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Appendix 3:

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%