How big is a big hazard ratio in clinical trials?
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Date
2023-09
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Abstract
Background: Thehazardratio(HR)hasbeenwidelyusedasanindexofeffectsizeinclinicaltrialsfortime-to-eventdata.TheuseoftheCoxproportionalhazardsmodelsandotherhazardcenteredmodelsisubiquitousinclinicaltrialsfortime-to-eventdata.Therelativityofeffectsizes(small,medium,large)hasbeenwidelydiscussedandacceptedwhencomparingmagnitudeofassociationforcontinuousandcategoricaldata,butnotyetfortime-to-eventoutcomes.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 (??0) by adding standard normal deviation with 0.2 (small), 0.5 (medium) and 0.8 (large) to the event rate in the case group (??1)based on equation ??1=1?(1???0)????.Results: OurresultsindicatethatHRsarefrom1.68to1.16whentheeventrateofcontrolgroupmovesfrom1%to90%,whichareequivalenttoCohen’sd=0.2(small).HRsarerangedbetween3.43and1.43whentheeventrateofcontrolgroupmovesfrom1%to90%,whichareequivalenttoCohen’sd=0.5(medium),HRsarevaluedbetween6.52and1.73whentheeventrateofcontrolgroupmovesfrom1%to90%,whichareequivalenttoCohen’sd=0.8(large).Conclusions: This study provides general guidelines in interpreting the magnitudes of HRs for time-to-event data in clinical trials
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Keywords
Hazard ratio, Clinical trial, Effect size, Time-to-event data
Citation
Lu Yuanyuan, Cen Weiliang, Wang Wei, Huang Yangxin, Chen Henian. How big is a big hazard ratio in clinical trials?. International Journal of Clinical Trials. 2023 Jul. 10(3). 195-200