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

Bias of the additive hazard model in the presence of causal effect heterogeneity