  We study the problem of inferring heterogeneous treatment effects (HTEs) from
time-to-event data in the presence of competing events. Albeit its great
practical relevance, this problem has received little attention compared to its
counterparts studying HTE estimation without time-to-event data or competing
events. We take an outcome modeling approach to estimating HTEs, and consider
how and when existing prediction models for time-to-event data can be used as
plug-in estimators for potential outcomes. We then investigate whether
competing events present new challenges for HTE estimation -- in addition to
the standard confounding problem --, and find that, because there are multiple
definitions of causal effects in this setting -- namely total, direct and
separable effects --, competing events can act as an additional source of
covariate shift depending on the desired treatment effect interpretation and
associated estimand. We theoretically analyze and empirically illustrate when
and how these challenges play a role when using generic machine learning
prediction models for the estimation of HTEs.
