Estimating Treatment Effects for Recurrent Events in the Presence of Rescue Medications: An Application to the Immune Thrombocytopenia Study

In many clinical studies, patients may experience the same type of event of interest repeatedly over time. However, the assessment of treatment effects is often complicated by the rescue medication uses due to ethical reasons. For example, in the motivating trial in studying the Immune Thrombocytopenia (ITP), when the interest lies in evaluating the treatment benefit of investigational product (IP) on reducing patient's repeated bleeding, rescue medication such as platelet transfusions may be allowed to raise platelet counts. Both the intention-to-treat analysis and treating the intermediate rescue medication as covariate tend to attenuate the treatment benefit, and the estimates can be biased if interpreted as causal. In this paper, we propose a general causal framework when intermediate rescue medications are informative. We adopt the inverse weighted estimation approach to estimate the treatment effect, where weights are constructed to reflect time-dependent medication use probabilities. The proposed estimators are shown to be asymptotically normal and are demonstrated to perform well in small-sample simulation studies. The application to the ITP studies reveals a stronger benefit of using IP in reducing bleeding.