Randomized clinical trials and the proportional hazards model for recurrent events

We consider how to compare treatments based on a randomized clinical trial (RCT) when the outcome of interest is the number of recurrent events. The interest from the medical perspective is to find the treatment that leads to the fewest number of recurrent events. This question can often be addressed by using Andersen-Gill-type models with robust standard errors. The efficiency can be improved using auxiliary covariate information that is often available. We show how this can be accomplished by extending the augmentation approach of Lu and Tsiatis (2008), and that this ensures robustness to misspecifications when testing for no treatment effects. Our results also cover the competing risks setting with cause-specific hazards. The efficiency gain obtained from auxiliary covariates is closely related to the use of covariate adaptive randomization techniques, and we also point out how to compute standard errors when the RCT is based on such techniques (Ye and Shao 2018; Bugni et al. 2018). Further, we demonstrate that the efficiency gain can be large and can be obtained without relying on any modeling assumptions. The techniques are shown to work in simulations and illustrated in practical use by the RCT that motivated the work. We also develop an augmented baseline estimator.