1. TEACHING ABOUT DIAGNOSIS
Tom Sensky
Teaching EBM/EBMH
St Hugh’s College Oxford
September 2005

2. BY THE END OF THIS SESSION, YOU SHOULD BE ABLE TO ….
describe and illustrate key measures of diagnostic test performance
describe some less commonly quoted measures of diagnostic test performance
represent diagnostic test performance in at least four different ways (five if time allows!)

3. METHOD 1: NATURAL FREQUENCIES GRID
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Assume that the prevalence of the disease is 4%

4. Assume that of the 4 people with the disease, 3 are picked up by the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test

5. Assume that of the test is positive for a further 7 people who don’t have the disease
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test

6. The remainder of the sample are negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test

7. SENSITIVITY
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
SENSITIVITY is the proportion of people with the disease correctly identified by the test
It measures the proportion of false NEGATIVES

8. SENSITIVITY In this case, sensitivity is ¾ or 75%
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
In this case, sensitivity is ¾ or 75%

9. SPECIFICITY
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
SPECIFICITY is the proportion of people without the disease correctly identified by the test
It measures the proportion of false POSITIVES

10. SPECIFICITY In this case, specificity is (96-7)/96 or 93%
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
In this case, specificity is (96-7)/96 or 93%

11. If someone is positive on the test, what are the chances that he/she has the disease?
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Probability = 3/10 = 30%
This is the POSITIVE PREDICTIVE VALUE (the value of the test in predicting a positive result)

12. If someone is negative on the test, what are the chances that he/she does not have the disease?
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Person without the disease
Person with the disease
Person who tests positive
Person who tests negative
True positive on the test
False positive on the test
True negative on the test
False negative on the test
Probability = 89/90 = 99%
This is the NEGATIVE PREDICTIVE VALUE (the value of the test in predicting a negative result)

13. SENSITIVITY, SPECIFICITY AND PREDICTIVE VALUES
For sensitivity and specificity, the reference variable (‘denominator) is the DISEASE
For predictive value, the reference variable (‘denominator’) is the TEST

14. METHOD 2: NATURAL FREQUENCIES TREE
Population
100

15. IN EVERY 100 PEOPLE, 4 WILL HAVE THE DISEASE
Population
100
Disease + 4
Disease - 96
If these 100 people are representative of the population at risk, the assessed rate of those with the disease (4%) represents the PREVALENCE of the disease – it can also be considered the PRE-TEST PROBABILITY of having the disease

16. OF THE 4 PEOPLE WITH THE DISEASE, THE TEST WILL DETECT 3
Population
100
Disease + 4
Disease - 96
In other words, the sensitivity is 75%
Test + 3
Test - 1

17. AMONG THE 96 PEOPLE WITHOUT THE DISEASE, 7 WILL TEST POSITIVE
In other words, the specificity is 93%
Population
100
Disease + 4
Disease - 96
Test + 3
Test - 1
Test + 7
Test - 89

18. AMONG THOSE WHO TEST POSITIVE, 3 IN 10 WILL ACTUALLY HAVE THE DISEASE
This is also the POST-TEST PROB- ABILITY of having the disease
Population
100
Disease + 4
Disease - 96
POSITIVE
PREDICTIVE
VALUE = 30%
Test + 3
Test + 7
Test - 1
Test - 89

19. AMONG THOSE WHO TEST NEGATIVE, 89 OF 90 WILL NOT HAVE THE DISEASE
Population
100
Disease + 4
Disease - 96
Test + 3
Test + 7
NEGATIVE
PREDICTIVE
VALUE = 99%
Test - 1
Test - 89

20. CONVERSELY, IF SOMEONE TESTS NEGATIVE, THE CHANCE OF HAVING THE DISEASE IS ONLY 1 IN 90
Population
100
Disease + 4
Disease - 96
Test + 3
Test + 7
Test - 1
Test - 89

21. PREDICTIVE VALUES AND CHANGING PREVALENCE
Population
1000
Disease + 4
Disease -
996
Prevalence reduced by an order of magnitude from 4% to 0.4%

22. PREDICTIVE VALUE AND CHANGING PREVALENCE
Population
1000
Sensitivity and Specificity unchanged
Disease + 4
Disease -
996
Test + 3
Test + 70
Test - 1
Test -
926

23. POSITIVE PREDICTIVE VALUE AT LOW PREVALENCE
Population
1000
Previously, PPV was 30%
Disease + 4
Disease -
996
POSITIVE
PREDICTIVE
VALUE = 4%
Test + 3
Test + 70
Test - 1
Test -
926

24. NEGATIVE PREDICTIVE VALUE AT LOW PREVALENCE
Population
1000
Previously, NPV was 99%
Disease + 4
Disease -
996
Test + 3
Test + 70
NEGATIVE
PREDICTIVE
VALUE >99%
Test - 1
Test -
926

