Causal effect estimation for competing risk data in randomized trial: adjusting covariates to gain efficiency

The double-blinded randomized trial is considered the gold standard to estimate the average causal effect (ACE). The naive estimator without adjusting any covariate is consistent. However, incorporating the covariates that are strong predictors of the outcome could reduce the issue of unbalanced covariate distribution between the treated and controlled groups and can improve efficiency. Recent work has shown that thanks to randomization, for linear regression, an estimator under risk consistency (e.g. Random Forest) for the regression coefficients could maintain the convergence rate even when a nonparametric model is assumed for the effect of covariates. Also, such an adjusted estimator will always lead to efficiency gain compared to the naive unadjusted estimator. In this paper, we extend this result to the competing risk data setting and show that under similar assumptions, the augmented inverse probability censoring weighting (AIPCW) based adjusted estimator has the same convergence rate and efficiency gain. Extensive simulations were performed to show the efficiency gain in the finite sample setting. To illustrate our proposed method, we apply it to the Women's Health Initiative (WHI) dietary modification trial studying the effect of a low-fat diet on cardiovascular disease (CVD) related mortality among those who have prior CVD.