1. Worked Example
Refer to Worksheet 2

2. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• An investigator invented a new diagnostic
tool for diagnosing liver impairment.
• the test gave readings ranging from 5 –
25.
• The investigator applied his test to a
sample of 25 volunteers. Of whom 10 were
known to have liver impairment and 15 are
known to be free.

3. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
5
10
15
20
25
Values obtained by the sample
Diseased
Free

4. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• Since there was an overlap of values
obtained from Diseased and Disease free
individuals, the investigator was very
confused.
• What value should be considered as
Positive?
• What should be the cutoff point that
separates Diseased from Non Diseased?

5. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• So , He decided to try different
cutoff points, and for each cutoff
calculate the predictive power of the
test.

6. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Step one:
• He decided that a value of 10 or
more will be considered as positive.
• And tried to construct a 2X2 table.

7. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Positive = 20
Negative = 5
5
10
15
20
25
Values obtained by the sample

8. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
All
Positives
All
Negatives
True
Positives
False
Negatives
True
Negatives
All
Disease
free
All Diseased
Test
Negative
Test
Positive
Diseased
Not
Diseased
False
Positives

9. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Test
Negative
Test
Positive
Diseased
Not
Diseased

10. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Sensitivity and specificity
• Sensitivity = True positives / all diseased
• 9/10 = 0.9 (90%)
• Specificity= True Negatives / all disease free
• 4/15 = 0.266 (26.6%)

11. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Step Two:
• He decided that a value of 15 or
more will be considered as positive.
• And tried to construct a 2X2 table.
• Calculated sensitivity and specificity

12. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Positive = 15
Negative = 10
5
10
15
20
25
Values obtained by the sample

13. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Test
Negative
Test
Positive
Diseased
Not
Diseased

14. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Sensitivity and specificity
• Sensitivity = True positives / all diseased
• 8/10 = 0.8 (80%)
• Specificity= True Negatives / all disease free
• 8/15 = 0.533 (53.3%)

15. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Step three:
• He decided that a value of 20 or
more will be considered as positive.
• And tried to construct a 2X2 table.
• Calculated sensitivity and specificity

16. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Positive = 10
Negative = 15
5
10
15
20
25
Values obtained by the sample

17. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Test
Negative
Test
Positive
Diseased
Not
Diseased

18. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Sensitivity and specificity
• Sensitivity = True positives / all diseased
• 6/10 = 0.6 (60%)
• Specificity= True Negatives / all disease free
• 11/15 = 0.733 (73.3%)

19. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Conclusions

20. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• No single PERFECT cutoff point
• Sensitivity # Specificity