We study causal inference and efficient estimation for the expected number of recurrent events in the presence of a terminal event. We define our estimand as the vector comprising both the expected number of recurrent events and the failure survival function evaluated along a sequence of landmark times. We identify the estimand in the presence of right-censoring and causal selection as an observed data functional under coarsening at random, derive the nonparametric efficiency bound, and propose a multiply-robust estimator that achieves the bound and permits nonparametric estimation of nuisance parameters. Throughout, no absolute continuity assumption is made on the underlying probability distributions of failure, censoring, or the observed data. Additionally, we derive the class of influence functions when the coarsening distribution is known and review how published estimators may belong to the class. Along the way, we highlight some interesting inconsistencies in the causal lifetime analysis literature.

翻译：我们研究在存在终止事件时，复发事件期望数的因果推断与高效估计。将目标参数定义为沿一系列标志时间点评估的复发事件期望数与失效生存函数构成的向量。在右删失和因果选择存在的情况下，我们证明该参数在随机粗化假设下可被识别为观测数据泛函，推导出非参数效率界，并提出一种达到该界且允许对 nuisance 参数进行非参数估计的多重稳健估计量。整个过程中，不对失效、删失或观测数据的潜在概率分布作绝对连续性假设。此外，我们推导了当粗化分布已知时影响函数的类别，并评述了已发表估计量可能属于该类别的方式。在此过程中，我们强调了因果生存分析文献中一些有趣的不一致性。