Multiply-robust estimator of cumulative incidence function difference for right-censored competing risks data

BACKGROUND: In causal inference, estimating the average treatment effects (ATE) for competing risk outcomes requires robust adjustment for confounding and specialized methods to handle competing events. Although doubly robust estimators offer protection against single-model misspecification, they become inconsistent if both the propensity score and outcome regression models are misspecified. To enhance reliability in observational studies, there is a critical need for methods that accommodate multiple candidate models, providing stronger protection against model misspecification in complex competing risks settings. METHODS: We propose a new multiply robust (MR) estimator for the difference in cause-specific cumulative incidence function (CIF) with right-censored competing risks data to estimate ATE in competing risks data. The proposed framework integrates the pseudo-value approach, which transforms the censored, time-dependent CIF into a complete-data outcome, with the multiply robust estimation framework. This framework not only avoids reliance on the proportional hazards assumption and effectively addresses right censoring, but also enhances the robustness of the estimation. By specifying multiple candidate models for both the propensity score and the outcome regression, the resulting estimator is consistent and asymptotically unbiased, provided that at least one of the multiple propensity score or outcome regression models is correctly specified. RESULTS: Monte Carlo simulations demonstrated that the proposed MR estimator maintains negligible bias and near-nominal 95% coverage probabilities, provided at least one candidate model is correctly specified. This robust performance was consistent across all investigated censoring rates. Notably, combinations featuring heterogeneous misspecifications exhibited superior performance compared to those with homogeneous error. Application to the Right Heart Catheterization dataset yielded treatment effect estimates consistent with existing literature, confirming the practical utility and reliability of the method in real-world observational studies. CONCLUSIONS: The multiply robust framework ensures superior robustness and consistency for estimating cause-specific CIFs, even under high censoring. This methodology offers a more resilient alternative to traditional estimators, providing researchers with a dependable solution for treatment effect estimation in the presence of competing events and complex confounding.