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Dichotomous Tests

Dichotomous Tests. Thomas B. Newman, MD, MPH September 27, 2012 Thanks to Josh Galanter and Michael Shlipak. Overview. Clarifications, chapter 1, chapter 2 material Definitions: sensitivity, specificity, prior and posterior probability, predictive value, accuracy 2 x 2 table method

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Dichotomous Tests

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  1. Dichotomous Tests Thomas B. Newman, MD, MPH September 27, 2012 Thanks to Josh Galanter and Michael Shlipak

  2. Overview • Clarifications, chapter 1, chapter 2 material • Definitions: sensitivity, specificity, prior and posterior probability, predictive value, accuracy • 2 x 2 table method • Likelihood ratios - WOWO • Probability and odds • FP/FN confusion • Test/treat thresholds

  3. Clarifications • EBD errata on book website • SLUBI= Self limited undiagnosed benign illness – not a term I use with parents

  4. Definitions: Sensitivity and Specificity Sensitivity = A/ (A+C) Specificity = D/ (B+D) P.I.D. = Positive in Disease N.I.H.= Negative in Health

  5. Accuracy = (A + D)/(A + B + C + D) = (A+D)/N Accuracy demonstration: screening for brain tumors Definitions: Positive and Negative Predictive value, Accuracy PPV=A/(A+B) NPV=D/(C+D)

  6. Definitions: Pretest (prior) and post-test (posterior) probability Pretest probability = (A+C)/(A+B+C+D) Posttest probability = A/(A+B) or C/(C+D) ONLY IF SAMPLING IS “CROSS-SECTIONAL”!

  7. Subjects are sampled randomly or consecutively, so that the proportion with disease (pretest probability, prevalence) is clinically meaningful “Cross-sectional” sampling PPV=A/(A+B) NPV=D/(C+D)

  8. Subjects with and without disease are sampled separately Proportion with disease is determined by investigator “Case-control” sampling PPV=A/(A+B) NPV=D/(C+D)

  9. Prevalence vs Pretest probability • Pretest probability is the more general term • For screening tests, pretest probability = prevalence • For diagnostic tests, pretest probability incorporates history and physical exam items

  10. Post-test probability vs. Predictive value • Posttest probability after a + test is the same as positive predictive value • Posttest probability after a – test is 1– negative predictive value

  11. 2  2 Table Method • Research vignette “Tom, you need to call this mother. She’s really upset.”

  12. Choroid Plexus Cyst

  13. Pretest probability 0.0003 Sensitivity 33% Specificity 98.5% Fill in table

  14. Likelihood Ratios

  15. Likelihood ratios • A ratio of likelihoods:P(Result|Disease)P(Result|No Disease) • WOWO = With Over WithOut • Pretest odds x LR = Posttest odds • (Prior odds x LR = Posterior odds)

  16. Negative test Positive test Reasurance Order a Test Treatment What Tests Do • Their results change the probability of disease HIV- HIV+ 0% 100% • A good test moves us across action thresholds.

  17. Likelihood of Disease Depends on 2 Things • Where you started from (low, medium, high risk) • Length and direction of the “arrow” • Basic paradigm: • What we thought before  test result  what we think now

  18. Likelihood ratio Effect of test result Very small (0.01) Greatly decreases P(disease) Less than 1 (0.5) Decreases P(disease) One No effect on P(disease) More than 1 (2) Increases P(disease) Very big (100) Greatly increases P(disease)

  19. Likelihood Ratios • Advantages • Calculation of post-test probability easier (especially when disease is rare) • Capture information for multi-level and continuous tests (next week) • Disadvantages • If either pretest or posttest probability is high (~> 10%) you need to use odds (or a slide rule or calculator)

  20. Switch to board • LR for the choroid plexus cyst example • Dichotomous test def of LR • Probability and odds

  21. Can Use Slide Rule

  22. False-negative confusion Sensitivity of rapid strep test is 85% Therefore, false negative rate is 15% 15% is too high, so always culture to confirm negative rapid strep tests

  23. What’s wrong? 2 definitions of “false negative rate” Def #1: 1-sensitivity = FN/(TP+FN). This one is easier because it’s (assumed to be) constant. Def #2: 1 - negative predictive value = FN/(FN+TN). This one is harder because it depends on prior probability, but it is the one that should determine clinical decisions. Strep No Strep Total Rapid Test + TP FP TP+FP Rapid Test - FN TN TN+FN TP+FN FP+TN

  24. If prior probability of strep = 20% and specificity is 98% False negative rate (def #2) = 15/407 = 3.7% NNC (number needed to culture) = 1/.037 = 27 to identify 1 false negative rapid test. (Pre-test probability of 20%) At some prior probability of strep, culture after negative quick test is not indicated.

  25. Sensitivity 85% Specificity 98% Prior probability = 20% Rapid test is NEGATIVE LR = Try it with slide rule!

  26. Similar examples: Sensitivity of UA for UTI is only 80%, therefore always culture after a negative UA Sensitivity of CT scan for subarachnoid hemorrhage is only 90%, therefore always do LP after a negative CT False positive confusion is similar: 1-specificity vs. 1-positive predictive value

  27. No test Test Treat Test/Treat Thresholds

  28. “X-Graph”

  29. New “X-Graph”

  30. Questions?

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