USING PROPERLY RELATIVE RISK AND ODDS RATIO

Both relative risk (RR) and odds ratio (OR) are common measures of treatment effect on randomized controlled trials, systematic reviews and meta-analyses. However few scientists interpret properly these measures, and many scientists mix-up their meanings and use either of them unsystematically, thus leading to misinterpretations. PURPOSE To systematize the proper usage of RR and OR on randomized controlled trials. METHODS We analyzed the complete relation between risk from 0 to 1 and odds from 0 to infinite with a precision of 0.01 for risk. Then, the relation between RR and OR was analyzed separately for both RR and OR values of either greater or less than one. When both of them were greater than one, the OR/RR ratio was analyzed at different control (5, 10, 15, 20, 30, 40, 50, 60 and 70%) and treatment (from 6 to 99%, with 1% of precision) event rates; in these cases the treatment event rate was always higher than the control event rate. When both RR and OR were less than one, we analyzed the RR/OR ratio at other control (10, 20, 30, 40, 50, 60, 70, 80, 90 and 95%) and treatment (from 1 to 94%, with 1% of precision) event rates; in these cases, the treatment event rate was always less than the control event rate. RESULTS Although odds was always higher than risk for all possible values, such risk overestimation by odds was low when risk was low. Actually, when the risk rose above 20% the gap between the odds and the risk widened. Since OR and RR are calculated by dividing these measures, the differences between RR and OR began from both control and treatment event rates higher than 20%. These differences (> 25%) were enough to misinterpret results. CONCLUSION OR is misleading when both treatment and control event rates are higher than 20%. In these instances, RR must be used instead of OR on randomized controlled trials.