1. Vahid Ashoorion MD. ,MSc, vahidashoorion@yahoo.com
Refining Probability
Test Informations
Vahid Ashoorion MD. ,MSc,
Dr. Vahid Ashoorion

2. Which one of these test is the best for SLE Dx?
Sensitivity%
Specificity%
ANA 99 80
dsDNA 70 95
ssDNA 50
Histone
30-80
Nucleoprotein 58 Sm 25
RNP
87-94
PCNA 5
Dr. Vahid Ashoorion

3. Diagnostic Tests Characteristics:
Sensitivity
Specificity
Predictive Value
Likelihood Ratio
Dr. Vahid Ashoorion

4. Sensitivity and specificity
Remember:
Sensitivity & Specificity can be used for diagnostic tests that have only two outcome (dichotomous tests)
Sensitivity & Specificity are meaningful only when the studied population underwent an acceptable “gold standard” that used to “Rule in” or “ Rule out” the disease.
Dr. Vahid Ashoorion

5. a b c d Disease Present Absent TP=True Positive FP= False Positive
FN=False Negative d
TN=True Negative
Positive
Test Result
Negative
Dr. Vahid Ashoorion

6. Sensitivity & Specificity
Sensitivity & Specificity are easily derived by thinking Vertically
Sensitivity: the proportion of patients with the disease who have a positive test result
Specificity: the proportion of patients without the disease who have a negative test result
Dr. Vahid Ashoorion

7. Specificity a/a+c a b c d Sensitivity d/b+d Disease Present Absent
TP=True Positive b
FP= False Positive c
FN=False Negative d
TN=True Negative
Positive
Test Result
Negative
Sensitivity
a/a+c
d/b+d
Dr. Vahid Ashoorion

8. Information for a dichotomous test
Disease
Present
Absent
True positive A
False positive B
False negative C
True negative D
Positive
Test
Result
Negative
Sensitivity = A / (A+C)
Specificity = D / (B+D)
Dr. Vahid Ashoorion

9. Information for a dichotomous test
Disease
Present
Absent
True positive
A = 103
False positive
B = 16
False negative
C = 12
True negative
D = 211
Positive
Test
Result
Negative
Sensitivity = A / (A+C)
Specificity = D / (B+D)
Dr. Vahid Ashoorion

10. Information for a dichotomous test
Disease
Present
Absent
True positive
A = 103
False positive
B = 16
False negative
C = 12
True negative
D = 211
Positive
Test
Result
Negative
Sensitivity=103/(103+12)=89%
Specificity=211/(16+211)=93%
Dr. Vahid Ashoorion

11. Sensitivity & Specificity Limitation
Sensitivity & Specificity describe the proportion of positive & negative test results in a population in whom we already know who has the disease or not.
So We don’t know who has the disease before the test
Dr. Vahid Ashoorion

12. The Usefulness of Predictive Value
It is based on both Sensitivity & Specificity AND Prevalence of target disease in the population being evaluated.
We care more about how “good” a test is at “predicting” who has the disease and who doesn’t, we will now think horizontally across in the table
Dr. Vahid Ashoorion

13. Predictive values
PPV : the proportion of patients with a positive test result who have the disease
NPV : the proportion of patients with a negative test result who do not have the disease
Dr. Vahid Ashoorion

14. Information for a dichotomous test
Disease
Present
Absent
True positive A
False positive B
False negative C
True negative D
a/a+b
Positive
Test
Result
d/c+d
Negative
Sensitivity = A / (A+C)
Specificity = D / (B+D)
PPV = A / (A+B)
NPV = D / (C+D)
Dr. Vahid Ashoorion

15. Information for a dichotomous test
Disease
Present
Absent
True positive
A = 103
False positive
B = 16
False negative
C = 12
True negative
D = 211
Positive
Test
Result
Negative
Sensitivity=103/(103+12)=89%
PPV = A / (A+B)
Specificity=211/(16+211)=93%
NPV = D / (C+D)
PPV = 103 / (103+16) = 86%
NPV = 211 / (12+211) = 94%
Dr. Vahid Ashoorion

