Variable selection in causal semiparametric transformation models with all-or-nothing treatment compliance

Assessing causal treatment effect on a time-to-event outcome and identifying important risk factors that contribute to the outcome of interest are crucial in many scientific studies. Although existing instrumental variable (IV) methods can address the endogenous treatment selection and yield an unbiased causal treatment effect estimate in the presence of censoring, the corresponding variable selection technique has not been investigated. In this paper, we propose a variable selection method for a wide class of causal semiparametric transformation models with all-or-nothing treatment compliance and right-censored data. Specifically, the minimum information criterion is embedded in the optimization step of the proposed expectation-maximization algorithm, rendering sparse estimators of the complier causal treatment effect and other regression parameters. The asymptotic properties of our method are established, including consistency and oracle property. Extensive simulation studies are conducted to evaluate the finite sample performance of the proposed method. An application to a colorectal cancer screening dataset is provided.