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## Pre-Test Odds

Aka: Pre-Test Odds, Post-Test Odds, Pre-Test Probability, Post-Test Probability
2. Evaluation
1. Calculation
1. Odds = P (disease) / (1 - P(disease))
2. Pre-Test Odds = (Have condition) / (Do not have condition)
3. Post-Test Odds = (Pre-Test Odds) x (Positive Likelihood Ratio)
2. Example
1. Positive Test
1. Disease Y Present in 75
2. Disease Y NOT Present in 25
2. Negative Test
1. Disease Y Present in 10
2. Disease Y NOT Present in 190
3. Odds
1. Pre-Test Odds = (Have condition) / (Do not have condition) = (75 + 10)/(25+190) = 0.4
2. Test Sensitivity = P(positive test | disease) / P(disease) = 75 / (75+10) = 0.88
3. Test Specificity = P(negative test | no disease) / P(no disease) = 190 / (25 + 190) = 0.88
4. Positive Likelihood Ratio = (Test Sensitivity) / (1 - Test Specificity) = 0.88 / (1-0.88) = 7.33
5. Post-Test Odds = (Pre-Test Odds) x (Positive Likelihood Ratio) = 0.4 * 7.33 = 2.93
4. Conclusion
1. Given a positive test, the Post-Test Odds of having the disease is 2.93
2. Solve for probability of disease if test positive
1. Odds = P (disease) / (1 - P(disease))
2. d / (1-d) = 2.93
3. d = 2.93/3.93 = 0.75
4. P(disease) = 75%
3. Positive Predictive Value (PPV) also gives probability of disease based on a positive test
1. PPV = P (test positive | Disease) / P (test positive) = 75 / (75 + 25) = 0.75 = 75%
3. Resources
1. Wikipedia
1. https://en.wikipedia.org/wiki/Pre-_and_post-test_probability
4. References
1. Desai (2014) Clinical Decision Making, AMIA’s CIBRC Online Course

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