Odds ratios should be avoided when events are common

BMJ 1998; 317 doi: http://dx.doi.org/10.1136/bmj.317.7168.1318 (Published 07 November 1998) Cite this as: BMJ 1998;317:1318
  1. Douglas G Altman, Director,
  2. Jonathon J Deeks, Statistician,
  3. David L Sackett, Professor
  1. ICRF/NHS Centre for Statistics in Medicine, Institute of Health Sciences, Oxford OX3 7LF
  2. NHS R&D Centre for Evidence-Based Medicine, John Radcliffe Hospital, Oxford OX3 9DU

    EDITOR—A news item stated that “a review article written by authors with affiliations to the tobacco industry is 88 times more likely to conclude that passive smoking is not harmful than if the review was written by authors with no connection to the tobacco industry.”1 We are concerned that readers may have interpreted this huge effect at face value. The proportions being compared (which were not given in the news item) were 29/31 (94%) and 10/75 (13%). The relative risk here is 7, which indicates a strong association but is an order of magnitude lower than the reported odds ratio of 88.2 This value is correct but is seriously misleading if presented or interpreted as meaning that the relative risk that affiliated authors would draw favourable conclusions was 88, as it was in this news item.

    The odds ratio is valuable in case-control studies where events are usually rare and the relative risk cannot validly be estimated directly. In prospective studies interpretation of the odds ratio as an approximation to the relative risk becomes unreliable when events are common, and thus its use for prospective studies, especially randomised trials and systematic reviews, has been criticised. 3 4 The distortion is especially large when the event rate is high in only one group, as in this example. The odds ratio should not be interpreted as an approximate relative risk unless the events are rare in both groups (say, less than 20-30%).

    The odds ratio remains especially useful when researchers need to adjust for other variables, for which logistic regression is the usual approach. While such analyses are valid, when the objective is to communicate study results to an audience unfamiliar with the relation between odds ratios and relative risks, surely it makes no sense also to report the relative risk when this differs markedly from the odds ratio.