16. Predictive values
Limitation: predictive values are dependent on the fixed prevalence (pretest probability) of disease in the studied population. If the pretest probability of the disease is equal to prevalence of disease then the post test probability of disease will be equal to PPV (e.g in screening)
Dr. Vahid Ashoorion

17. Homework1: Prevalence of a disease =5% Test Sensitivity:98%
Test Specificity:80%
What is Positive Predictive Value?
What is Negative Predictive Value?
Dr. Vahid Ashoorion

18. c=0.1 a=4.9 b=19 d=76 5 95 Disease Presence Absence PPV= 20% Test NPV=
Positive
PPV=
20%
Test
NPV=
99.8%
Negative
a+b+c+d=100 5 95
Dr. Vahid Ashoorion

19. Homework2: Prevalence of a disease =10% Test Sensitivity:98%
Test Specificity:80%
What is Positive Predictive Value?
What is Negative Predictive Value?
Dr. Vahid Ashoorion

20. c=0.2 a=9.8 b=18 d=72 10 90 Prevalence:5% 10% PPV:20% 35% NPV:99.8%
99.7%
Disease
Presence Absence
a=9.8
b=18
c=0.2
d=72
Positive
PPV=
35%
Test
NPV=
99.7%
Negative
a+b+c+d=100 10 90
Dr. Vahid Ashoorion

21. Properties of Diagnostic Tests
Effect of prevalence on predictive values
As prevalence decreases so does (+) PV, and (-) PV increases
The PV can be improved by selecting more sensitive or specific tests, however, don’t expect any dramatic improvement
More sensitive test improves (+) PV (fewer false-negative results)
More specific test improves (-) PV (fewer false-positive results)
Dr. Vahid Ashoorion

22. Likelihood Ratio: The Final Frontier
Probability of an event depends on new information applied to what is previously known about the event
“WHAT WE THINK AFTER”
“WHAT WE THOUGHT BEFORE” +
”TEST INFORMATION” =
Pretest Probability
Posttest Probability
Likelihood Ratio
Dr. Vahid Ashoorion

23. Why Likelihood Ratios Are Useful?
We don’t have truly perfect test ( Gold Standard)
Test results only increase or decrease our likelihood (probability) of disease.
Diagnostic tests with different level or categories of results can give us more Informations
LR from different, independent tests can be used together sequentially to easily calculate a single estimate of a patient’s post test probability of disease
Dr. Vahid Ashoorion

24. Some Rules
When magnitude of LR applied to pretest probability directly affect the magnitude of post-test probability.
In diagnostic tests with multiple levels/categories of results, each possible level/category has its own LR with a value ranging from 0-+∞
Dr. Vahid Ashoorion

25. Posttest probability of DiseaseLR
Posttest probability of Disease
No Disease
0.1
Lower 1
Unchanged 10
Higher +∞
Disease Certain
Dr. Vahid Ashoorion

26. With Over Without (WOWO)
Likelihood of a particular test result in someone with the disease
LR=
Likelihood of a particular test result in someone without the disease
A test has a result: A
Likelihood of test result “A” in Pt with the disease
LR=
Likelihood of test result “A” in Pt without the disease
Dr. Vahid Ashoorion

27. a=207 True Positive b=231 False Positive c=44 False Negative d=399
Pulmonary Embolism
Present Absent a + b =
438
a=207
True Positive
b=231
False Positive
c=44
False Negative
d=399
True Negative
Positive
V/Q
Scan
Negative c + d =
443
a+c=251
b+d=630
Dr. Vahid Ashoorion

28. With Over Without (WOWO)
Likelihood of a Positive test result in Pts with PE
LR(+)=
Likelihood of a Positive test result in Pts without PE
Sensitivity
a/a+c
b/b+d
1-Specificity
Dr. Vahid Ashoorion

29. Sensitivity
1-Specificity
LR(+)=
Dr. Vahid Ashoorion

30. Homework3:
What is the LR(+) for a V/Q scan using data in slide #29?
207/251
231/630
What is the LR(-) for a V/Q scan using data in slide #29?
44/251
399/630
=2.4
=0.26
Dr. Vahid Ashoorion