25. PREDICTION OF LOW PREVALENCE EVENTS
Even highly specific tests, when applied to low prevalence events, yield a high number of false positive results
Because of this, under such circumstances, the Positive Predictive Value of a test is low
However, this has much less influence on the Negative Predictive Value

26. RELATIONSHIP BETWEEN PREVALENCE AND PREDICTIVE VALUE
Difference between PPV and NPV relatively small
Difference between PPV and NPV relatively large
Based on a test with 90% sensitivity and 82% specificity

27. RELATIONSHIP BETWEEN PREVALENCE AND PREDICTIVE VALUE
Based on a test with 75% sensitivity and 93% specificity

28. PERFORMANCE OF A TEST WITH CHANGING PREVALENCE
A : Sensitivity = Specificity = 0.9
LR+ = 9.0
B : Sensitivity = Specificity = 0.7
LR+ = 3.0
C : Sensitivity = Specificity = 0.5
LR+ = 1.0
POST-TEST PROBABILITY

29. LIKELIHOOD Population 100 Disease + 4 Test + 3 Test - 1
The likelihood that someone with the disease will have a positive test is ¾ or 75%
This is the same as the sensitivity
Test + 3
Test - 1

30. LIKELIHOOD II Population 100 Disease - 96 Test + 7 Test - 89
The likelihood that someone without the disease will have a positive test is 7/96 or 7%
This is the same as the (1-specificity)
Test + 7
Test - 89

31. LIKELIHOOD RATIO LIKELIHOOD OF POSITIVE TEST GIVEN THE DISEASE=
LIKELIHOOD OF POSITIVE TEST
IN THE ABSENCE OF THE DISEASE
SENSITIVITY
1- SPECIFICITY
0.75
0.07 = =
= 10.7
A Likelihood Ratio of 1.0 indicates an uninformative test (occurs when sensitivity and specificity are both 50%)
The higher the Likelihood Ratio, the better the test (other factors being equal)

32. METHOD 3: ‘TRADITIONAL’ 2x2 TABLES

33. SENSITIVITY SENSITIVITY
FALSE NEGATIVES
SENSITIVITY
The proportion of people with the diagnosis (N=4) who are correctly identified (N=3)
Sensitivity = a/(a+c) = 3/4 = 75%

34. SPECIFICITY SPECIFICITY
FALSE POSITIVES
SPECIFICITY
The proportion of people without the diagnosis (N=96) who are correctly identified (N=89)
Specificity = d/(b+d) = 89/96 = 93%

35. PRE-TEST ODDS
In the sample as a whole, the odds of having the disease are 4 to 96 or 4% (the PRE-TEST ODDS)

36. POST-TEST ODDS
In the sample as a whole, the odds of having the disease are 4 to 96 or 4% (the PRE-TEST ODDS)
In those who score positive on the test, the odds of having the disease are 3 to 7 or 43% (the POST-TEST ODDS)

37. POST-TEST ODDS
In the sample as a whole, the odds of having the disease are 4 to 96 or 4% (the PRE-TEST ODDS)
In those who score positive on the test, the odds of having the disease are 3 to 7 or 43% (the POST-TEST ODDS)
In those who score negative on the test, the odds of having the disease are 1 to 89 or approximately 1%

38. DIAGNOSTIC ODDS RATIO
Potentially useful as an overall summary measure, but only in conjunction with other measures (LR, sensitivity, specificity)
The Diagnostic Odds Ratio is the ratio of odds of having the diagnosis given a positive test to those of having the diagnosis given a negative test

39. LIKELIHOOD RATIO x PRE-TEST ODDS
BAYES THEOREM
POST-TEST ODDS =
LIKELIHOOD RATIO x PRE-TEST ODDS

40. LIKELIHOOD RATIO AND PRE- AND POST-TEST PROBABILITIES
For a given test with a given likelihood ratio, the post-test probability will depend on the pre-test probability (that is, the prevalence of the condition in the sample being assessed)

41. SENSITIVITY ANALYSIS OF A DIAGNOSTIC TEST
Value
95% CI
Pre-test probability
35%
26% to 44%

42. SENSITIVITY ANALYSIS OF A DIAGNOSTIC TEST
Value
95% CI
Pre-test probability
35%
26% to 44%
Likelihood ratio
5.0
3.0 to 8.5
Applying the 95% confidence intervals above to the nomogram, the post-test probability is likely to lie in the range 55-85%

