Estimating Risk Ratios and Risk Differences: Alternatives to Odds Ratios

INTRODUCTION

This JAMA Guide to Statistics and Methods explains the differences between risk ratios and odds ratios and when each is the more appropriate statistic to estimate measures of effect or association in research findings.

The goal of many medical research studies is to estimate the direction and magnitude of the effect of an intervention or treatment on a clinical outcome (in clinical trials) or the association between an exposure and an outcome (in observational studies). This effect or association can be presented in various forms, depending on the measured outcome. For example, if the outcome is a continuous measure (eg, blood pressure), the effect or association could be represented as a mean difference between the groups. If the outcome is a time-to-event outcome (eg, time to death), the effect or association is often expressed as a hazard ratio.

For binary outcomes (eg, 90-day survival), the measure of the effect or association is often presented as an odds ratio (ie, dividing the odds of the outcome in one group with the odds of the outcome in another), in which the odds are the probability divided by 1 minus the probability. Odds ratios are commonly reported in clinical research because of the frequent use of logistic regression when there is a need to adjust for various characteristics (eg, to adjust for potential confounders in an observational study). Logistic regression yields odds ratios, is relatively straightforward to perform, and is widely available in statistical software. However, as explained in another JAMA Guide to Statistics and Methods chapter,¹ there are limitations to odds ratios. For instance, odds ratios do not approximate risk ratios when the outcome is frequent (Table 1) and odds ratios are easily misinterpreted by researchers, clinicians, and patients.

An observational study by Grunau et al² in JAMA evaluated survival to hospital discharge among patients who received ongoing resuscitation for out-of-hospital cardiac arrest during transport to the hospital compared with continuous resuscitation at the scene. Instead of reporting odds ratios, the authors estimated risk ratios and risk differences, measures of association that are more intuitive to interpret.

WHAT ARE RISK RATIOS AND RISK DIFFERENCES?

A risk ratio is the probability (or risk) of an outcome in one group divided by the probability in another, whereas the risk difference is the probability of an outcome in one group minus the probability in ...