Quantile regression models have become a widely used statistical tool in genetics and in the omics fields because they can provide a rich description of the predictors’ effects on an outcome without imposing stringent parametric assumptions on the outcome-predictors relationship. This work considers the problem of selecting grouped variables in high-dimensional linear quantile regression models. We introduce a group penalized pseudo quantile regression (GPQR) framework with both group-lasso and group non-convex penalties. We approximate the quantile regression check function using a pseudo-quantile check function. Then, using the majorization–minimization principle, we derive a simple and computationally efficient group-wise descent algorithm to solve group penalized quantile regression. We establish the convergence rate property of our algorithm with the group-Lasso penalty and illustrate the GPQR approach performance using simulations in high-dimensional settings. Furthermore, we demonstrate the use of the GPQR method in a gene-based association analysis of data from the Alzheimer’s Disease Neuroimaging Initiative study and in an epigenetic analysis of DNA methylation data.

分位数回归模型已成为遗传学和组学领域广泛使用的统计工具，因为它们可以提供预测因子对结果的影响的丰富描述，而无需对结果-预测因子关系强加严格的参数假设。这项工作考虑了在高维线性分位数回归模型中选择分组变量的问题。我们引入了具有组套索和组非凸惩罚的组惩罚伪分位数回归 (GPQR) 框架。我们使用伪分位数检查函数来近似分位数回归检查函数。然后，使用主化-最小化原理，我们推导出一种简单且计算效率高的分组下降算法来解决分组惩罚分位数回归问题。我们使用 group-Lasso 惩罚建立了我们算法的收敛速度特性，并使用高维设置中的模拟来说明 GPQR 方法的性能。此外，我们展示了 GPQR 方法在阿尔茨海默病神经成像计划研究数据的基于基因的关联分析和 DNA 甲基化数据的表观遗传分析中的使用。