Odds ratios should be avoided when events are common

BMJ 1998;317:1318 ( 7 November )

Letters

Odds ratios should be avoided when events are common

EDITOR $---$ A news item stated that "a review article written by authors with affiliations to the tobacco industry is 88 timesmore likely to conclude that passive smoking is not harmful thanif the review was written by authors with no connection to thetobacco industry."¹ We are concerned that readers may haveinterpreted this huge effect at face value. The proportions beingcompared (which were not given in the news item) were 29/31 (94%)and 10/75 (13%). The relative risk here is 7, which indicatesa strong association but is an order of magnitude lower than thereported odds ratio of 88.² This value is correct but is seriouslymisleading if presented or interpreted as meaning that the relativerisk that affiliated authors would draw favourable conclusionswas 88, as it was in this newsitem.

The odds ratio is valuable in case-control studies where events are usually rare and the relative risk cannot validly be estimateddirectly. In prospective studies interpretation of the odds ratioas an approximation to the relative risk becomes unreliable whenevents are common, and thus its use for prospective studies, especiallyrandomised trials and systematic reviews, has been criticised. ³ ⁴ The distortion is especially large when the event rate is highin only one group, as in this example. The odds ratio should notbe interpreted as an approximate relative risk unless the eventsare rare in both groups (say, less than20-30%).

The odds ratio remains especially useful when researchers need to adjust for other variables, for which logistic regressionis the usual approach. While such analyses are valid, when theobjective is to communicate study results to an audience unfamiliarwith the relation between odds ratios and relative risks, surelyit makes no sense also to report the relative risk when this differsmarkedly from the odds ratio.

Douglas G Altman, Director.
Jonathon J Deeks, Statistician.
ICRF/NHS Centre for Statistics in Medicine, Institute of Health Sciences, Oxford OX3 7LF

David L Sackett, Professor.
NHS R&D Centre for Evidence-Based Medicine, John Radcliffe Hospital, Oxford OX3 9DU

Wise J. Links to tobacco industry influences review conclusions. BMJ 1998; 316: 1554. (23 May.)
Barnes DE, Dero LA. Why review articles on the health effects of passive smoking reach different conclusions. JAMA 1998; 279: 1566-1570 [Abstract/Free Full Text].
Sackett DL, Deeks JJ, Altman DG. Down with odds ratios! Evidence-Based Med 1996; 1: 164-166.
Deeks JJ. When can odds ratios mislead? BMJ 1998; 317: 1155-1156 [Free Full Text]. (25 October.)

© BMJ 1998

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