Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis

In a longitudinal clinical study to compare two groups, the primary end point is often the time to a specific event (eg, disease progression, death). The hazard ratio estimate is routinely used to empirically quantify the between-group difference under the assumption that the ratio of the two hazard functions is approximately constant over time. When this assumption is plausible, such a ratio estimate may capture the relative difference between two survival curves. However, the clinical meaning of such a ratio estimate is difficult, if not impossible, to interpret when the underlying proportional hazards assumption is violated (ie, the hazard ratio is not constant over time). Although this issue has been studied extensively and various alternatives to the hazard ratio estimator have been discussed in the statistical literature, such crucial information does not seem to have reached the broader community of health science researchers. In this article, we summarize several critical concerns regarding this conventional practice and discuss various well-known alternatives for quantifying the underlying differences between groups with respect to a time-to-event end point. The data from three recent cancer clinical trials, which reflect a variety of scenarios, are used throughout to illustrate our discussions. When there is not sufficient information about the profile of the between-group difference at the design stage of the study, we encourage practitioners to consider a prespecified, clinically meaningful, model-free measure for quantifying the difference and to use robust estimation procedures to draw primary inferences.