypothesis testing are discussed. Given the capability of penalized regression in selecting causal variants and its sometimes promising performance, further studies are warranted.