Overcoming Dependent Censoring in the Evaluation of Survival Models

Christian Marius Lillelund, Shi-ang Qi, Russell Greiner
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:3841-3866, 2026.

Abstract

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

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-lillelund26a, title = {Overcoming Dependent Censoring in the Evaluation of Survival Models}, author = {Lillelund, Christian Marius and Qi, Shi-ang and Greiner, Russell}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {3841--3866}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/lillelund26a/lillelund26a.pdf}, url = {https://proceedings.mlr.press/v337/lillelund26a.html}, abstract = {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} }
Endnote
%0 Conference Paper %T Overcoming Dependent Censoring in the Evaluation of Survival Models %A Christian Marius Lillelund %A Shi-ang Qi %A Russell Greiner %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-lillelund26a %I PMLR %P 3841--3866 %U https://proceedings.mlr.press/v337/lillelund26a.html %V 337 %X 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
APA
Lillelund, C.M., Qi, S. & Greiner, R.. (2026). Overcoming Dependent Censoring in the Evaluation of Survival Models. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:3841-3866 Available from https://proceedings.mlr.press/v337/lillelund26a.html.

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