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1 Diagnostic tests Subodh S Gupta MGIMS, Sewagram

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Standard 2 X 2 table Standard 2 X 2 table (For Diagnostic Tests) Disease Status Present (D+) Absent (D-) Total Diagnostic test Positive (T+) aba+b Negative (T-) cdc+d Totala+cb+dN Gold Standard

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Standard 2 X 2 table Standard 2 X 2 table (For Diagnostic Tests) Disease Status Present (D+) Absent (D-) Diagnostic test Positive (T+) TPFP Negative (T-) FNTN Gold Standard

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Gold standard In any study of diagnosis, the method being evaluated has to be compared to something The best available test that is used as comparison is called the GOLD STANDARD Need to remember that all gold standards are not always gold; New test may be better than the gold standard

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Test parameters Sensitivity = Pr(T+|D+) = a/(a+c) --Sensitivity is PID (Positive In Disease) Specificity = Pr(T-|D-) = d/(b+d) --Specificity is NIH (Negative In Health) Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) aba+b Negative (T-) cdc+d Totala+cb+dN Gold Standard

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Test parameters False Positive Rate (FP rate) = Pr(T+|D-) = b/(b+d) False Negative Rate (FN rate) = Pr(T-|D+) = c/(a+c) Diagnostic Accuracy = (a+d)/n Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) aba+b Negative (T-) cdc+d Totala+cb+dN Gold Standard

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Test parameters Positive Predictive Value (PPV) = Pr(D+|T+) = a/(a+b) Negative Predictive Value (NPV) = Pr(D-|T-) = d/(c+d) Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) aba+b Negative (T-) cdc+d Totala+cb+dN Gold Standard

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Sensitivity = 90/(90+10), Specificity = 95/(95+5) FP rate = 5/ (95+5); FN Rate = 10/ (90+10) Diagnostic Accuracy = (90+95) / ( ) PPV = 90/(90+5); NPV = 95/(95+10) Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) Negative (T-) Total Test parameters: Example Gold Standard

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Sensitivity90% Specificity95% False Negative Rate10% False Positive Rate5% PPV94.7% NPV90.5% Diagnostic Accuracy92.5% PPV & NPV with Prevalence

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Healthy population vs sick population Healthy Sick

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Predictive Values in hospital-based data

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Predictive Values in population-based data

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Prevalence = 50% PPV = 94.7% NPV = 90.5% Diagnostic Accuracy = 92.5% Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) Negative (T-) Total Test Parameters: Example Gold Standard

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Prevalence = 5% PPV = 48.6% NPV = 99.4% Diagnostic Accuracy = 94.8% Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) Negative (T-) Total Test Parameters: Example Gold Standard

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Prevalence = 0.5% PPV = 8.3% NPV = 99.9% Diagnostic Accuracy = 95% Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) Negative (T-) Total Test Parameters: Example Gold Standard

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Prevalence = 0.05% PPV = 0.9% NPV = 100% Diagnostic Accuracy = 95% Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) Negative (T-) Total Test Parameters: Example Gold Standard

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Prevalence50%5%0.5%0.05% Sensitivity90% Specificity95% PPV94.7%48.6%8.3%0.9% NPV90.5%99.4%99.9%100% Diagnostic Accuracy 92.5%94.8%95% PPV & NPV with Prevalence

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Trade-offs between Sensitivity and Specificity

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BE-Workshop-DT-July When we use Diagnostic test clinically, we do not know who actually has and does not have the target disorder, if we did, we would not need the Diagnostic Test. Our Clinical Concern is not a vertical one of Sensitivity and Specificity, but a horizontal one of the meaning of Positive and Negative Test Results. Sensitivity and Specificity solve the wrong problem!!!

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BE-Workshop-DT-July When a clinician uses a test, which question is important ? If I obtain a positive test result, what is the probability that this person actually has the disease? If I obtain a negative test result, what is the probability that the person does not have the disease?

