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.

翻译：在复发事件情境下，我们提出一种新型评分指标，用于评估模型对复发事件期望累积数的预测能力。该评分通过纳入患者的外部协变量来考量个体历史信息，可视为针对单终点事件时间的Brier评分在复发事件场景的拓展，且适用于伴或不伴终止事件的复发事件分析。理论研究表明，在复发事件分析的标准假设下，该评分可渐近分解为模型与真实期望累积数之间的理论均方误差项，以及一个与模型无关的不可分离项。通过模拟研究进一步验证了这一分解性质。此外，该评分需与不包含协变量的非参数估计等零模型进行对比使用。最终，我们利用该评分对房颤患者数据集进行住院预测，并比较了Cox模型与Aalen模型等不同模型的预测性能。