A 57-year-old man presents with progressively worsening low back pain, numbness in his right buttock and thigh, and weakness in his right lower limb. His temperature is elevated and he has tenderness in his lower back and decreased sensation in his right foot. The doctor suspects a 20% chance of spinal malignancy. ESR has 78% sensitivity and 67% specificity for detection, while MRI has 95% sensitivity and 95% specificity. Using the 2x2 table method and likelihood ratios, the doctor determines that a positive ESR would increase the probability of malignancy from 20% to 37%, while a positive MRI would increase it to 92%.

1. Continue Dx Test Evaluation
DR Amita Kashyap
Sr. Prof. PSM
SMS Med College Jaipur

2. Decide whether to order ESR or directly do MRI?
• A 57 yr old man presents with h/o aching low back pain
that persists at rest and is worse by bending and lifting.
• Progressively getting worse in last 6 wks-waking from sleep.
• Within past 10 days he has noticed numbness in Rt buttock
and thigh and weakness in Rt lower limb.
• He had no fever but has lost 10 lb Wt. in last 4 months.
• O/E Temp. is 99.6F, tenderness in the lower lumber spine,
decrease sensation over dorso-lateral aspect of Rt. foot,
weakness in Rt ankle aversion. Deep tendon reflexes Norm.
• You suspect that man has 20% chance of spinal Malignancy
• ESR ≥20 mm/h has 78% sensitivity & 67% specificity
• MRI has 95% sensitivity AND 95% specificity!!
• Suppose we have 1000 patients

3. We can use any of the following methods
• 2 X 2 Table Method
• Likelihood Ratio (gives odds)
• Decision Tree method And
• Bayes Theoram

4. How will the prior probability of 20% Change with +ve ESR
(78% sensitivity & 67% specificity) 2X2 Table method
Disease
Test
(ESR)
D+ D-
T+ (TP)
156
(FP)
264
420
T- (FN)
44
(TN)
536
580
200 800 1000
Predictive Value of a Positive test
PPV (PV+) = 156/420 = 0.37
Increased from 20% to 37%
Predictive Value of a Negative test
NPV = 536/580 = 0.92
A) - What is the probability of FP Rate ?
B)- What is the probability of FN Rate?
A) - 264/420 = 0.63 (hence minimal use as screening test),
B) - 44/580 = 0.08

5. MRI has 95% sensitivity AND 95% specificity
And will have PVs as follows:-
Disease
Test (MRI) D+ D-
T+ (TP) 351.5 (FP) 31.5 383
T- (FN) 18.5 (TN) 598.5 617
370 630 1000
PPV (PV+) = 351.5/383 = 0.918
FP Rate = 31.5/383 = 0.08
NPV (NPV) = 598.5/617= 0.970
FN Rate = 18.5/ 617 = 0.03

6. • Definition: An LR is the probability of a particular test
result for a persons with the disease divided by the
probability of that test result in non-diseased persons
How will the prior probability of 20% change with +ve ESR?
Likelihood Ratio Method
LR+ =
Probability of +ve test result in Diseased persons
(True positive / total diseased i.e. Sensitivity)
Probability of +ve test result in Disease Free persons
(False positive/ total Non-diseased i.e. 1- Specificity)
LR¯ =
Probability of -ve test result in Diseased persons
(False Negative / total diseased i.e. 1- Sensitivity)
Probability of -ve test result in Disease Free persons
(True negatives/ total Non-diseased i.e. Specificity)

7. LR+ = Sensitivity / 1-specificity
= 0.78 / 1-0.67
= 0.78 / 0.33 = 2.36
LR¯ - 1-Sensitivity) / Specificity
= 1- 0.78 / 0.67
= 0.22/ 0.67 = 0.328
With ESR having 78% sensitivity & 67% specificity

8. Pre Test odds = Prior Probability
1- Prior Probability
Post Test odds = LR X Pre test odds
= 2.36 X 0.25 = 0.59
Posterior probability (PPV)
= post test odds/ 1+ post test odds
= 0.59/ 1+ 0.59 = 0.37 = 37%
Likelihood Ratio to
Post Test Probability
= 0.20 /1- 0.2 = 0.25
Pre Test odds (with 20% Prev)

9. 0.3
13
20 40 60 80 100
64
After positive
FNA result
54 yr old women
Before Mammogram
After positive
mammogram
Probability of Breast Cancer (Percent)
palpable lump
Prior to
mammogram
Estimated Probability of Breast Cancer
1) In a 54 yr old women without palpable Breast Mass,
2) After a positive mammogram and
3) Following a positive FNA test result
1% with
H/o Br Ca
In mother

