Title: Reimaging Semi-competing Risks Data Analysis: Enhancing Variable Selection with Preliminary Sufficient Dimension Reduction

Abstract: We introduce a new framework for feature screening in the challenging context of ultrahigh dimensional semi-competing risks data. Specifically, our two-stage procedure initially employs a dual screening mechanism to select a coarse set of features that are potentially relevant to both terminal and nonterminal endpoints. This leads to the estimation of the augmented central subspace, pivotal for both endpoints and censoring, based on the selected features. In the second stage, refined sets of important features for the nonterminal and terminal events, respectively, are further identified using an inverse probability-of-censoring weighted filter, where the central subspace estimator is used to obtain the weights adjusting for censoring. The proposed framework is model-free and it does not require independent censoring. Asymptotic properties are established under minor assumptions. We demonstrate the promising performance of the proposed method through simulations and gene expression data analysis.