Education And Debate Statistics Notes

# The odds ratio

BMJ 2000; 320 (Published 27 May 2000) Cite this as: BMJ 2000;320:1468
1. J Martin Bland, professor of medical statisticsa,
2. Douglas G Altman, professor of statistics in medicineb
1. a Department of Public Health Sciences, St George's Hospital Medical School, London SW17 0RE
2. b ICRF Medical Statistics Group, Centre for Statistics in Medicine, Institute of Health Sciences, Oxford OX3 7LF
1. Correspondence to: Professor Bland

In recent years odds ratios have become widely used in medical reports—almost certainly some will appear in today's BMJ. There are three reasons for this. Firstly, they provide an estimate (with confidence interval) for the relationship between two binary (“yes or no”) variables. Secondly, they enable us to examine the effects of other variables on that relationship, using logistic regression. Thirdly, they have a special and very convenient interpretation in case-control studies (dealt with in a future note).

The odds are a way of representing probability, especially familiar for betting. For example, the odds that a single throw of a die will produce a six are 1 to 5, or 1/5. The odds is the ratio of the probability that the event of interest occurs to the probability that it does not. This is often estimated by the ratio of the number of times that the event of interest occurs to …

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