On Defense of the Hazard Ratio

There has been debate on whether the hazard function should be used for causal inference in time-to-event studies. The main criticism is that there is selection bias because the risk sets beyond the first event time are comprised of subsets of survivors who are no longer balanced in the risk factors, even in the absence of unmeasured confounding, measurement error, and model misspecification. In this short communication we use the potential outcomes framework and the single-world intervention graph to show that there is indeed no selection bias when estimating the average treatment effect, and that the hazard ratio over time can provide a useful interpretation in practical settings.