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LETTERS: Douglas G Altman, Jonathon J Deeks, and David L Sackett Odds ratios should be avoided when events are common BMJ 1998; 317: 1318 [Full text]

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Rare Distinction and Common Fallacy

Stephen Senn   (10 May 1999)

Rare Distinction and Common Fallacy 10 May 1999
Stephen Senn, Professor of pharmaceutical health statistics University College London Send response to journal: Re: Rare Distinction and Common Fallacy	Altman, Deeks and Sackett1 claim that the odds ratio should be avoided except when events are rare because the odds ratio becomes unreliable as an approximation to the relative risk when events are common. The correct advice, however, is the opposite of what they give. The odds ratio and not the relative risk is the gold standard. The relative risk is only acceptable when events are rare, when it becomes adequate as an approximation to the odds ratio. The odds ratio is invariant to the arbitrary decision of deciding whether we concentrate on the relative risk of dying or the relative risk of living, being the product of the two.It is only when the latter is nearly equal to one that using the former alone is acceptable. How many statisticians, in examining their medical students, would give them full marks if in carrying out a test of association on a two by two table they worked only with the discrepancy between observed and expected for the two cells corresponding to 'events' rather than for all four? However, this is the exact analogy of working with relative risk rather than odds ratios. It gives an approximately correct answer when 'events' are rare relative to 'non-events' but it is generally and philosophically unsound. 1 Douglas G Altman, Jonathon J Deeks, and David L Sackett Odds ratios should be avoided when events are common BMJ 1998; 317: 1318