10. How will the prior probability of 13% Change
2X2 Table method
Surgical Biopsy
Cancer No Cancer
FNA
Result
+
-
Total 15 99
22
92
114
Total
Prevalence = 13%
Sensitivity = 93%
Specificity = 92%
PPV = 64%
NPV = 99%

11. LR+ = Sensitivity / 1-specificity
= 0.93 / 1-0.92
= 0.93 / 0.08 = 11.63
LR¯ - 1-Sensitivity) / Specificity
= 1- 0.93 / 0.92
= 0.07/ 0.92 = 0.08
With FNA having 93% sensitivity & 92% specificity
In contrast to PV, LR does not vary as a function of Prevalence

12. Pre Test odds = Prior Probability
1- Prior Probability
Post Test odds = LR X Pre test odds
= 11.63 X 0.15 = 1.74
Posterior probability (PPV)
= post test odds/ 1+ post test odds
= 1.74/ 1+ 1.74 = 0.64 = 64%
Likelihood Ratio to
Post Test Probability
= 0.13 /1- 0.13 = 0.15
Pre Test odds (with 13 % Prev)

13. Receiver Operating Characteristic (ROC) Curve
• Diagnostic tests giving quantitative outcome e.g.
serum levels of enzymes, there are many options
about where to set a cut off point – as the cut off
point rises (from 200 to 250mg/dl for total cholesterol)
the sensitivity will increase with a corresponding
decrease in specificity.
•To get a most suitable cutoff point at each cutoff
point, sensitivity and (1- specificity) are calculated
and plotted on ‘y’ and ‘x’ axis respectively along
the full range of cutoff points

14. Test Result
without the disease
with the disease
‘‘-’’ ‘‘+’’
Moving the Threshold: right

15. Test Result
without the disease
with the disease
‘‘-’’ ‘‘+’’
Moving the Threshold: left

16. 1 0
%1s
%0s
Say
1
Say
0

17. Say
1
Say
0

18. Say
1
Say
0

19. Say
1
Say
0

20. Say
0
Say
1

21. Say
1
Say
0

22. Say
1
Say
0

23. Say
0
Say
1

25. True
Positive
Rate
0%
100%
False Positive Rate
0
%
100%
True
Positive
Rate
0%
100%
False Positive Rate
0% 100%
A good test: A poor test:
ROC curve comparison

26. Best Test: Worst test:
True
Positive
Rate
0
%
100%
False Positive Rate
0
%
100
%
True
Positive
Rate
0
%
100%
False Positive
Rate
0
%
100
%
The distributions
don’t overlap at all
The distributions
overlap completely
ROC curve extremes

27. Reliability or Repeatability of a Test
• Factors responsible for variation in the results:
1. Intra subject (within the individual) variation
2. Intra observer variation (variation in the
reading of test result by the same observer)-
greater the subjective element in the reading
more is this error
3. Inter observer variation (variation in the
reading of test result between observers)

28. Inter observer Variation
Reading
No. 1
Reading No.
2
Abnormal Suspect Doubtful Normal
Abnormal A B C D
Suspect E F G H
Doubtful I J K L
Normal M N O P
Percent Agreement =
A + F + K + P
Total readings
X 100

29. In general, most persons who are tested have Negative Test Result,
& there is likely to be Considerable agreement on this
Ob 1
Ob 1

30. Kappa Statistics
• The extent to which two observers (physician/
nurse/ radiologist/ Dx Test) agree is an important
Index of good quality of care
• Yet, there is a fraction based ‘solely on chance’
for agreement between two observers
• What we want to know is – to what extent did
the education/ training that the observers
received improve the quality of their observation
(how much increased percent agreement
between them beyond chance! )

31. Rationale of the kappa statistics
• First find out– “how much better is the agreement
between the observers’ readings than would be
expected by chance”
i.e. = (% agreement observed - % agreement
expected by Chance alone)
• We Know that the maximum improvement the
observers can have than expected by chance is:-
100% - % agreement expected by Chance alone
• Kappa Statistics expresses the extent to which
the observed agreement exceeds chance
agreement relative to maximum that the
observer can hope to improve

32. • Kappa =
[Percent Agreement
Observed]
[ Percent Agreement
expected by chance alone ]
-
[ Percent Agreement
expected by chance alone ]
100% -
Landis and Koch suggested that :-
kappa greater than 0.75 = excellent agreement
Kappa of 0.40 to 0.75 = intermediate to good agreement

33. Histological grading
Of lung cancer by
two pathologist