Nonparametric Estimation of the Patient-Weighted While-Alive Estimand

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, Statistics in Biopharmaceutical Research 15, no. 2: 238-248). In this study, we focus 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. Specifically, we derive the corresponding efficient influence function and develop a one-step estimator initially applied to the simpler irreversible illness-death model. For the broader context of recurrent events, due to the increased complexity, this one-step estimator is practically intractable due to likely misspecification of the needed conditional transition intensities that depend on a patient's unique history. Therefore, we suggest an alternative estimator that is expected to have high efficiency, focusing on the randomized treatment setting. In addition, we apply our proposed estimator to two real-world case studies, demonstrating the practical applicability of this second estimator and benefits of this while-alive approach over currently available alternatives.