43. RECEIVER OPERATING CHARACTERISTIC CURVE
The diagonal line (representing Sensitivity=0.5 and Specificity=0.5) represents performance no better than chance
RECEIVER OPERATING CHARACTERISTIC CURVE
Overall shape is predicted by the reciprocal relationship between sensitivity and specificity
The closer the curve gets to Sensitivity=1 and Specificity=1, the better the overall performance of the test
TRUE POSITIVE RATE (Sensitivity)
Hence the area under the curve gives a measure of the test’s performance
FALSE POSITIVE RATE (1-Specificity)

44. AREA UNDER ROC CURVES
Sensitivity and specificity both 100% - TEST PERFECT
AREA=1.0
Sensitivity and specificity both 50% - TEST USELESS
The area under a ROC curve will be between 0.5 and 1.0
AREA=0.5

45. AREA UNDER ROC CURVES
Area = 0.7 (between 0.5 and 1.0)
Consider (hypothetically) two patients drawn randomly from the DISEASE+ and DISEASE- groups respectively
If the test is used to guess which patient is from the DISEASE+ group, it will be right 70% of the time

46. APPLYING A DIAGNOSTIC TEST IN DIFFERENT SETTINGS
The Positive Predictive Value of a test will vary (according to the prevalence of the condition in the chosen setting)
Sensitivity and Specificity are usually considered properties of the test rather than the setting, and are therefore usually considered to remain constant
However, sensitivity and specificity are likely to be influenced by complexity of differential diagnoses and a multitude of other factors (cf spectrum bias)

47. RECEIVER OPERATING CHARACTERISTIC (ROC) CURVE
This study compared the performance of a dementia screening test in a community sample (ACAT) and a memory clinic sample (MC)
Flicker L, Loguidice D, Carlin JB, Ames D. The predictive value of dementia screening instruments in clinical populations. International Journal of Geriatric Psychiatry 1997 ; 12 :

48. METHOD 4: A TEST WITH NORMALLY DISTRIBUTED VALUES
Assessing the performance of the test assumes that these two distributions remain constant. However, each of them will vary (particularly through spectrum or selection bias)
Test cut-off
% of Group
NON-DESEASED
DISEASED
Negative
Positive
Degree of ‘positivity’ on test

49. PERFORMANCE OF A DIAGNOSTIC TEST
NON-CASES
CASES
FALSE NEGATIVES
Test cut-off
FALSE POSITIVES
% of Group
NON-DESEASED
DISEASED
Negative
Positive
Degree of ‘positivity’ on test

50. MINIMISING FALSE NEGATIVES: A SENSITIVE TEST
NON-CASES
CASES
Cut-off shifted to minimise false negatives ie to optimise sensitivity
CONSEQUENCES:
Specificity reduced
A Negative result from a seNsitive test rules out the diagnosis - snNout
Test cut-off
% of Group
NON-DESEASED
DISEASED
Negative
Positive
Degree of ‘positivity’ on test

51. MINIMISING FALSE POSITIVES: A SPECIFIC TEST
Cut-off shifted to minimise false positives ie to optimise specificity
CONSEQUENCES:
Sensitivity reduced
A Positive result from a sPecific test rules in the diagnosis - spPin
Test cut-off
% of Group
NON-DESEASED
DISEASED
Negative
Positive
Degree of ‘positivity’ on test

52. METHOD 5: USING SCALES WITH DIFFERENT CUT-OFFS
CASES
NON-CASES
Sensitivity = A/A+C
Specificity = D/B+D
FALSE
POSITIVES
POSITIVES
TRUE A B
MMSE Score C D
Chosen cut-off
TRUE
NEGATIVES
NEGATIVES
FALSE

53. INCREASING SENSITIVITY
CASES
NON-CASES
Sensitivity = A/A+C
Specificity = D/B+D
In a seNsitive test, false Negatives are minimised
A negative result from a sensitive test rules out the diagnosis (snNnout)
TRUE
POSITIVES
MMSE Score A B C D
FALSE
NEGATIVES

54. INCREASING SPECIFICITY
CASES
NON-CASES
Sensitivity = A/A+C
Specificity = D/B+D
FALSE
POSITIVES A B
In a sPecific test, false Positives are minimised
A positive result from a specific test rules in the diagnosis (spPin) C D
MMSE Score
TRUE
NEGATIVES

55. KEY REFERENCES
Sedlmeier P and Gigerenzer G. Teaching Bayesian reasoning in less than two hours. Journal of Experimental Psychology: General. 130 (3): ,
Knotternus JA (ed). The Evidence Base of Clinical Diagnosis. London: BMJ Books, 2002.
Sackett DL, Haynes RB, Guyatt G, and Tugwell P. Clinical Epidemiology : A Basic Science for Clinical Medicine. Boston, Mass: Little, Brown & Co, 1991.
Loong TW. Understanding sensitivity and specificity with the right side of the brain. BMJ 2003: 327: