Assessing model prediction performance for the expected cumulative number of recurrent events

In a recurrent event setting, we introduce a new score designed to evaluate the prediction ability, for a given model, of the expected cumulative number of recurrent events. This score can be seen as an extension of the Brier Score for single time to event data but works for recurrent events with or without a terminal event. Theoretical results are provided that show that under standard assumptions in a recurrent event context, our score can be asymptotically decomposed as the sum of the theoretical mean squared error between the model and the true expected cumulative number of recurrent events and an inseparability term that does not depend on the model. This decomposition is further illustrated on simulations studies. It is also shown that this score should be used in comparison with a reference model, such as a nonparametric estimator that does not include the covariates. Finally, the score is applied for the prediction of hospitalisations on a dataset of patients suffering from atrial fibrillation and a comparison of the prediction performances of different models, such as the Cox model, the Aalen Model or the Ghosh and Lin model, is investigated.