Overcoming Dependent Censoring in the Evaluation of Survival Models
Authors: Christian Marius Lillelund, Shi-ang Qi, Russell Greiner
Organizations: Department of Computing Science, University of Alberta, Edmonton, Canada · Department of Electrical and Computer Engineering, Aarhus University, Aarhus, Denmark · Alberta Machine Intelligence Institute, Edmonton, Canada · Vector Institute, Toronto, Canada
Dependent censoring occurs when the event time and censoring time are not conditionally independent given the observed covariates. This complicates survival model evaluation because widely used metrics, such as the Brier score, typically handle right-censoring using inverse probability of censoring weighting (IPCW). Unfortunately, IPCW is valid only when the estimated censoring distribution is independent of the event time. We propose a dependent Brier score based on an Archimedean copula and the Copula-Graphic estimator, and establish consistency and asymptotic normality of its margin-time estimator. To evaluate the metric, we introduce a semi-synthetic framework that creates realistic dependent censoring while preserving the original covariate structure and known event times. Across 12 datasets, the proposed metric reduces estimation error by 12-16% on average relative to IPCW. Source code is available at https://github.com/thecml/DependentEVAL.