Treatment Effect Estimation with Censored Outcome and Covariate Selection

Covariates selection is essential when faced with many variables in modern causal inference in a data-rich environment. Particularly, the efficiency of the average causal effect (ACE) can be improved by including covariates only related to the outcome and reduced by including covariates related to the treatment but not the outcome in the propensity score (PS) model. In this paper, we estimate the causal effect in the presence of censored outcome and high-dimensional covariates. To improve the efficiency of the estimation of ACE, we propose the censored outcome adaptive Lasso (COAL) to select covariates, where the weighted least square method is applied to account for censoring. Based on the covariate selection, we propose a double inverse propensity weighted estimator for ACE. Furthermore, we establish the oracle properties of the variable selection and derive the asymptotic properties of the proposed estimator