<< contents Appendix 2 Test Photographs

## Sensitivity and Specificity of a Diagnostic Test

Atopic eczema
present absent

Atopic eczema according to diagnostic criteria under test

present
a
b
absent
c
d

 Prevalence of atopic eczema = a+c a+b+c+d

 Sensitivity of test criteria = proportion of genuine cases correctly identified by test criteria = a a+c

 Specificity of test criteria = proportion of genuine non-cases correctly identified by test criteria = d b+d

 Positive predictive value = proportion of genuine cases identified given a positive test result = a a+b

 Negative predictive value = proportion of genuine non-cases identified given a negative test result = d c+d

 Systematic error = a+b a+c

### Worked example of calculation of positive predictive value in two settings

Suppose a new set of diagnostic criteria were shown to have a sensitivity of 70% and specificity of 95% when compared to an external standard in the following two settings:

### 1. Hospital outpatient scenario.

In a hospital outpatient study where, say, 25% of 1000 consecutive patients have atopic eczema, the test indices will be as follows:

Reference test

Positive
Negative
Total
Test result Positive
175
37
212
Negative
75
713
788
Total
250
750
1000

Sensitivity = 175/250 = 70%

Specificity = 713/750 = 95%

Positive predictive value = 175/212 = 83%

Negative predictive value = 713/788 = 90%

### 2. Community study scenario.

Supposing the same diagnostic criteria (sensitivity 70% and specificity 95%) were now applied to a community study where only 5% of consecutive schoolchildren were found to have atopic eczema:

Reference test

Positive
Negative
Total
Test result Positive
35
47
82
Negative
15
903
918
Total
50
950
1000

Sensitivity = 35/50 = 70%

Specificity = 903/950 = 95%

Positive predictive value = 35/82 = 43%

Negative predictive value = 903/918 = 98%