Prediction errors for state occupation and transition probabilities in multi-state models

In this paper, we consider the estimation of prediction errors for state occupation probabilities and transition probabilities for multistate time-to-event data. We study prediction errors based on the Brier score and on the Kullback-Leibler score and prove their properness. In the presence of right-censored data, two classes of estimators, based on inverse probability weighting and pseudo-values, respectively, are proposed, and consistency properties of the proposed estimators are investigated. The second part of the paper is devoted to the estimation of dynamic prediction errors for state occupation probabilities for multistate models, conditional on being alive, and for transition probabilities. Cross-validated versions are proposed. Our methods are illustrated on the CSL1 randomized clinical trial comparing prednisone versus placebo for liver cirrhosis patients.