Potential misinterpretation of treatment effects due to use of odds ratios and logistic regression in randomized...

In randomized controlled trials (RCTs), the odds ratio (OR) can substantially overestimate the risk ratio (RR) if the incidence of the outcome is over 10%. This study determined the frequency of use of ORs, the frequency of overestimation of the OR as compared with its accompanying RR in published RCTs, and we assessed how often regression models that calculate RRs were used.

We included 288 RCTs published in 2008 in five major general medical journals (Annals of Internal Medicine, British Medical Journal, Journal of the American Medical Association, Lancet, New England Journal of Medicine). If an OR was reported, we calculated the corresponding RR, and we calculated the percentage of overestimation by using the formula .

Of 193 RCTs with a dichotomous primary outcome, 24 (12.4%) presented a crude and/or adjusted OR for the primary outcome. In five RCTs (2.6%), the OR differed more than 100% from its accompanying RR on the log scale. Forty-one of all included RCTs (n = 288; 14.2%) presented ORs for other outcomes, or for subgroup analyses. Nineteen of these RCTs (6.6%) had at least one OR that deviated more than 100% from its accompanying RR on the log scale. Of 53 RCTs that adjusted for baseline variables, 15 used logistic regression. Alternative methods to estimate RRs were only used in four RCTs.

ORs and logistic regression are often used in RCTs and in many articles the OR did not approximate the RR. Although the authors did not explicitly misinterpret these ORs as RRs, misinterpretation by readers can seriously affect treatment decisions and policy making.