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 a model. Such data with multiple events of interest are frequently encountered in medical research and clinical trials. In this framework, terminal event can censor the non-terminal event but not vice versa. It is known that variable selection is practical in identifying significant risk factors in high-dimensional data. While some recent works on penalized variable selection deal with these competing risks separately without incorporating possible correlation between them, we perform variable selection in an illness-death model using shared frailty where semiparametric hazard regression models are used to model the effect of covariates. We propose a broken adaptive ridge (BAR) penalty to encourage sparsity and conduct extensive simulation studies to compare its performance with other popular methods. We perform variable selection in an event specific manner so that the potential risk factors and covariates effects can be estimated and selected, simultaneously corresponding to each event in the study. The grouping effect, as well as the oracle property of the proposed BAR procedure are investigated using simulation studies. The proposed method is then applied to real-life data arising from a Colon Cancer study.