Doubly robust estimation and causal inference for recurrent event data

Many longitudinal databases record the occurrence of recurrent events over time. In this article, we propose a new method to estimate the average causal effect of a binary treatment for recurrent event data in the presence of confounders. We propose a doubly robust semiparametric estimator based on a weighted version of the Nelson-Aalen estimator and a conditional regression estimator under an assumed semiparametric multiplicative rate model for recurrent event data. We show that the proposed doubly robust estimator is consistent and asymptotically normal. In addition, a model diagnostic plot of residuals is presented to assess the adequacy of our proposed semiparametric model. We then evaluate the finite sample behavior of the proposed estimators under a number of simulation scenarios. Finally, we illustrate the proposed methodology via a database of circus artist injuries.