Partial Identification of Survival Prediction Performance under Dependent Right Censoring

Survival prediction models are usually evaluated under right censoring by inverse probability of censoring weighting (IPCW), which assumes independent censoring, an assumption that cannot generally be verified from right-censored data. Leaving the dependence between event and censoring times unrestricted, we derive sharp bounds on the integrated Brier score (IBS) of a fixed model and on IBS differences between models by partial identification. The bounds use the fact that each individual’s event time is shared across evaluation times and models, and for more than two models we also derive the sharp upper bound on the difference from the best competitor. A negative upper bound on a difference shows that one model has a smaller IBS than the other under every full-data distribution compatible with the observed data. For a fixed observed-data distribution, we develop estimators, confidence regions, a test of robust strict dominance, and an intersection–union test. In simulations, the confidence regions and pairwise tests performed close to their nominal levels. In three applications, the tests supported the IPCW ranking only for mortgage prepayment data with little censoring, whereas for the other two data sets the observed data alone did not support it.