# Odds Ratio

Reference work entry

**DOI:**https://doi.org/10.1007/978-1-4419-9863-7_235

## Definition

The odds ratio is the ratio of the odds of an event happening in one group compared to the odds of the same event happening in another group. For example, the odds ratio is often used in case-control studies to determine if being exposed to a certain substance or factor increases the risk of a disease. In statistics, the odds of an event occurring is the probability of the event divided by the probability of an event not occurring. The odds ratio allows to compare the odds of the outcome of interest (e.g., apparition of a tumor) in two different groups (e.g., surgery versus chemotherapy) (Lachin
2000). Let us consider a study aiming at comparing two sample populations, referred to as group 1 and 2, with respective sizes of

*n*_{1}and*n*_{2}. In each sample, we suppose that*a*and*b*individuals have a positive response or characteristic of interest, respectively. The resulting data can be summarized in the following 2 × 2 contingency table (see Table 1).
Odds Ratio, Table 1

2 × 2...

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### References

- Bland JM, Altman DG (2000) Statistics notes: the odds ratio. BMJ 320(7247):1468PubMedGoogle Scholar
- Davies HT, Crombie IK, Tavakoli M (1998) When can odds ratios mislead? BMJ 316(7136):989–991PubMedGoogle Scholar
- Lachin JM (2000) Biostatistical methods: the assessment of relative risks. Wiley, New YorkGoogle Scholar

## Copyright information

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