  In time-to-event settings, the presence of competing events complicates the
definition of causal effects. Here we propose the new separable effects to
study the causal effect of a treatment on an event of interest. The separable
direct effect is the treatment effect on the event of interest not mediated by
its effect on the competing event. The separable indirect effect is the
treatment effect on the event of interest only through its effect on the
competing event. Similar to Robins and Richardson's extended graphical approach
for mediation analysis, the separable effects can only be identified under the
assumption that the treatment can be decomposed into two distinct components
that exert their effects through distinct causal pathways. Unlike existing
definitions of causal effects in the presence of competing events, our
estimands do not require cross-world contrasts or hypothetical interventions to
prevent death. As an illustration, we apply our approach to a randomized
clinical trial on estrogen therapy in individuals with prostate cancer.
