Describing Differences in Survival Curves.

Abstract

WecongratulatePeronetal1ontheir contribution to themedical canon of a newmeasure of survival time treatment effect inaclinical trial. Thismeasure,whichequals thechanceof surviving longer in an experimental group vs a control group minus the reverse, is robust in that it depends on no distributional assumptions. It is easily interpretable and clinically relevant: if the measure is 100%, the experimental group is always better, if it is –100%, the experimental group is always worse, and if it is 0%, the 2 treatments are equivalent.Theauthorsalsodescribeabroaderoutcome inwhichsurvival is exceeded by a specified number ofmonths. However, for simplicitywe focushereon the situation inwhich themeasure is 0%; that is, we are interested in superiority by any amount of time. In this case, we suggest for the sake of interpretability thatwe rescale to the simple chance of superiority by adding 100% and dividing by 2, yielding 100% and 0% for the extremes and 50% for equality of treatments. This contributionmakesadesiredcomplement to thehazard ratio (HR),2 the most commonly used way of comparing survival curves, estimatedwith theCoxproportional hazards regression model and compared via the log-rank test.3 Although the HR has many virtues, its interpretation as the ratio between instantaneous risks, or the conditional derivatives of the survival curves, may be nonintuitive and also requires a strong assumption regarding the relationship between thedistributionof failures in theexperimental andcontrol groups: that this ratio is constant over time. On the first point, Cox4 himself commented that a constant HR is not associated with a simple underlying generating process and, therefore, other outcomes may be more interpretable. Thus, we are led, for the benefit of clinicians and trialists, to briefly list thecommonmeasuresof survival timetreatmenteffectand their relative advantages.