Dichotomous Tests (Tom)

Their results change the probability of disease Negative testPositive test Reassurance Treatment Order a Test A good test moves us across action thresholds. 0%100% T+ T- The best tests are definitive What tests do

Post-Test Probability of Disease Depends on 2 Things 1. Where you started from (low, medium, high) 2. Length and direction of the arrow Basic paradigm: What we thought before + test result = what we think now Prior probability + LR from test = post-test probability LR = P(Result|Disease)/P(Result|No Disease)

Assessing information from dichotomous tests (review): Disease +Disease -Total Test +aba+b True PositivesFalse PositivesTotal Positives Test -cdc+d False NegativesTrue NegativesTotal Negatives Totala+cb+dTotal N Total With Disease Total without Disease Sensitivity=a/(a+c)Specificity =d/(b+d) Positive predictive value (PPV) = a/(a+b); Negative predictive value (NPV) d/(c+d) Prior probability = P(D); Posterior probability = P(D|test result)

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

Whats wrong? StrepNo StrepTotal Rapid Test + TPFPTP+FP Rapid Test - FNTNTN+FN TP+FNFP+TN 2 definitions of false negative rate 1-sensitivity = FN/(TP+FN). This one is easier because its (assumed to be) constant. 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.

If prior probability of strep = 20% 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. (Assumes 98% specificity)

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

Importance of Sampling Scheme If sampling separately from Disease+ and Disease– groups (case-control sampling), cannot calculate prevalence, positive predictive value, or negative predictive value.

Dx Test:Case-Control Sampling Disease + Sampled Separately Disease – Sampled Separately Test + a True Positives b False Positives Test - c False Negatives d True Negatives Total a + c Total With Disease b + d Total Without Disease Sensitivity = a/(a + c) Specificity = d/(b + d)

Dx Test: Cross-sectional Sampling Prevalence = (a + c)/N Positive Predictive Value = a/(a + b) Negative Predictive Value = d/(c + d) Disease +Disease -Total Test +a True Positives b False Positives a + b Total Positives Test -c False Negatives d True Negatives c + d Total Negatives Totala + c Total With Disease b + d Total Without Disease a + b + c + d Total N

R. henselae titers and Cat Scratch Disease* CaseControl R. henselae titer Positive38442 Negative *Zangwill, N Engl J Med. 1993;329:8-13. EBD Problem 3.2 Authors stated negative predictive value = 38/42 = 90.5%. Is there a problem?

Example from Chapter 3 65-year-old woman with mammogram suspicious for malignancy Pre-test probability LR(suspicious for malignancy) 100 Post-test probability = ?

Update Pre-Test Probability Using LR(test result) 1) Convert pre-test probability (P) to pre- test odds. Pre-Test Odds = P/(1-P) 2) Calculate LR. P(result|D+)/P(result|D-). 3) Post-Test Odds = Pre-Test Odds × LR 4) Convert post-test odds to post-test probability. Prob = Odds/(1+Odds)

Update Pre-Test Probability Using LR(test result) 1) Pre-test probability P = Pre-test odds = P/(1-P) ) LR(Suspicious for Malignancy) = 100 3) Post-Test Odds = × 100 = 1.5 4) Post-test probability = Odds/(1+Odds) = 1.5/2.5 = 0.60

Can Use Slide Rule

Threshold Model Single disease (D+,D-) with single treatment (no further testing available) Cost of failing to treat D+ = B Cost of treating D- unnecessarily = C Treat if P(D) > C/(C+B) C/(C+B) = Treatment Threshold Probability = P TT Pauker SG, Kassirer JP.. N Engl J Med Jul 31;293(5):

Define Costs B and C

X-Graph

Introduce a Dichotomous (+/-) Test P(+|D+) = Probability of positive test given D+ = Sensitivity P(-|D-) = Probability of negative test given D- = Specificity P(+|D-) = 1 – Specificity or False Positive Rate P(-|D+) = 1 – Sensitivity of False Negative Rate T = Cost of Test

Pauker SG, Kassirer JP. N Engl J Med May 15;302(20):

X-Graph

New X-Graph

Threshold Formulas

Assumptions in the Threshold Model Threshold Model: One disease One dichotomous test Only two post-test options: treat and no treat Real world: Multiple possible diseases Multiple possible test results (not just +/-) Multiple possible tests Multiple post-test options including observation and additional testing

2) Multilevel Tests (Michael) Likelihood ratios for results other than + or -