1. GerstmanChapter 41 Epidemiology Kept Simple Chapter 4 Screening for Disease

2. GerstmanChapter 42 Identifying Cases “Case” ≡ someone who truly has the condition we are looking for “Diagnostic test” ≡ any method used to detect a cases (not just medical tests)

3. GerstmanChapter 43 Reproducibility & Validity Reproducibility and validity are different aspects of accuracy Reproducibility ≡ agreement upon repetition, i.e., consistency Validity ≡ ability to discriminate accurately

4. GerstmanChapter 44 §4.2 Reproducibility Two independent raters classify each patient as either positive or negative Cross-tabulate results Rater B Rater A +−Total +abp1p1 −cdq1q1 p2p2 q2q2 N We quantify reproducibility with this kappa (κ) statistic Link to Formula sheetFormula sheet

5. GerstmanChapter 45 Kappa Interpretation κ = 1 → perfect agreement 0.7 < κ < 1 → excellent agreement 0.3 < κ < 0.7 → fair agreement κ < 0.3 → poor agreement κ ≈ 0 → random agreement κ = −1 → perfect disagreement κ quantifies agreement above chance

6. GerstmanChapter 46 Example: Kappa Rater B Rater A D+D−Total D+20424 D−57176 Total2575100 To what extent are these results reproducible?  Excellent agreement

7. GerstmanChapter 47 §4.3 Validity Compare test results to gold standard Each patient is classified as either true positive (TP), true negative (TN), false positive (FP), or false negative (FN) Crosstab results Test D+D−D−Total T+TPFPTP+FP T−FNTNFN+TN TotalTP+FNFP+TNN

8. GerstmanChapter 48 Sensitivity Test D+D−D−Total T+TPFPTP+FP T−FNTNFN+TN TotalTP+FNFP+TNN Sensitivity (SEN) ≡ proportion of cases that test positive

9. GerstmanChapter 49 Specificity Specificity (SPEC) ≡ proportion of noncases that test negative Test D+D−D−Total T+TPFPTP+FP T−FNTNFN+TN TotalTP+FNFP+TNN

10. GerstmanChapter 410 Predictive Value Positive Test D+D−D−Total T+TPFPTP+FP T−FNTNFN+TN TotalTP+FNFP+TNN Predictive value positive (PVP) ≡ proportion of positive tests that are actually cases

11. GerstmanChapter 411 Predictive Value Negative Test D+D−D−Total T+TPFPTP+FP T−FNTNFN+TN TotalTP+FNFP+TNN Predictive value negative (PVN) ≡ proportion of negative tests that are actually non-cases

12. GerstmanChapter 412 Prevalence [True] prevalence = (TP + FN) / N Apparent prevalence = (TP + FP) / N Test D+D−D−Total T+TPFPTP+FP T−FNTNFN+TN TotalTP+FNFP+TNN

13. GerstmanChapter 413 Conditional Probabilities Pr(A|B) ≡ “the probability of A given B”, e.g., Pr(T+|D+) ≡ “probability test positive given disease positive” SEN = Pr(T+|D+) SPEC ≡ Pr(T−|D−) PVP = Pr(D+|T+) PVN= Pr(D−|T−)

14. GerstmanChapter 414 Example: Low Prevalence Population D+D−Total T+ T− Total 1000 1,000,000 Conditions: N = 1,000,000; Prevalence =.001 Prevalence = (those with disease) / N Therefore: (Those with disease) = Prevalence × N =.001× 1,000,000 = 1000

15. GerstmanChapter 415 Example: Low Prevalence Population D+D−Total T+ T− Total1000 999,000 1,000,000 Number of non-cases, i.e., TN + FP 1,000,000 – 1,000 = 999,000

16. GerstmanChapter 416 Example: Low Prevalence Population D+D−Total T+990 T− Total1000 TP = SEN × (TP + FN) = 0.99 × 1000 = 990 Assume test SENsitivity =.99, i.e., Test will pick up 99% of those with disease

17. GerstmanChapter 417 Example: Low Prevalence Population D+D−Total T+990 T− 10 Total1000 FN = 1000 – 990 = 10 It follows that:

18. GerstmanChapter 418 Example: Low Prevalence Population D+D−Total T+ T− 989,010 Total999,000 TN = SPEC × (TN + FP) = 0.99 × 999,000 = 989,010 Suppose test SPECificity =.99 i.e., it will correctly identify 99% of the noncases

19. GerstmanChapter 419 Example: Low Prevalence Population D+D−Total T+ 9,990 T−989,010 Total999,000 FPs = 999,000 – 989,010 = 9,900 It follows that:

20. GerstmanChapter 420 Example: Low Prevalence Population D+D−Total T+9909,99010,980 T−10989,010989,020 Total1000999,0001,000,000 PVP = TP / (TP + FP) = 990 / 10,980 = 0.090 Strikingly low PVP! It follows that the Predictive Value Positive is :

21. GerstmanChapter 421 Example: Low Prevalence Population D+D−Total T+9909,99010,980 T−10989,010989,020 Total1000999,0001,000,000 PVN = TN / (TN + FP) = 989010 / 999000 = 0.99 It follows that the Predictive Value Negative is:

22. GerstmanChapter 422 Example: High prevalence population D+D−Total T+99,0009,000108,000 T−1,000891,000892,000 Total100,000900,0001,000,000 SEN = 99000 / 100,000 = 0.99 SPEC = 891,000 / 900,000 = 0.99 Prev = 100000 / 1,000,000 = 0.10 Same test parameters but used in population with true prevalence of.10

23. GerstmanChapter 423 Example: High prevalence population D+D−Total T+99,0009,000108,000 T−1,000891,000892,000 Total100,000900,0001,000,000 PVP = 99,000 / 108,000 = 0.92 PVN = 891,000 / 900,000 = 0.99 Prevalence = 100000 / 1,000,000 = 0.10 An HIV screening test is used in one million people. Prevalence in population is now 10%. SEN and SPEC are again 99%.

24. GerstmanChapter 424 PVP and Prevalence PVP a function of –PREValence –SENsitivity –Specificity Figure shows relation between PVP, PREV, & SPEC (test SEN = constant.99)

25. GerstmanChapter 425 Screening Strategy First stage  high SENS (few cases missed) Second stage  high SPEC (sort out false positives from true positives)

26. GerstmanChapter 426 Cutoff Point Concept Sensitivity and specificity are influenced by they cutoff point used to determine positive results Example: Immunofluorescence HIV optical density ratio At what point do we say optical density is sufficiently high to say the test is positive?

27. GerstmanChapter 427 Low Cutoff High sensitivity and low specificity

28. GerstmanChapter 428 High Cutoff Low sensitivity and high specificity

29. GerstmanChapter 429 Intermediate Cutoff moderate sensitivity & moderate specificity