Variable selection in proportional hazards model with left-truncated survival data: a penalized composite likelihood approach

Variable selection is a fundamental tool to identify important factors from a large number of candidate covariates and has been successfully adopted in various fields. In survival analysis, developing variable selection techniques is often intractable since the failure times of interest are accompanied by censoring and other complex features, such as left truncation. Despite enormous variable selection methods for right-censored data, they seldom accommodate left truncation. In this work, for the left-truncated and right-censored data, we present a penalized composite likelihood approach to achieve variable selection and parameter estimation simultaneously in the proportional hazards model. To be specific, the composite likelihood is essentially a combination of the conditional likelihood and the pairwise likelihood that can properly take into account the marginal distribution of the observed truncation times. An explicit solution of the baseline hazard function is obtained through solving a series of self-consistent estimating equations. The sparse estimators of regression parameters under various classical penalty functions are calculated with a unified shooting algorithm. Simulation results indicate that the proposed method performs reasonably well and has some desirable advantages over the penalized conditional likelihood approach and the approach that ignores the presence of left truncation. An application to a set of left-truncated breast cancer data is also provided.