  In this short communication, we describe the recent debate on whether the
hazard function should be used for causal inference in time-to-event studies
and consider three different potential outcomes frameworks (by Rubin, Robins,
and Pearl, respectively) as well as use the single-world intervention graph to
show mathematically that the hazard function has causal interpretations under
all three frameworks. In addition, we argue that the hazard ratio over time can
provide a useful interpretation in practical settings.
