How Big is a Big Hazard Ratio? Yuanyuan Lu, Henian Chen, MD, Ph.D. Department of & Biostatistics, College of Public Health, University of South Florida

Background Objective v A growing concern about the difficulty of evaluating research findings v The purpose of this study was to propose a new method for interpreting including treatment effects of medical interventions. the size of hazard ratio by relating hazard ratio with Cohen‘s D. v A statistically significant finding indicates only that the sample size was v We also proposed a new method to interpret the size of by large enough to detect a non-random effect since p value is related to relating relative risk to hazard ratio. sample size. v = 1.68, 3.47, and 6.71 are equivalent to Cohen’s d = 0.2 Methods (small), 0.5 (medium), and 0.8 (large), respectively, when rate is 1% in the non-exposed group (Cohen 1988, Chen 2010). v Cohen’s d is the standardized mean difference between two group means. v Number of articles using keywords “Hazard Ratio” escalated rapidly since v Cox proportional hazards regression is semiparametric survival model, 2000. which uses the rank of time instead of using exact time. The hazard v About 153 hazard ratio were reported significant in 52 articles from function of the Cox proportional hazards model is: American Journal of Epidemiology from 2017/01/01 to 2017/11/02. Over 55 hazards ratios are within 1 to 1.5. v The hazard ratio is the ratio of the hazard rates corresponding to two levels of an explanatory variable. " ($|&'() HR= = +, " $ &'*) v Relative risk is the ratio of the probability of one event occurring in the exposed group to the probability of the event occurring in the non- exposed group. - (0123{05 7 89} (0((0- );< RR= . = 6 = / -/ (0123{056(7)} (0((0-/)

Results Cohen's D <0.2 Cohen's D 0.5 Cohen's D >0.8 Disease Rate in Non-exposed Group HR RR HR RR HR RR

1% <1.70 <1.69 3.5 3.46 >6.50 >6.32

10% <1.50 <1.46 2.50 2.32 >3.50 >3.08

MORSANI Conclusions v When disease rate is COLLEGE1% in the nonexposed OF MEDICINEgroup, the reference points reflecting a "weakMO association"RSANI hazard ratio, a "moderate association" hazard ratio, UNIVERSITY OF SOUTH FLORIDA and a "strong association"UNIVERSITY hazard OF ratio SOUTH are FLORIDA1.70, 3.5 and 6.5, and the reference pointsCOLLEGE reflection a "weak OF association" MEDICINE relative risk, a "moderate association" relative risk, and a "strong association" relative risk are 1.69, 3.46 and 6.32. v When disease rate is 10% in the nonexposed group, the reference points reflecting a "weak association" hazard ratio, a "moderate association" hazard ratio, and a "strong association" hazard ratio are 1.50, 2.50 and 3.50, and the reference points reflection a "weak association" relative risk, a "moderate association" relative risk, and a "strong association" relative risk are 1.46, 2.32 and 3.08. COLLEGE OF PUBLIC HEALTH UNIVERSITY OF SOUTH FLORIDA Our Practice Is Our Passion

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