In clinical trials with recurrent events, such as repeated hospitalizations terminating with death, it is important to consider the patient events overall history for a thorough assessment of treatment effects. The occurrence of fewer events due to early deaths can lead to misinterpretation, emphasizing the importance of a while-alive strategy as suggested in Schmidli et al. (2023). We focus in this paper on the patient weighted while-alive estimand represented as the expected number of events divided by the time alive within a target window and develop efficient estimation for this estimand. We derive its efficient influence function and develop a one-step estimator, initially applied to the irreversible illness-death model. For the broader context of recurrent events, due to the increased complexity, the one-step estimator is practically intractable. We therefore suggest an alternative estimator that is also expected to have high efficiency focusing on the randomized treatment setting. We compare the efficiency of these two estimators in the illness-death setting. Additionally, we apply our proposed estimator to a real-world case study involving metastatic colorectal cancer patients, demonstrating the practical applicability and benefits of the while-alive approach.

翻译：在涉及复发事件（如以死亡告终的反复住院）的临床试验中，全面评估治疗效果需考虑患者的整体事件史。因早期死亡导致事件数量减少可能引起误解，这凸显了Schmidli等人（2023）提出的存活期内策略的重要性。本文聚焦于患者加权存活期内估计量，其定义为目标时间窗内预期事件数与存活时间的比值，并针对该估计量开发了高效估计方法。我们推导了其有效影响函数，并构建了一步估计量，首先应用于不可逆的疾病-死亡模型。对于更广泛的复发事件场景，由于复杂性增加，一步估计量在实际中难以处理。因此，我们提出了一种替代估计量，该估计量在随机化治疗设定下同样预期具有高效率。我们在疾病-死亡设定中比较了这两种估计量的效率。此外，我们将所提出的估计量应用于一项涉及转移性结直肠癌患者的真实世界案例研究，展示了存活期内方法的实际适用性与优势。