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In a recurrent events setting, we introduce a new score designed to evaluatethe prediction ability, for a given model, of the expected cumulative number ofrecurrent events. This score allows to take into account the individual historyof a patient through its external covariates and can be seen as an extension ofthe Brier Score for single time to event data but works for recurrent eventswith or without a terminal event. Theoretical results are provided that showthat under standard assumptions in a recurrent event context, our score can beasymptotically decomposed as the sum of the theoretical mean squared errorbetween the model and the true expected cumulative number of recurrent eventsand an inseparability term that does not depend on the model. Thisdecomposition is further illustrated on simulations studies. It is also shownthat this score should be used in comparison with a null model, such as anonparametric estimator that does not include the covariates. Finally, thescore is applied for the prediction of hospitalisations on a dataset ofpatients suffering from atrial fibrillation and a comparison of the predictionsperformance of different models, such as the Cox model or the Aalen Model, isinvestigated.

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