🤖 AI Summary
This paper addresses unbiased estimation of the marginal counterfactual cumulative incidence function (CIF) in observational studies under competing risks. We propose a modified Nelson–Aalen estimator based on inverse probability weighting (IPW), incorporating estimated propensity scores. Our key contribution is the first rigorous asymptotic theory for such an adjusted estimator within the competing risks framework: we explicitly characterize the additional variability induced by propensity score estimation and prove its asymptotically negligible impact on final inference. Leveraging counting process theory and influence function analysis, we derive influence functions for both the counterfactual cumulative hazard and the CIF, establishing consistency and asymptotic normality of the estimator. Simulation studies and real-data analyses demonstrate low bias, robust performance across scenarios, and accurate standard error estimation. The proposed method thus provides a theoretically sound and practically viable tool for causal inference in competing risks settings.
📝 Abstract
Inverse probability of treatment weighting (IPW) has been well applied in causal inference to estimate population-level estimands from observational studies. For time-to-event outcomes, the failure time distribution can be estimated by estimating the cumulative hazard in the presence of random right censoring. IPW can be performed by weighting the event counting process and at-risk process by the inverse treatment probability, resulting in an adjusted Nelson--Aalen estimator for the population-level counterfactual cumulative incidence function. We consider the adjusted Nelson--Aalen estimator with an estimated propensity score in the competing risks setting. When the estimated propensity score is regular and asymptotically linear, we derive the influence functions for the counterfactual cumulative hazard and cumulative incidence. Then we establish the asymptotic properties for the estimators. We show that the uncertainty in the estimated propensity score contributes to an additional variation in the estimators. However, through simulation and real-data application, we find that such an additional variation is usually small.