  In a recurrent events 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 allows to take into account the individual history
of a patient through its external covariates and 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 null 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 predictions
performance of different models, such as the Cox model or the Aalen Model, is
investigated.
