Intended for healthcare professionals

Research Methods & Reporting

Converting an odds ratio to a range of plausible relative risks for better communication of research findings

BMJ 2014; 348 doi: https://doi.org/10.1136/bmj.f7450 (Published 24 January 2014) Cite this as: BMJ 2014;348:f7450

This article has a correction. Please see:

  1. Robert L Grant, senior lecturer in health and social care statistics
  1. 1St George’s, University of London and Kingston University, London SW17 0RE, UK
  1. Correspondence to: R L Grant robert.grant{at}sgul.kingston.ac.uk
  • Accepted 1 November 2013

Odds ratios are a necessary evil in medical research; although used as a measure of effect size from logistic regressions and case-control studies, they are poorly understood. This paper provides practical advice for authors and readers on converting odds ratios to relative risks

The odds ratio is a common measure in medical research of the effect size comparing two groups (treatments or risk factors) in terms of an outcome that is either present or absent. However, the odds ratio is poorly understood.1 2 3 The relative risk (also called the risk ratio) is more intuitive, but cannot be obtained from case-control studies or (except in rare instances) logistic regressions. Because the misunderstanding arises from the odds itself, simply describing it as a proportional change (for example, explaining an odds ratio of 0.8 as “treatment X was associated with a 20% reduction in the odds of the outcome”) is not helpful for most people. This is a problem when communicating results to healthcare professionals and policy makers, discussing treatment options with patients, or seeking to conduct a meta-analysis of studies reporting effect sizes in a mixture of odds ratios and relative risks.

Unfortunately, confusion about odds is not the only problem; there is also a danger of inaccuracy when communicating odds ratios. When the outcome is rare, the odds ratio and relative risk are about the same. Medical papers sometimes rely too heavily on this approximation, discussing odds ratios in terms of risks. Not only is the odds ratio a poor approximation for outcomes which are not “rare” in the study, a statistical analysis with a single odds ratio, common to all participants, does not imply a single common relative risk. In fact, the relative risk depends also on the risk of the outcome in the baseline or control group. …

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