How big is a big hazard ratio in clinical trials?

Background: The hazard ratio has been widely used as an index of effect size in clinical trials for time-to-event data. The use of the Cox proportional hazards models and other hazard centered models is ubiquitous in clinical trials for time-to-event data. The relativity of effect sizes (small, medium, large) has been widely discussed and accepted when comparing magnitude of association for continuous and categorical data, but not yet for time-to-event outcomes. Methods: We review published hazard ratios, investigate the relationships among HR, relative risk (RR), odds ratio (OR), and Cohen’s d, and calculate the corresponding HRs for given event rate in control group ( ) by adding standard normal deviation with 0.2 (small), 0.5 (medium) and 0.8 (large) to the event rate in the case group (  based on equation . Results: Our results indicate that HRs are from 1.68 to 1.16 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.2 (small). HRs are ranged between 3.43 and 1.43 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.5 (medium), HRs are valued between 6.52 and 1.73 when the event rate of control group moves from 1% to 90%, which are equivalent to Cohen’s d = 0.8 (large). Conclusions: This study provides general guidelines in interpreting the magnitudes of HRs for time-to-event data in clinical trials.