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Test parameters Sensitivity = Pr(T+|D+) = a/(a+c) Specificity = Pr(T-|D-) = d/(b+d) PPV = Pr(D+|T+) = a/(a+b) NPV = Pr(D-|T-) = d/(c+d) Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) aba+b Negative (T-) cdc+d Totala+cb+dN Gold Standard

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24 Likelihood Ratios Likelihood Ratio is a ratio of two probabilities Likelihood ratios state how many time more (or less) likely a particular test results are observed in patients with disease than in those without disease. LR+ tells how much the odds of the disease increase when a test is positive. LR- tells how much the odds of the disease decrease when a test is negative

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25 The likelihood ratio for a positive result (LR+) tells how much the odds of the disease increase when a test is positive. The likelihood ratio for a negative result (LR-) tells you how much the odds of the disease decrease when a test is negative

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26 The LR for a positive test is defined as: LR (+) = Prob (T+|D) / Prob(T+|ND) LR (+) = [TP/(TP+FN)] [FP/(FP+TN)] LR (+) = (Sensitivity) / (1-Specificity) Likelihood Ratios

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27 The LR for a negative test is defined as: LR (-) = Prob (T-|D) / Prob(T-|ND) LR (-) = [FN/(TP+FN)] [TP/(FP+TN)] LR (-) = (1-Sensitivity) / (Specificity) Likelihood Ratios

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28 What is a good Likelihood Ratios? A LR (+) more than 10 or a LR (-) less than 0.1 provides convincing diagnostic evidence. A LR (+) more than 5 or a LR (-) less than 0.2 is considered to give strong diagnostic evidence.

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Likelihood Ratio for a positive test = (90/100) / (5/100) = 90/ 5 = 18 Likelihood Ratio for a negative test = (10/100) / (95/100) = 10/ 95 = 0.11 Disease Status Present (D+) Absent (D-) Total Diagnostic Test Positive (T+) Negative (T-) Total Likelihood Ratio: Example Gold Standard

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Exercise In a hypothetical example of a diagnostic test, serum levels of a biochemical marker of a particular disease were compared with the known diagnosis of the disease. 100 international units of the marker or greater was taken as an arbitrary positive test result:

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Example Disease Status PresentAbsentTotal Marker >= < Total

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Exercise Initial creatine phosphokinase (CK) levels were related to the subsequent diagnosis of acute myocardial infarction (MI) in a group of patients with suspected MI. Four ranges of CK result were chosen for the study:

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Exercise Disease Status PresentAbsentTotal CPK >= Total

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35 Odds and Probability Probability of Disease = (# with disease) / (# with & # without disease) = a/ (a+b) Odds of a disease = (# with disease) / (# without disease) = a/ b Probability = Odds/ (Odds+1); Odds = Probability / (1-Probability) Disease Status PresentAbsentTotal aba+b

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36 Use of Likelihood Ratio Employment of following three step procedure: 1. Identify and convert the pre-test probability to pre-test odds. 2. Determine the post-test odds using the formula, Post-test Odds = Pre-test Odds * Likelihood Ratio 3. Convert the post-test odds into post-test probability.

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37 Likelihood Ratio: Example A 52 yr woman presents after detecting 1.5 cm breast lump on self-exam. On clinical exam, the lump is not freely movable. If the pre-test probability is 20% and the LR for non-movable breast lump is 4, calculate the probability that this woman has breast cancer.

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38 Likelihood Ratio: Solution First step Pre-test probability = 0.2 Pre-test odds = Pre-test prob / (1-pre-test prob) Pre-test odds = 0.2/(1-0.2) = 0.2/0.8 = 0.25 Second step Post-test odds Pre-test odds * LR Post-test odds = 0.25*4 = 1 Third step Post-test probability = Post-test odds / (1 + Post-test odds) Post-test probability = 1/(1+1) = ½ = 0.5

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Receiver Operating Characteristic (ROC) Finding a best test Finding a best cut-off Finding a best combination probably negative Equivocal Probably positive Definitive positive

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ROC curve constructed from multiple test thresholds

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Receiver Operating Characteristic (ROC) ROC Curve allows comparison of different tests for the same condition without (before) specifying a cut-off point. The test with the largest AUC (Area under the curve) is the best.

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Features of good diagnosis study Comparative (compares new test against old test). Should be a gold standard Should include both positive and negative results Usually will involve blinding for both patient, tester and investigator.

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Gold standard In any study of diagnosis, the method being evaluated has to be compared to something The best available test that is used as comparison is called the GOLD STANDARD Need to remember that all gold standards are not always gold; New test may be better than the gold standard

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Typical setting for finding Sensitivity and Specificity Best if everyone who gets the new test also gets gold standard Doesnt happen in the real world Not even a sample of each (case-control type) Case series of patients who had both tests

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Setting for finding Sensitivity and Specificity Sensitivity should not be tested in sickest of sick Should include spectrum of disease Specificity should not be tested in healthiest of healthy Should include similar conditions.

