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## Odds Ratio

*Aka: Odds Ratio*

- See Also
- Definition
- Odds Ratio
- Similar to Relative Risk when the condition at risk is rare
- Odds Ratio is typically used instead of Relative Risk when the disease Incidence is unknown
- Used when comparing discrete, dichotomous data points (e.g. death, complication, disease), especially in meta-analysis
- Ratio of probability of an event in an exposed group to that in an unexposed group

- Odds Ratio
- Evaluation: Odds Ratio
- Calculation
- Odds Ratio = (P(disease I exposure) / P(healthy I exposure)) / (P(disease I no exposure) / P(healthy I no exposure))
- Number Needed to Treat can also be calculated based on Odds Ratio and expected event rate

- Example
- Exposure to Substance X
- Disease Y Contracted in 25
- Disease Y NOT Contracted in 75

- NO Exposure to Substance X
- Disease Y Contracted in 10
- Disease Y NOT Contracted in 190

- Probabilities
- Odds of disease if exposed = (P(disease I exposure) / P(healthy I exposure)) = 25 / 75 = 0.334
- Odds of disease if not exposed = (P(disease I no exposure) / P(healthy I no exposure)) =10 /190= 0.0526

- Conclusion
- Odds Ratio = (odds of disease if exposed) / (odds of disease if not exposed) = 0.334/0.0526 = 6.35
- Patients exposed to Substance X have a more than 6 fold increased odds of developing disease Y than if unexposed

- Exposure to Substance X

- Calculation
- Interpretation
- Odds Ratio may also be used to describe effectiveness of a medication that prevents the development of a disease
- Odds Ratio of <1 suggests benefit of a treatment (if the Confidence Intervals do not cross 1)

- Resources
- References
- Hersh (2014) Evidence Based Medicine, AMIA’s CIBRC Online Course
- Szumilas (2010) J Can Acad Child Adolesc Psychiatry 19(3): 227–9 +PMID: [PubMed]