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University of South Florida Univers How Big is a Big Hazard Ratio? Yuanyuan Lu, Henian Chen, MD, Ph.D. Department of Epidemiology & 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 relative risk by large enough to detect a non-random effect since p value is related to relating relative risk to hazard ratio. sample size. v Odds Ratio = 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 disease 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 COLLEGE OF NURSING UNIVERSITY OF SOUTH FLORIDA COLLEGE OF PHARMACY UNIVERSITY OF SOUTH FLORIDA SCHOOL OF PHYSICAL THERAPY & REHABILITATION SCIENCES UNIVERSITY OF SOUTH FLORIDA.
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