Data irregularity in cancer genomics studies has been widely observed in the form of outliers and heavy-tailed distributions in the complex traits. In the past decade, robust variable selection methods have emerged as powerful alternatives to the non-robust ones to identify important genes associated with heterogeneous disease traits and build superior predictive models. In this study, to keep the remarkable features of the quantile LASSO and fully Bayesian regularized quantile regression while overcoming their disadvantage in the analysis of high-dimensional genomics data, we propose the spike-and-slab quantile LASSO through a fully Bayesian spike-and-slab formulation under the robust likelihood by adopting the asymmetric Laplace distribution (ALD). The proposed robust method has inherited the prominent properties of selective shrinkage and self-adaptivity to the sparsity pattern from the spike-and-slab LASSO (Ro\v{c}kov\'a and George, 2018). Furthermore, the spike-and-slab quantile LASSO has a computational advantage to locate the posterior modes via soft-thresholding rule guided Expectation-Maximization (EM) steps in the coordinate descent framework, a phenomenon rarely observed for robust regularization with non-differentiable loss functions. We have conducted comprehensive simulation studies with a variety of heavy-tailed errors in both homogeneous and heterogeneous model settings to demonstrate the superiority of the spike-and-slab quantile LASSO over its competing methods. The advantage of the proposed method has been further demonstrated in case studies of the lung adenocarcinomas (LUAD) and skin cutaneous melanoma (SKCM) data from The Cancer Genome Atlas (TCGA).

翻译：癌症基因组学研究中的数据不规则性广泛表现为复杂性状中的异常值与重尾分布。过去十年中，稳健变量选择方法已成为识别与异质性疾病性状相关的重要基因并构建优越预测模型的强有力替代方案，弥补了非稳健方法的不足。为在保留分位数LASSO和完全贝叶斯正则化分位数回归显著特性的同时克服其在高维基因组数据分析中的局限性，本研究通过采用非对称拉普拉斯分布（ALD）的稳健似然函数，基于完全贝叶斯尖峰-板岩框架提出了尖峰-板岩分位数LASSO。所提出的稳健方法继承了尖峰-板岩LASSO的选择性收缩特性以及对稀疏模式的自适应性优势（Ročková和George，2018）。此外，尖峰-板岩分位数LASSO具有计算优势，可通过坐标下降框架中基于软阈值规则的期望最大化（EM）步骤定位后验众数，这一现象在采用不可微损失函数的稳健正则化方法中鲜有出现。我们在同质与异质性模型设置下进行了包含多种重尾误差的综合性模拟研究，验证了尖峰-板岩分位数LASSO相较于竞争方法的优越性。通过癌症基因组图谱（TCGA）中肺腺癌（LUAD）和皮肤黑色素瘤（SKCM）数据的案例研究，进一步证明了该方法的优势。