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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
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
Competing interests: No competing interests