Efficient estimation of the marginal mean of recurrent events in randomized controlled trials

Recurrent events data are often encountered in biomedical settings, where individuals may also experience a terminal event such as death. A useful estimand to summarize such data is the marginal mean of the cumulative number of recurrent events up to a specific time horizon, allowing also for the possible presence of a terminal event. Recently, it was found that augmented estimators can estimate this quantity efficiently, providing improved inference. Improvement in efficiency by the use of covariate adjustment is increasing in popularity as the methods get further developed, and is supported by regulatory agencies EMA (2015) and FDA (2023). Motivated by these arguments, this article presents novel efficient estimators for clinical data from randomized controlled trials, accounting  for additional information from auxiliary covariates.   Moreover, in randomized studies when both right censoring and competing risks are present, we propose a novel doubly augmented estimator of the marginal mean  , which has two optimal augmentation components due to censoring and randomization. We provide theoretical and asymptotic details for the novel estimators,   also confirmed by simulation studies. Then, we discuss how to improve efficiency, both theoretically by computing the expected amount of variance reduction, and practically by showing the performance of different working regression models that are needed in the augmentation, when they are correctly specified or misspecified. The methods are applied to the   LEADER study, a randomized controlled trial that studied cardiovascular safety of     treatments in type 2 diabetes patients.