  Hazard ratios are prone to selection bias, compromising their use as causal
estimands. On the other hand, the hazard difference has been shown to remain
unaffected by the selection of frailty factors over time. Therefore, observed
hazard differences can be used as an unbiased estimator for the causal hazard
differences in the absence of confounding. However, in the presence of effect
(on the hazard) heterogeneity, the hazard difference is also affected by
selection. In this work, we formalize how the observed hazard difference (from
a randomized controlled trial) evolves by selecting favourable levels of effect
modifiers in the exposed group and thus deviates from the causal hazard
difference of interest. Such selection may result in a non-linear integrated
hazard difference curve even when the individual causal effects are
time-invariant. Therefore, a homogeneous time-varying causal additive effect on
the hazard can not be distinguished from a constant but heterogeneous causal
effect. We illustrate this causal issue by studying the effect of chemotherapy
on the survival time of patients suffering from carcinoma of the oropharynx
using data from a clinical trial. The hazard difference can thus not be used as
an appropriate measure of the causal effect without making untestable
assumptions.
