A robust weighted Kaplan-Meier approach for data with dependent censoring using linear combinations of prognostic covariates

The weighted Kaplan-Meier (WKM) estimator is often used to incorporate prognostic covariates into survival analysis to improve efficiency and correct for potential bias. In this paper, we generalize the WKM estimator to handle a situation with multiple prognostic covariates and potential-dependent censoring through the use of prognostic covariates. We propose to combine multiple prognostic covariates into two risk scores derived from two working proportional hazards models. One model is for the event times. The other model is for the censoring times. These two risk scores are then categorized to define the risk groups needed for the WKM estimator. A method of defining categories based on principal components is proposed. We show that the WKM estimator is robust to misspecification of either one of the two working models. In simulation studies, we show that the robust WKM approach can reduce bias due to dependent censoring and improve efficiency. We apply the robust WKM approach to a prostate cancer data set.