Diagnostic Testing. Coniecturalem artem esse medicinam

Transcription

1 Diagnostic Testing Coniecturalem artem esse medicinam

2 Game of Dice A: a fair die shows an even number B: a fair die shows at least 4 points A: B: A B: P(A=1/2 P(B=1/2 P(A B=2/6 P(A B = 2/6 > 1/4 = 1/2 1/2 = P(A P(B A and B are not independent

3 Conditional Probability B: A? The conditional probability, P(A B, of A "given B has occurred" is 2/3, i.e. larger than the unconditional probability P(A=1/2. P(A B = P(A B P(B

4 Conditional Probability A B A B= A and B independent P(A B P (A B = = 0 P(B P(A P(B P (A B = = P(A P(B

5 Blood Pressure and Cholesterol A: random adult US American has high blood pressure P(A=0.25 B: random adult US American has a high blood cholesterol level A B: random adult US American is both hypertensive and hyperlipidemic P(B=0.20 P(A B=0.17 P(A B 0.17 P (A B = = = 0.85 > 0.25 = P(B 0.20 P(A

6 Bayes' Theorem Essay Towards Solving a Problem in the Doctrine of Chances. Thomas Bayes ( published posthumously by Richard Price in the Philosophical Transactions of the Royal Society of London 1763

7 Bayes' Theorem Bayes' theorem relates posteriorprobabilities to prior and conditional probabilities. P(A B = P(B A P(B P(A Proof: P(A B = P(A B P(B = P(B A P(A P(A P(B = P(B A P(B P(A

8 Law of Total Probability B A A c P(B = P(B A P(A P(B A C P(A C

9 Bayes' Theorem From the Law of Total Probability: P(A B = P(B A P(B A P(A P(A P(B A C P(A C

10 Diagnostic Test Any testing procedure designed to separate people or objects according to a fixed characteristic or property.

11 HIV Infection and ELISA Test The ELISA test for HIV infection returns a positive result for 99.5% of infected, and a negative result for 99.5% of non-infected individuals tested. What is the probability that an individual with a positive test result is infected, given that the prevalence of HIV infection is 0.01% in the general ("low-risk" population? D: individual is infected D C : individual is not infected T : test result is positive T - : test result is negative P (T D = C D = 1 P (D = P(D C = C D = = P(D T D P(D D P(D D = P(D = C C

12 Diagnostic Test Nomenclature D: presence of (predisposition to disease D C : absence of (predisposition to disease T : test result is positive T - : test result is negative test-dependent D: sensitivity - D C : specificity population-dependent P(D: prevalence test-dependent, population-dependent P(D T : positive predictive value (PPV P(D C T - : negative predictive value (NPV

13 Diagnostic Test Bayes Theorem (Positive Predictive Value P(D T D P(D D P(D D C P(D = C D P(D D P(D [1 D = C ] [1 P(D] PPV = sensitivity prevalence sensitivity prevalence (1 specificity (1 prevalence

14 Diagnostic Test Bayes Theorem (Negative Predictive Value prevalence sensitivity (1 prevalence (1 specificity prevalence (1 specificity NPV = P(D D P(D D P(D D T (D P C C C C C = P(D D] [1 P(D] [1 D P(D] [1 D C C =

15 Hypothetical Population (n=100 NPV: 49/55 = 89% specificity: 49/70 = 70% sensitivity: 24/30 = 80% PPV: 24/45 = 53%

16 HIV Infection and ELISA Test Predictive Value Prevalence : PPV : NPV

17 Schizophrenia and Brain Atrophy Some 30% of schizophrenic patients suffer from brain atrophy, compared to only 2% of the unaffected ("normal" population. If the prevalence of schizophrenia is assumed to be 1.5%, what is the probability that an atrophic individual is schizophrenic? P (T D = D C = P (D = P(D C = P(D T D P(D D P(D D = P(D = C C 0.186

18 Schizophrenia and Brain Atrophy Predictive Value Prevalence : PPV : NPV

19 Likelihood Ratio compares the probability of a given test result in affected and non-affected individuals positive likelihood ratio negative likelihood ratio LR = D C D LR = D C D 1 sensitivity specificity 1 sensitivity specificity

20 Bayes' Theorem Likelihoods and Odds P(D T P(D T = P(D P(D C C D D C posterior odds = prior odds. likelihood ratio

21 Creatine Kinase and Myocardial Infarction creatine kinase 80 U/l myocardial infarction yes no total 231 <80 U/l total prior odds likelihood ratio posterior odds /230 = 1.77 = = /130 45

22 Diagnostic Studies Aim In order to make reasonable decisions about the utility of a new diagnostic test, the quality of the test needs to be assessed in a diagnostic study. This includes addressing - the performance(i.e. how sensitive and specific is the test? -the validity(i.e. how accurate is the test? - the reliability(i.e. how precise is the test?

