Odds Ratio

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

Calculation
1. Odds Ratio = (P(disease I exposure) / P(healthy I exposure)) / (P(disease I no exposure) / P(healthy I no exposure))
2. Number Needed to Treat can also be calculated based on Odds Ratio and expected event rate
Example
1. Exposure to Substance X
  1. Disease Y Contracted in 25
  2. Disease Y NOT Contracted in 75
2. NO Exposure to Substance X
  1. Disease Y Contracted in 10
  2. Disease Y NOT Contracted in 190
3. Probabilities
  1. Odds of disease if exposed = (P(disease I exposure) / P(healthy I exposure)) = 25 / 75 = 0.334
  2. Odds of disease if not exposed = (P(disease I no exposure) / P(healthy I no exposure)) =10 /190= 0.0526
4. Conclusion
  1. Odds Ratio = (odds of disease if exposed) / (odds of disease if not exposed) = 0.334/0.0526 = 6.35
  2. Patients exposed to Substance X have a more than 6 fold increased odds of developing disease Y than if unexposed

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)