  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. 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.
