Letters

When can odds ratios mislead?

BMJ 1998; 317 doi: http://dx.doi.org/10.1136/bmj.317.7166.1155a (Published 24 October 1998) Cite this as: BMJ 1998;317:1155

Odds ratios should be used only in case-control studies and logistic regression analyses

  1. Jon Deeks, Medical statistician (J.Deeks@icrf.icnet.uk)
  1. Centre for Statistics in Medicine, Institute of Health Sciences, Oxford OX3 7LF
  2. Yale University School of Medicine, Department of Epidemiology and Public Health, New Haven, CT, 06510, USA
  3. McMaster University, Hamilton, Ontario, Canada L8N 3Z5
  4. Department of Management, University of St Andrews, St Andrews, Fife KY19 9AL
  5. Department of Epidemiology and Public Health, University of Dundee, Ninewells Hospital and Medical School, Dundee DD1 9SY

    EDITOR—Expressing the results of clinical trials and systematic reviews in terms of odds ratios can be more seriously misleading than Davies et al advise us.1 They gave a correct analysis of situations in which odds ratios are used to describe increases in event rates, but their consideration of the more common situation, in which treatments reduce event rates, is short sighted. Here, effectiveness is more commonly expressed as the percentage relative risk reduction (100=D7(1−relative risk)%) than the actual relative risk. The discrepancy between a relative risk reduction and the equivalent relative odds reduction (100=D7(1−odds ratio)%) can be misleading. When event rates are high (commonly the case in trials and systematic reviews) the relative odds reduction can be many times larger than the equivalent relative risk reduction.

    For example, Brent et al report results of a trial of a programme aimed at increasing the duration of breast feeding.2 By three months 32/51(63%) women had stopped breast feeding in the intervention group, compared with 52/57(91%) in the control group. Whereas the relative risk reduction is 31% the relative odds reduction is 84%: nearly three times as large. The same problem can occur in systematic reviews: a summary of the results of seven trials of antimicrobial treatment on premature rupture of membranes showed a 49% relative odds reduction of delivery by seven days, whereas the relative risk reduction was only 19%.3

    Although relative odds and relative risk reductions always go in the same direction, these discrepancies …

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