Flexible copula-based variable selection for interval-censored semi-competing risks data: application to aging research.

Semi-competing risks data, where a non-terminal event (e.g., disability) may be censored by a terminal event (e.g., death), are common in aging research. These data pose unique analytical challenges when the non-terminal event is interval-censored, and a large number of covariates have distinct effects on each outcome. Existing variable selection methods typically focus on right-censored data and often rely on computationally intensive tuning procedures, limiting their utility in aging studies. We propose a flexible and computationally efficient copula-based variable selection framework for interval-censored semi-competing risks data. The method incorporates three key components: (1) a two-parameter copula that flexibly captures both upper and lower tail dependence between non-terminal and terminal events; (2) semiparametric transformation models for the marginal distributions, accommodating common specifications such as proportional hazards and proportional odds; and (3) a tuning-free variable selection procedure based on minimizing an approximated information criterion. To enable high-dimensional estimation, we develop a new coordinate-wise optimization procedure combined with sieve estimation, which decomposes the high-dimensional problem into low-dimensional subproblems. The asymptotic properties of the proposed estimators are also established. Simulation studies demonstrate that the proposed method achieves accurate variable selection with substantial computational gains. Applied to the Chinese Longitudinal Healthy Longevity and Happy Family Study, it identifies key comorbidities and lifestyle factors associated with disability and mortality, offering novel insights into aging trajectories. The framework provides an interpretable and scalable tool for aging research involving chronic functional decline and intermittent follow-up.