Hierarchical False Discovery Rate Control for High-dimensional Survival Analysis with Interactions.

With the development of data collection techniques, analysis with a survival response and high-dimensional covariates has become routine. Here we consider an interaction model, which includes a set of low-dimensional covariates, a set of high-dimensional covariates, and their interactions. This model has been motivated by gene-environment (G-E) interaction analysis, where the E variables have a low dimension, and the G variables have a high dimension. For such a model, there has been extensive research on estimation and variable selection. Comparatively, inference studies with a valid false discovery rate (FDR) control have been very limited. The existing high-dimensional inference tools cannot be directly applied to interaction models, as interactions and main effects are not "equal". In this article, for high-dimensional survival analysis with interactions, we model survival using the Accelerated Failure Time (AFT) model and adopt a "weighted least squares + debiased Lasso" approach for estimation and selection. A hierarchical FDR control approach is developed for inference and respect of the "main effects, interactions" hierarchy. The asymptotic distribution properties of the debiased Lasso estimators are rigorously established. Simulation demonstrates the satisfactory performance of the proposed approach, and the analysis of a breast cancer dataset further establishes its practical utility.