Interpretation of Odds and Risk Ratios

BACKGROUND: Odds ratio and risk ratio are measures of association used to describe the efficacy of interventions and disease determinates; however, they are not interchangeable measures of association. OBJECTIVES: To illustrate that interpretation of the odds ratio as a risk-based measure of efficacy can be misleading. ANIMALS: None. METHODS: A meta-analysis reported, the odds ratio and the risk ratio as measures of vaccine effect. Example data were obtained from a meta-analysis of the risk of infection with Tritrichomonas fetus (T. fetus), in trials that assessed whole-cell killed T. fetus vaccination in beef heifers. RESULTS: When risk was used as the measure of disease frequency, the summary risk ratio was 0.82 (95% CI = 0.7-1.01), a 18% decrease in risk of infection. When odds were used as the measure of disease frequency and the summary odds ratio was 0.41 (95% CI = 0.2-0.84), a 59% decrease in odds of infection. CONCLUSIONS AND CLINICAL IMPORTANCE: Problems arise for clinicians or authors when they interpret the odds ratio as a risk ratio. In the example provided, the efficacy of protective interventions was overestimated. In the case of disease determinates that increase the occurrence of disease, the interpretation of the odds ratio as a risk ratio would also lead to overestimation of the effect. It is important not to use the terms risk or probability of disease when the odds are the measure of disease frequency.