Doubly robust estimator of risk in the presence of censoring dependent on time-varying covariates: application to a primary prevention trial for coronary events with pravastatin

Abstract

Abstract Background In the presence of dependent censoring even after stratification of baseline covariates, the Kaplan–Meier estimator provides an inconsistent estimate of risk. To account for dependent censoring, time-varying covariates can be used along with two statistical methods: the inverse probability of censoring weighted (IPCW) Kaplan–Meier estimator and the parametric g-formula estimator. The consistency of the IPCW Kaplan–Meier estimator depends on the correctness of the model specification of censoring hazard, whereas that of the parametric g-formula estimator depends on the correctness of the models for event hazard and time-varying covariates. Methods We combined the IPCW Kaplan–Meier estimator and the parametric g-formula estimator into a doubly robust estimator that can adjust for dependent censoring. The estimator is theoretically more robust to model misspecification than the IPCW Kaplan–Meier estimator and the parametric g-formula estimator. We conducted simulation studies with a time-varying covariate that affected both time-to-event and censoring under correct and incorrect models for censoring, event, and time-varying covariates. We applied our proposed estimator to a large clinical trial data with censoring before the end of follow-up. Results Simulation studies demonstrated that our proposed estimator is doubly robust, namely it is consistent if either the model for the IPCW Kaplan–Meier estimator or the models for the parametric g-formula estimator, but not necessarily both, is correctly specified. Simulation studies and data application demonstrated that our estimator can be more efficient than the IPCW Kaplan–Meier estimator. Conclusions The proposed estimator is useful for estimation of risk if censoring is affected by time-varying risk factors.

Keywords

• Double robustness
• Dependent censoring
• Prediction
• Time-varying covariate