Doubly Robust Estimation of the Hazard Difference for Competing Risks Data

TL;DR

This paper develops doubly robust estimators for the treatment effect on hazard differences in competing risks data, allowing flexible modeling with machine learning while ensuring valid inference.

Contribution

It introduces rate double robustness for hazard difference estimation, combining semiparametric theory with machine learning for improved causal inference.

Findings

Estimators exhibit root-n asymptotic normality with machine learning.

Simulation studies demonstrate estimator performance.

Application to cohort data reveals insights on drinking behavior and cognitive outcomes.

Abstract

We consider the conditional treatment effect for competing risks data in observational studies. While it is described as a constant difference between the hazard functions given the covariates, we do not assume specific functional forms for the covariates. 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 asymptotic result 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-$n$ asymptotic normality of the estimators 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.