Using the Restricted Mean Survival Time Difference as an Alternative to the Hazard Ratio for Analyzing Clinical Cardiovascular Studies
Authors: Zachary R. McCaw, Guosheng Yin, Lee-Jen Wei
Journal: Circulation (2019)

ardiovascular trials often use the time to a clinical event as the primary end point when evaluating a new treatment, versus control, via clinical and statistical significance criteria.For the past 50 years, the hazard ratio (HR) has been routinely used for quantifying the treatment effect.However, it is difficult to interpret clinical significance using a ratio measure, such as HR, when there is no reference hazard available from the control arm.Moreover, valid HR analysis requires the proportional hazards (PH) assumption: that the ratio of hazard curves is constant over time.This assumption is hardly plausible in practice.When PH is not met, HR may lack statistical power to detect a true treatment effect.Furthermore, without PH, the estimated HR is not a simple average of HRs over time, and is even more difficult to interpret. 1,2In this article, we discuss the advantages of an alternative analytical procedure based on the restricted mean survival time (RMST) 1,2 via 3 examples.The first example comes from the CHARM-Overall (Candesartan in Heart Failure-Assessment of Mortality and Morbidity-Overall) trial, which evaluated the effect of candesartan on all-cause mortality in patients with chronic heart failure. 3The HR (candesartan vs placebo) of 0.91 (95% CI, 0.83-1.00;P=0.055) did not provide strong statistical evidence of a benefit from candesartan.Moreover, it is unclear whether a HR of 0.91 is clinically significant.This does not suggest that candesartan reduced the risk of mortality by 9% versus placebo, because the hazard is not a probability measure like risk.To explore whether HR analysis was appropriate, we reconstructed patient-level survival data from the Kaplan-Meier curves presented in the CHARM-Overall article. 3Here, the reconstructed Kaplan-Meier curves are presented in Figure ,A.Because the Kaplan-Meier curves separate initially but remain parallel after 0.5 years, the PH assumption was not met, as was confirmed via the Schoenfeld goodness-of-fit test (P=0.0005).An alternative is to use the difference in RMSTs to quantify the treatment effect.RMST is the average time-to-event over a fixed follow-up period (for example, 3.5-years in Figure ,A).Graphically, RMST corresponds to the area under the survival curve.The higher the curve, the greater the RMST.As presented in Figure ,B, the area under the curve for candesartan was 3.07 years.That is, across 3.5 years of follow-up, patients treated with candesartan survived for 3.07 years on average.The corresponding RMST for placebo was 3.00 years.The difference of 0.07 years (95% CI, 0.03-0.11;P=0.0016) was highly statistically significant in favor of candesartan.This example demonstrates that RMST can be more statistically efficient than HR when PH is not met.After passing the statistical significance hurdle, the clinical utility of candesartan can be evaluated using individual RMSTs (3.07 and 3.00 years).For the present case, it is debatable whether the 0.07-year (3.6-week) survival gain is clinically significant.A limitation of RMST-based analysis is the need to specify a truncation time.Ideally, this would be prespecified via clinical considerations during study design.Otherwise, one can choose the last observed event or