Clinical Trials

❘❙❚■ Chapter 20 | Comparison of ProportionsFigure 1. Relationship between odds ratio and risk ratio.5Risk = 0.014Risk = 0.05Risk = 0.10Risk ratio32Risk = 0.20Risk = 0.501Risk = 0.8000 12 3 45Odds ratioWhy use odds ratios?If odds ratios are difficult to interpret, why do we not always use risk ratiosinstead? There are several reasons for this, most of which are related to thesuperior mathematical properties of odds ratios. Firstly, odds ratios can alwaystake values between zero and infinity, which is not the case for risk ratios. Forexample, if the risk of death is 0.60, it is not possible to double it. Odds ratios alsopossess symmetry: if the outcomes in the analysis are reversed, the relationshipswill have reciprocal odds ratios. In case of the MI trial data, we have:OR(death) = 1 / OR(survival)However, no such relationship exists for risk ratios. In addition, if we need tomake adjustments for confounding factors using regression, odds ratios can bemodeled very easily by a logistic regression model, whereas a regression model forrisk ratios cannot always be fitted. Furthermore, while a risk ratio is only accuratewith complete subject follow-up, an odds ratio is a useful measure of associationfor a variety of study designs, such as a case-control study.230