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## Pre-Test Odds

*Aka: Pre-Test Odds, Post-Test Odds, Pre-Test Probability, Post-Test Probability*

- See Also
- Screening Test
- Contingency Grid or Cross Tab (includes Statistics Example)
- Bayes Theorem (Bayesian Statistics)
- Fagan Nomogram
- Experimental Error (Experimental Bias)
- Lead-Time Bias
- Length Bias
- Selection Bias (Screening Bias)
- Likelihood Ratio (Positive Likelihood Ratio, Negative Likelihood Ratio)
- Number Needed to Screen (Number Needed to Treat, Absolute Risk Reduction, Relative Risk Reduction)
- Negative Predictive Value
- Positive Predictive Value
- Receiver Operating Characteristic
- Test Sensitivity (False Negative Rate)
- Test Specificity (False Positive Rate)
- U.S. Preventive Services Task Force Recommendations

- Evaluation
- Calculation
- Odds = P (disease) / (1 - P(disease))
- Pre-Test Odds = (Have condition) / (Do not have condition)
- Post-Test Odds = (Pre-Test Odds) x (Positive Likelihood Ratio)

- Example
- Positive Test
- Disease Y Present in 75
- Disease Y NOT Present in 25

- Negative Test
- Disease Y Present in 10
- Disease Y NOT Present in 190

- Odds
- Pre-Test Odds = (Have condition) / (Do not have condition) = (75 + 10)/(25+190) = 0.4
- Test Sensitivity = P(positive test | disease) / P(disease) = 75 / (75+10) = 0.88
- Test Specificity = P(negative test | no disease) / P(no disease) = 190 / (25 + 190) = 0.88
- Positive Likelihood Ratio = (Test Sensitivity) / (1 - Test Specificity) = 0.88 / (1-0.88) = 7.33
- Post-Test Odds = (Pre-Test Odds) x (Positive Likelihood Ratio) = 0.4 * 7.33 = 2.93

- Conclusion
- Given a positive test, the Post-Test Odds of having the disease is 2.93
- Solve for probability of disease if test positive
- Odds = P (disease) / (1 - P(disease))
- d / (1-d) = 2.93
- d = 2.93/3.93 = 0.75
- P(disease) = 75%

- Positive Predictive Value (PPV) also gives probability of disease based on a positive test
- PPV = P (test positive | Disease) / P (test positive) = 75 / (75 + 25) = 0.75 = 75%

- Positive Test

- Calculation
- Resources
- References
- Desai (2014) Clinical Decision Making, AMIA’s CIBRC Online Course