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

Richard A. J. Post (), Edwin R. van den Heuvel and Hein Putter
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Richard A. J. Post: Eindhoven University of Technology
Edwin R. van den Heuvel: Eindhoven University of Technology
Hein Putter: Leiden University Medical Center

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2024, vol. 30, issue 2, No 5, 383-403

Abstract: Abstract Hazard ratios are prone to selection bias, compromising their use as causal estimands. On the other hand, if Aalen’s additive hazard model applies, the hazard difference has been shown to remain unaffected by the selection of frailty factors over time. Then, in the absence of confounding, observed hazard differences are equal in expectation to the causal hazard differences. However, in the presence of effect (on the hazard) heterogeneity, the observed hazard difference is also affected by selection of survivors. 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 effect 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 cannot be distinguished from a time-invariant 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.

Keywords: Causal inference; Causal hazard difference; Individual effect modification; Selection bias; Aalen additive hazard model; 62D20; 62N02 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10985-024-09616-z

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