Penalized variable selection with broken adaptive ridge regression for semi-competing risks data

Semi-competing risks data arise when both non-terminal and terminal events are considered in an illness-death model. Such data with multiple events of interest are frequently encountered in medical research and clinical trials. Unlike some recent works on penalised variable selection that deal with the competing risks separately without incorporating possible correlation between them, we perform variable selection in the illness-death model using shared frailty. We propose a broken adaptive ridge (BAR) penalty to encourage sparsity and perform variable selection in an event-specific manner so that the potential risk factors can be selected and their effects can be estimated simultaneously, corresponding to each event in the study. The oracle property of the proposed BAR procedure is established, and its performance is evaluated and compared with other commonly used methods by simulation studies. The proposed method is then applied to the real-life data arising from a colon cancer study.