Prevention Book

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Pre-Test Odds

Aka: Pre-Test Odds, Post-Test Odds, Pre-Test Probability, Post-Test Probability
  1. See Also
    1. Screening Test
    2. Contingency Grid or Cross Tab (includes Statistics Example)
    3. Bayes Theorem (Bayesian Statistics)
    4. Fagan Nomogram
    5. Experimental Error (Experimental Bias)
    6. Lead-Time Bias
    7. Length Bias
    8. Selection Bias (Screening Bias)
    9. Likelihood Ratio (Positive Likelihood Ratio, Negative Likelihood Ratio)
    10. Number Needed to Screen (Number Needed to Treat, Absolute Risk Reduction, Relative Risk Reduction)
    11. Negative Predictive Value
    12. Positive Predictive Value
    13. Receiver Operating Characteristic
    14. Test Sensitivity (False Negative Rate)
    15. Test Specificity (False Positive Rate)
    16. U.S. Preventive Services Task Force Recommendations
  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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