Properties of two while-alive estimands for recurrent events and their potential estimators

Chronic diseases are often characterized through the repeated occurrence of unfavorable events. In chronic heart failure, recurrent hospitalizations characterize disease burden but the risk of death is not negligible. This leads to two main challenges. First, the definition of a clinically interpretable treatment effect measure (estimand) needs careful attention. Second, finding suitable analysis methods (estimators) that target the estimand of interest is difficult. In this paper we study the two estimands using the while-alive strategy described by Schmidli et al. (2021). For realistic chronic heart failure populations based on joint frailty model assumptions, we calculate the estimand values analytically and discuss their clinical interpretability. We also show that Quasi-Poisson regression leads to an asymptotically unbiased estimator for the two estimands using the while-alive strategy, and that Lin-Wei-Yang-Ying is asymptotically unbiased under constant event rate conditional on being alive, by both analytic derivation and numerical simulations. We also investigate these estimators, together with the method-of-moments-estimator, in two chronic heart failure clinical trials. The findings in this paper support the claim that treatment effect measures can be defined based on recurrent event endpoints that are clinically interpretable and statistically estimable.