Doubly robust estimation of the hazard difference for competing risks data

We consider the conditional treatment effect for competing risks data in observational studies. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to (1) the assumed propensity score for treatment and the censoring model, and (2) the outcome models for the competing risks. An important property regarding the estimators is rate double robustness, in addition to the classical model double robustness. Rate double robustness enables the use of machine learning and nonparametric methods in order to estimate the nuisance parameters, while preserving the root- $$ asymptotic normality of the estimated treatment effect for inferential purposes. We study the performance of the estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life drinking behavior on late life cognitive outcomes. The approaches developed in this article are implemented in the R package "HazardDiff".