Identification of significant genetic variants via SLOPE, and its extension to Group SLOPE

The method of Sorted L-One Penalized Estimation, abbreviated as SLOPE, is a novel sparse regression method for model selection introduced in a sequence of recent papers, [4], [3] and [7] by Bogdan, van den Berg, Sabatti, Su and Candes. It estimates the coefficients of a linear model that possibly has more unknown parameters than observations. In many settings the SLOPE method is shown to successfully control the false discovery rate (the proportion of the irrelevant among all selected predictors) at a user specified level. In this paper we evaluate its performance on genetic data, and show its superiority over LASSO which is a related and popular method. Often in genetic data sets, group structures among the predictor variables are given as prior knowledge, such as SNPs in a gene or genes in a pathway. Following this motivation we extend SLOPE in the spirit of Group LASSO to Group SLOPE, a method that can handle group structures between the predictor variables, which are ubiquitous in real genetic data. Our simulation results show that the proposed Group SLOPE method is capable of controlling the false discovery rate at a specified level. Moreover, our simulations show that compared to Group LASSO, Group SLOPE in general achieves a higher power as well as a lower false discovery rate.