The Brier Score under Administrative Censoring: Problems and a Solution
Håvard Kvamme, Ørnulf Borgan; 24(2):1−26, 2023.
Abstract
The Brier score is commonly utilized to evaluate probability predictions. In survival analysis, when there are right-censored observations of event times, this score can be weighted by the inverse probability of censoring (IPCW) in order to maintain its original interpretation. It is a common practice to estimate the censoring distribution using the Kaplan-Meier estimator, despite assuming that the censoring distribution is independent of the covariates. This paper examines the problems that may arise for the IPCW weighting scheme when the covariates used in the prediction model contain information about the censoring times. This issue may particularly occur for administratively censored data if the distribution of the covariates varies with calendar time. For administratively censored data, we propose an alternative version of the Brier score. This administrative Brier score does not necessitate estimation of the censoring distribution and remains valid even when the censoring times can be predicted from the covariates.
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