Causal inference for recurrent events via aggregated marginal odds ratio

Researchers often work with treatments and outcomes that vary over time. For example, psychologists are interested in the curative effect of cognitive behavior therapies on patients' recurrent depression symptoms. While there are various causal effect measures designed for one-time treatment, the causal effect measures for time-varying treatment and recurrent events are relatively under-developed. In this article, a new causal measure is proposed to quantify the causal effect of time-varying treatments on recurrent events. We suggest estimators with robust standard errors that are based on various weight models for both conventional causal measures and the proposed measure in different time settings. We outline the approaches and describe how using some stabilized inverse probability weight models are more advantageous than others. We demonstrate that the proposed causal estimand can be consistently estimated for study periods of moderate length, and the estimation results are compared under different treatment settings with various weight models. We also find that the proposed method is suitable for both absorbing and nonabsorbing treatments. The methods are applied to the 1997 National Longitudinal Study of Youth as an illustrative example.