Receiver Operating Characteristics

1. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
ROC Curve interpretation
Dr. Alaa El Dine Hassan
MB BCh, MSc (PH), MD
Consultant- Community and Preventive
Medicine

2. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
How Much is Too Much?

3. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• In real life situation we rarely have a test which
give you Positive / Negative readings
• A test mainly gives you a numerical value and it
is our role to decide:
– what values should be considered positive
– what values should be considered negative.

4. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• A sphygmomanometer gives
a reading for blood pressure.
• It is Your role do decide how
much means that the
patient is hypertensive.

5. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• The job would have been much easier if there
was no overlap between the values of
diseased and disease free individuals

6. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Diseased
Disease
free
5
10
15
20
25
30
35
The job would have
been much easier if
there was no overlap
between the values of
diseased and disease
free individuals

7. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• In practice, we choose a cutoff level above which we
consider the test to be Positive and below which we
consider the test to be Negative.
• The position of the cut point will determine the
number of :
– true positive, true negatives,
– false positives and false negatives.
• We may wish to use different cutoff levels for
different clinical situations if we wish to minimize
one of the erroneous types of test results.

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

9. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
• Receiver Operating Characteristic (ROC) curves
plot the sensitivity of a test versus its false
positive rate (1-Specificity) for various Cut-off
points

10. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
If we recall the values from the worksheet:
Cut-off point Sensitivity Specificity
10 0.9 0.266
15 0.8 0.53
20 0.6 0.733

11. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
calculate 1- specificity
Cut-off point Sensitivity Specificity 1- Specificity
10 0.9 0.266 0.734
15 0.8 0.53 0.47
20 0.6 0.733 0.267

12. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Cutoff =10
Sensitivity = 0.9
1-Specificity = 0.734
Cutoff =15
Sensitivity = 0.8
1-Specificity = 0.47
Cutoff =20
Sensitivity = 0.6
1-Specificity = 0.267

13. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Optimum Cut-off Point
The nearer to the Upper
Left Corner

14. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Hisotry
• The name "Receiver Operating Characteristic" came from
"Signal Detection Theory" developed during World War II for
the analysis of radar images.
• Radar operators had to decide whether a blip on the screen
represented an enemy target, a friendly ship, or just noise.
• Signal detection theory measures the ability of radar receiver
operators to make these important distinctions.
• Their ability to do so was called the Receiver Operating
Characteristics.
• It was not until the 1970's that signal detection theory was
recognized as useful for interpreting medical test results.

15. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
The area under the ROC Curve (AUC)
• Measure of a diagnostic test's discriminatory power.
• An AUC value of 1.0 indicates a (theoretically)
perfect test (i.e., 100% sensitive and 100% specific).
• An AUC value of 0.5 indicates no discriminative value
(i.e., 50% sensitive and 50% specific) and is
represented by a straight, diagonal line extending
from the lower left corner to the upper right

16. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
Sensitivity
1 - Specificity
Area under ROC Curve

17. Dr. Alaa Hassan - MB BCh, MSc (PH), MD
It is important to note that ROC performance
may change when the diagnostic test is
applied to different Populations