23 Diagnostic Studies Quality Was there an independent, blind comparison with a reference ('gold' standard of diagnosis? Was the reference standard applied regardless of the diagnostic test result? Was the diagnostic test evaluated in an appropriate spectrum of patients(like those in whom it would be used in practice? Was the test validated in a second, independent groupof patients?

24 Diagnostic Test Reliability Criteria Does the test result depend on clinical features such as severity and chronicity? Does the test result depend on the disease pathology(location, extent? Is the test result influenced by the presence of other diseases?

25 Diagnostic Test Practical Applicability Is the diagnostic test sensible, availableand affordable in your setting? Can you generate a sensible estimate of your proband's prior probability of disease? Will the resulting posterior probability affect your management of the proband? Will the consequences of the test help your proband?

26 Measures of Test Performance sensitivity and specificity Youden's index likelihood ratios ROC curve population-dependent positive and negative predictive values diagnostic accuracy

27 Measures of Test Performance Sensitivity sensitivity: probability that an affected (or predisposed individual tests positive test result disease positive negative present absent true positive false negative false positive true negative The 'SnNOut'Rule: With a test of high Sensitivity, a Negative test result rules Out disease (or predisposition.

28 Measures of Test Performance Specificity specificity: probability that an unaffected (or nonpredisposed individual tests negative test result disease positive negative present absent true positive false negative false positive true negative The 'SpPIn'Rule: With a test of high Specificity, a Positive test result rules In disease (or predisposition.

29 Measures of Test Performance Practical Criteria aim: high sensitivity high costs of false negatives treatable disease no side effects of treatment fatal if untreated strong confidence in negative results required Example: Guthrie Test (phenylketonuria aim: high specificity high costs of false positives untreatable disease strong side effects of treatment not fatal if untreated strong confidence in positive results required Example: Pre-surgery tumour grading

30 Measures of Test Performance Youden's Index Youden's index: total improvement over random choice of diagnosis ("coin tossing" test result disease positive negative present absent true positive false negative false positive true negative D 1 2 D C 1 2

31 Measures of Test Performance Diagnostic Accuracy diagnostic accuracy: probability of a correct test result test result disease positive negative present absent true positive false negative false positive true negative D P(D D C P(D C

32 Schizophrenia and Brain Atrophy P (T D = D C = 0.30 sensitivity: 0.30 specificity: P (D = P(D C = PPV : NPV: Youden's index: 0.28 diagnostic accuracy: 0.97

33 Continuous Test Results Dichotomization Continuous test resultsare often dichotomized(i.e. turned into "positive" or "negative" outcomes by means of comparing them to a predefined threshold ('cut-off' value. The choice of the cut-off value depends critically upon the purpose of the test and can be based upon - a Gaussian criterion - predefined sensitivity or specificity -the ROC curve

34 Gestational Diabetes Mellitus A prospective, population-based study of 520 pregnant women was undertaken at the University Hospital Zurich in order to evaluate whether measuring fasting plasma glucose concentration is an acceptable screening procedure for gestational diabetes, avoiding a screening (50 g glucose challenge test. Perucchini D et al. (1999 BMJ 319: Cut-off values of the diagnostic glucose tolerance test ("gold-standard" Time Fasting 1 hour 2 hours 3 hours Plasma Concentration 5.3 mmol/l 10.0 mmol/l 8.6 mmol/l 7.8 mmol/l Gestational diabetes is diagnosed if two or more values equal or exceed the cut-off

35 Continuous Test Results Gaussian Criterion distribution of test results in unaffected controls 95% 95% positive negative positive negative positive Problems: - no attention given to sensitivity - distribution may not be normal - controls may not be representative

36 Continuous Test Results Predefined Sensitivity or Specificity specificity sensitivity specificity sensitivity controls patients specificity sensitivity negative result positive result

37 Continuous Test Results ROC Curve Sensitivity Specificity

38 Continuous Test Results ROC Curve Sensitivity maximizes Youden's index Specificity

39 Gestational Diabetes Mellitus sensitivity 1-specificity

40 Summary -Bayes' theorem relates posteriorprobabilities to priorand conditionalprobabilities. -Diagnostic tests serve to distinguish between groupsof individuals on the basis of associated characteristics. -The performance of a diagnostic test is characterised by its sensitivity and specificity. -The utility of a diagnostic test in a given population depends upon the disease prevalence, and is measured by the two (population-dependent predictive values. -Continuous test resultscan be dichotomized, for example, by determining a cut-off value using an ROC curve.

41 Appendix Differential Diagnostics A diagnostic marker may be indicative of a number (k of different diseases. T: individual shows the marker K i : individual suffers from the i th disease P(K i T = k j = 1 K K i P(K j i P(K j

42 Appendix: Genetic Lesions and Lung Cancer Mutations in the p53 and K-ras genes, together with hypermethylation of the p16 INK4a promoter, in exfoliative material from patients with bronchial disease are a marker (T of lung cancer and tumour type. Kersting M et al. (2000 J Clin Oncol 18: i K i K i smokers P(K i P(K i T non-smokers P(K i P(K i T 1 NSCLC SCLC benign