31. What should we do with different levels/categories of results?
Scan Category PE
No PE
High Probable
102 14
Intermediate Probability
106
217
Low Probability 39
273
Near NL/NL 5
126
Total
251
630
Dr. Vahid Ashoorion

32. Homework4:
Calculate the LR for each test result by the use of generic equation:
LR (High Probable)=102/251=18.3
14/630
LR( Intermediate Probability)=105/251=1.2
217/630
LR (Low Probability)=39/251=0.4
273/630
LR (Near NL/NL)= 5/ =0.1
126/630
Dr. Vahid Ashoorion

33. Putting The Equation Back Together Using LR: “WHAT WE THINK AFTER”
There are two methods we can apply LR to refine probability:
Using Nomogram
Simple Math
Dr. Vahid Ashoorion

34. Nomogram for interpreting Diagnostic test result
0.1
0.2
0.5 1 2 5 10 20 30 40 50
Pre-test
probability
Post-test 99 95 90 80 70 60
Likelihood
ratio
100
0.05
0.02
0.01
0.005
0.002
0.001
200
500
1000
Nomogram for interpreting
Diagnostic test result
Dr. Vahid Ashoorion

35. Homework5: Ms Klott’s pretest probability is 10%:
What is her post test probability of having a pulmonary embolism?
What is her post test probability if she had an intermediate probability V/Q scan?
What is her post test probability if she had NL V/Q scan?
Dr. Vahid Ashoorion

36. Using LR with simple math
First: We should learn how to getting odd straight
Odds are a ratio of proportions:
The probability of Sth happening
The probability of Sth not happening
Odds= P
1-p
Odds=
Dr. Vahid Ashoorion

37. Let’s think about Odds Visually
What proportion of the pie do you take?
What proportion of the pie you don’t take?
What is the ratio of the proportion you take to the proportion you don’t take?
Dr. Vahid Ashoorion

38. Converting Probability to Odds and Vice Versa
Odds= Probability
1-Probability
Probability= Odds
1+Odds
Dr. Vahid Ashoorion

39. Homework6: Probability Odds 0.01 .01 0.1 1/9 0.5 1 3/4 3 5/6 5 19/20
Fill in The Table Below Through Converting Between Probabilities and Odds
Probability
Odds
0.01
.01
0.1
1/9
0.5 1
3/4 3
5/6 5
19/20 19
Dr. Vahid Ashoorion

40. Some Simple Rules
When either probability or odds is low (<0.1) they are essentially interchangeable values.
When the probability is 0.5 the odds are 1
Probability is limited to values between 0-1, whereas odds range from 0 to +∞
Dr. Vahid Ashoorion

41. Putting It All Together
Pret. p=0.003
Postt p:
Odds=p/(1-p)
P=odds/(odds+1) =
Pret. Odds: 
LR:
Postt. Odds:
Pretest odds likelihood ratio=posttest odds
Dr. Vahid Ashoorion

42. Four steps to estimate post-test probability:
Estimate the pretest probability
Convert pretest probability to pretest odds
Multiply the pretest odds by the likelihood ratio to get posttest odds
Convert the post test odds to a posttest probability
Dr. Vahid Ashoorion

43. Let’s compare Nomogram results and Simple Math
Pretest probability=10%
Pretest Odds=1/9
LR=18
Posttest Odds=2
Posttest Probability=2/3=67%
Dr. Vahid Ashoorion

44. Table 2a: Likelihood Ratios of Tests for the Diagnosis of Appendicitis
Dr. Vahid Ashoorion

45. Table 2b: Likelihood Ratios of Tests for the Diagnosis of Appendicitis
Dr. Vahid Ashoorion

46. Table 3: Likelihood Ratios of Tests for the Diagnosis of Acute MI in Patients Admitted for suspected MI
Dr. Vahid Ashoorion

47. Which one of these test is the best for SLE Dx?
Sensitivity
Specificity
LR(+)
ANA 99 80
4.95
dsDNA 70 95 14
ssDNA 50
1.6
Histone
30-80
1.1
Nucleoprotein 58
1.16 Sm 25
RNP
87-94
PCNA 5 1
Dr. Vahid Ashoorion

48. Thank You
Dr. Vahid Ashoorion