1. Medical decision making

2. 2 Predictive values 57-years old, Weight loss, Numbness, Mild fewer What is the probability of low back cancer? Base on demographic prevalence ~20% Should he receive the low-cost ESR-test with sensitivity of 78% and specificity of 67% Expensive MRI scanning with sensitivity and specificity of 95% surgery at once be send home

3. 3 The threshold model for a patient with low back pain The doctor worries about cancer, should the doctor send him home, test, or treat him?

4. 4 The accuracy of a test Sensitivity; The ability to detect patients with the condition Definition: The probability of a positive result in patients who have the condition: True Positive rate High sensitivity ↔ few false negative Specificity; The ability to detect patients without the condition Definition: The probability of a negative result in patients who do not have the condition: True negative rate or1- False Positive rate High specificity ↔ few false positive

5. 5 The accuracy of a test Accuracy = (TP + TN) / total N Known truth Positive D + Negative D - TestPositive T + TP (true-positive)FP (false-positive) Negative T - FN (false-negative)TN (true-negative)

6. 6 The accuracy of a ECG test for myocardial infarction Sensitivity: TP ratio: 6/31 = 0.19 Specificity: TN ratio: 59/72 = 0.82 Known truth MI PresentMI Absent TestST > 5mmTP: 6FP: 13 ST < 5mmFN: 25TN: 59 Total3172

7. 7 Predictive values Assuming 20% chance for this specific patient ESR test has sensitivity = 78% and specificity = 67% (Joines et al. 2001) TP = 78% of 200 = 156 TN = 67% of 800 = 536 FN = 200 – 156 = 44 FP = 800 – 536 = 264 156 + 264 = 420 tested positive 44 + 536 = 580 tested negative D+D+ D-D- TestT+T+ TP: 156FP: 264420 T-T- FN: 44TN: 536580 Total2008001000

8. 8 Predictive values PV + = 156/420 = 0.37 PV - = 536/580 = 0.92 If the test is positive we are 37% sure that it is spinal cancer If it is negative we are 92 % sure it is not D+D+ D-D- TestT+T+ TP: 156FP: 264420 T-T- FN: 44TN: 536580 Total2008001000

9. 9 Predictive values of MRI scan is ESR tested positive Assuming 37% chance for this specific patient FMR test has sensitivity = 95% and specificity = 95% (Joines et al. 2001) PV + = TP/(TP+FP) = 0.92 PV - = TN/(TN+FN) = 0.97 D+D+ D-D- TestT+T+ TP: 351.5FP: 31.5383 T-T- FN: 18.5TN: 598.5617 Total3706301000

10. 10 Likelihood ratio Assuming 20% chance for this specific patient ESR test has sensitivity = 78% and specificity = 67% (Joines et al. 2001) Pretest odds = Prior probability / (1 - Prior probability) = 0.2 / (1 – 0.2) = 0.25 Likelihood ratio (LR) = sensitivity / false positive rate = 0.78 / (1 – 0.67) = 2.36 Posttest odds = 0.25*2.36 = 0.59

11. 11 Probability vs. odds Posttest odds = 0.59 PV + = 0.37

12. 12 Negative likelihood ratio Positive likelihood ratio ( + LR) = 2.36 Is the likelihood ratio that he has the disease if he is tested positive Negative likelihood ratio ( - LR) Is the likelihood ratio that he has the disease if he is tested negative

13. 13 Test with continuous outcome What if the test outcome is continuous? Which threshold should be chosen? Optimizing Specificity and sensitivity Increasing sensitivity at to loss of specificity

14. 14 Receiver operating characteristics (ROC) curve X-axis: 1-Specificity Y-axis: Sensitivity The ROC curve describes the test. Poor test → large overlap → ROC curve close to diagonal Good test → little overlap → ROC curve close to vertical / horizontal

15. 15 Receiver operating characteristics (ROC) curve From wikipedia

16. 16 ROC curve to test beast cancer by mammography StatusNormal 1 Benign 2 Probably benign 3 Suspicious 4 Malignant 5 Total Cancer106111230 No Cancar92118030

17. 17 ROC curve to test beast cancer by mammography How good is the test? Where to put the threshold? StatusNormal 1 Benign 2 Probably benign 3 Suspicious 4 Malignant 5 Total Cancer106111230 No Cancar92118030 Threshold<11.52.53.54.5>5 TPR (sensitivity) 30/30 = 1.00 29/30 = 0.97 23/30 = 0.77 12/30 = 0.40 0/30 = 0.00 FPR (1-specificity) 30/30 = 1.00 21/30 = 0.70 19/30 = 0.63 8/30 = 0.270/30 = 0.00

18. 18 ROC curve to test beast cancer by mammography How good is the test? Where to put the threshold? Threshold<11.52.53.54.5>5 TPR (sensitivity)1.000.97 0.770.400.00 FPR (1-specificity)1.000.700.630.270.00

19. 19 The area under the ROC curve The area under the ROC gives the intrinsic accuracy of a diagnostic test and can be interpreted in several ways (see Hanley et al.): The average sensitivity for all values of specificity The average specificity for all values of sensitivity The probability that the diagnostic score of a diseased patient is more of an indication of disease than the score of a patient without the disease.