Inference for Cumulative Incidences and Treatment Effects in Randomized Controlled Trials with Time-to-Event Outcomes under ICH E9 (E1)

In randomized controlled trials (RCT) with time-to-event outcomes, intercurrent events occur as semi-competing/competing events, and they could affect the hazard of outcomes or render outcomes ill-defined. Although five strategies have been proposed in ICH E9 (R1) addendum to address intercurrent events in RCT, they did not readily extend to the context of time-to-event data for studying causal effects with rigorously stated implications. In this study, we show how to define, estimate, and infer the time-dependent cumulative incidence of outcome events in such contexts for obtaining causal interpretations. Specifically, we derive the mathematical forms of the scientific objective (i.e., causal estimands) under the five strategies and clarify the required data structure to identify these causal estimands. Furthermore, we summarize estimation and inference methods for these causal estimands by adopting methodologies in survival analysis, including analytic formulas for asymptotic analysis and hypothesis testing. We illustrate our methods with the LEADER Trial on investigating the effect of liraglutide on cardiovascular outcomes. Studies of multiple endpoints and combining strategies to address multiple intercurrent events can help practitioners understand treatment effects more comprehensively.