For the survival of cancer and many other complex diseases, gene–environment (G-E) interactions have been established as having essential importance. G-E interaction analysis can be roughly classified as marginal and joint, depending on the number of G variables analyzed at a time. In this study, we focus on joint analysis, which can better reflect disease biology and is statistically more challenging. Many approaches have been developed for joint G-E interaction analysis for survival outcomes and led to important findings. However, without rigorous statistical development, quite a few methods have a weak theoretical ground. To fill this knowledge gap, in this article, we consider joint G-E interaction analysis under the Cox model. Sparse group penalization is adopted for regularizing estimation and selecting important main effects and interactions. The “main effects, interactions” variable selection hierarchy, which has been strongly advocated in recent literature, is satisfied. Significantly advancing from some published studies, we rigorously establish the consistency properties under high dimensionality. An effective computational algorithm is developed, simulation demonstrates competitive performance of the proposed approach, and analysis of The Cancer Genome Atlas (TCGA) data on stomach adenocarcinoma (STAD) further demonstrates its practical utility.

对于癌症和许多其他复杂疾病的生存，基因-环境 (GE) 相互作用已被确定为具有至关重要的意义。根据一次分析的 G 变量的数量，GE 相互作用分析大致可分为边际和联合。在这项研究中，我们专注于联合分析，它可以更好地反映疾病生物学，并且在统计学上更具挑战性。许多方法已被开发用于联合 GE 相互作用分析以获取生存结果，并产生了重要的发现。然而，如果没有严格的统计发展，很多方法的理论基础都很薄弱。为了填补这一知识空白，在本文中，我们考虑了 Cox 模型下的联合 GE 相互作用分析。采用稀疏组惩罚来正则化估计并选择重要的主效应和交互作用。近期文献中大力提倡的“主效应、交互作用”变量选择层次得到满足。从一些已发表的研究中显着进步，我们严格地建立了高维下的一致性属性。开发了一种有效的计算算法，模拟证明了所提出方法的竞争性能，并且对胃腺癌 (STAD) 的癌症基因组图谱 (TCGA) 数据的分析进一步证明了其实用性。我们严格地建立了高维下的一致性属性。开发了一种有效的计算算法，模拟证明了所提出方法的竞争性能，并且对胃腺癌 (STAD) 的癌症基因组图谱 (TCGA) 数据的分析进一步证明了其实用性。我们严格地建立了高维下的一致性属性。开发了一种有效的计算算法，模拟证明了所提出方法的竞争性能，并且对胃腺癌 (STAD) 的癌症基因组图谱 (TCGA) 数据的分析进一步证明了其实用性。