Making sense of odds and odds ratios

Odds and odds ratios are hard for many clinicians to understand. Odds are the probability of an event occurring divided by the probability of the event not occurring. An odds ratio is the odds of the event in one group, for example, those exposed to a drug, divided by the odds in another group not exposed. Odds ratios always exaggerate the true relative risk to some degree. When the probability of the disease is low (for example, less than 10%), the odds ratio approximates the true relative risk. As the event becomes more common, the exaggeration grows, and the odds ratio no longer is a useful proxy for the relative risk. Although the odds ratio is always a valid measure of association, it is not always a good substitute for the relative risk. Because of the difficulty in understanding odds ratios, their use should probably be limited to case-control studies and logistic regression, for which odds ratios are the proper measures of association.