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51 How precise are the estimates of Sensitivity, Specificity, False Positive Rate, False Negative Rate, Positive Predictive Value and Negative Predictive Value? If reported without a measure of precision, clinicians cannot know the range within which the true values of the indices are likely to lie. When evaluations of diagnostic accuracy are reported the precision of test characteristics should be stated. Precision

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Sample size for adequate sensitivity

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Sample size for adequate specificity

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Exercise Dr Egbert Everard wants to test a new blood test (Sithtastic) for the diagnosis of the dark side gene. He wants the test to have a sensitivity of at least 70% and a specificity of 90% with 5% confidence levels. Disease prevalence in this population is 10%. (i) How many patients does Egbert need to be 95% sure his test is more than 70% sensitive? (ii) How many patients does Egbert need to be 95% sure that his test is more than 90% specific?

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BE-Workshop-DT-July Biases in Research on Diagnostic Tests Observer Bias Spectrum Bias Reference Test Bias Bias Index Work-Up (Verification Bias) Diagnostic Suspicion Bias

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BE-Workshop-DT-July Observer bias Blinding Investigators should be blinded to the test results when interpreting the reference test, and blinded to the reference test results when interpreting the test. Should they also be blinded to other patient characteristics?

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BE-Workshop-DT-July Indeterminate results dropped from analysis Spectrum bias

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BE-Workshop-DT-July Reference Test Bias What if the Gold Standard is not gold after all? Absence of Gold standard Methods to deal with the absence of a gold standard: Correcting for Reference Test Bias (Gart & Buck) Bayesian estimations (Joseph, Gyorkos, Coupal) Latent class modeling (Walter, Cook, Irwig)

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BE-Workshop-DT-July BIAS INDEX What if the test itself commits a certain types of errors more commonly than the other? BI = (b-c)/N

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BE-Workshop-DT-July Work-up (Verification Bias) Occurs when a test efficacy study is restricted to patients in whom the disease status is known. A study by Borow et al (Am Heart J,1983) on patients who were referred for valve surgery on the basis of echocardiographic assessment reported excellent diagnostic agreement between the findings at echocardiography and at surgery.

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BE-Workshop-DT-July Review Bias The Test and Gold Standard should follow a randomized sequence of administration. This tends to offset the Diagnostic Suspicion Bias that may creep in, when the Gold Standard is always applied and interpreted last. It will also balance any effect of time on rapidly increasing severity of the disease and thereby avoid a bias towards more positives in the test which is performed later.

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BE-Workshop-DT-July Ethical Issues in Diagnostic Test Research Invasive techniques Labeling Confidentiality Human subjects

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BE-Workshop-DT-July QUALITIES OF STUDIES EVALUATING DIAGNOSTIC TESTS Reid MC et al. Use of methodological standards in diagnostic test research: getting better but still not good. JAMA 1995; 274: 645. Review of studies published between Work-up Bias: 38% Studies Observer Bias (Blinding): 53% Studies Bias from Indeterminate Results: 62% Studies No assessment of variability across test observers, test instruments, or time: 68% Studies

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BE-Workshop-DT-July QUALITIES OF STUDIES EVALUATING DIAGNOSTIC TESTS Small Sample Size, with no description of Confidence Intervals: 76% Studies Patient Characteristics not described: 68% Studies Possible Interactions or Effect Modification Ignored: 88% Studies Only two (6%) of 34 articles published from (N Engl J Med, JAMA, Lancet, BMJ) met six or more of the Standards.

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BE-Workshop-DT-July USERS GUIDES TO THE MEDICAL LITERATURE How to use an Article about a Diagnostic Test? Are the results of the study valid? What are the results and will they help me in caring for my patients?

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66 1. Was there an independent, blind comparison with a gold standard of diagnosis? 2. Was the setting for the study as well as the filter through which the study patients passed, adequately described? 3. Did the patient sample include an appropriate spectrum of disease? 4. Have they done analysis of the pertinent subgroups 5. Where the tactics for carrying out the test described in sufficient detail to permit their exact replication? Methodological Questions for Appraising Journal Articles about Diagnostic Tests

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67 6. Was the reproducibility of the test result (precision) and its interpretation (observer variation) determined? 7. Was the term normal defined sensibly? 8. Was precision of the test statistics given? 9. Was the indeterminate test results presented? 10. If the test is advocated as a part of a cluster or sequence of tests, was its contribution to the overall validity of the cluster or sequence determined? 11. Was the utility of the test determined?

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Thank you

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