Calculating Sensitivity and Specificity

The table below illustrates how sensitivity and specificity are derived mathematically:



General Decision Matrix
  Target Disorder  
    Present Absent Totals
Diagnostic Test Result Positive True Positive
a
False Positive
b
a + b
  Negative False Negative
c
True Negative
d
c + d
    a + c b + d a + b + c + d
    Sensitivity = a / (a + c)
     = TP / (TP+FN)
Specificity = d / (b + d)
     = TN / (FP+TN)
 
Gehlback, S. H. (2006). Interpreting the Medical Literature. Columbus, OH, McGraw-Hill Companies.

Quiz

Question 1:

Refer to the table above and complete this example:


A total of 1500 children have a rapid strep test (RST) done by a standardized culture technique. Of the 1500 children, 1338 have a negative RST and 162 have a positive RST. In addition, a backup throat culture (gold standard) was done on all children. Of those children with a negative RST, 1302 have a negative throat culture. In the group with a positive RST, 159 have a positive throat culture. Calculate the sensitivity and specificity of the RST.



  Target Disorder
(strep tonsillitis)
 
    Present Absent Totals
Diagnostic Test Result Positive RST      
  Negative RST      
         
Show answer >>


  Target Disorder
(strep tonsillitis)
 
    Present Absent Totals
Diagnostic Test Result Positive RST 159 3 162
  Negative RST 36 1302 1338
    195 1305 1500

**FP ** b = (a + b) - a
FP = Total Positives-TP
FP = 162-159
FP = 3


**FN **
c = (c + d) - d
FN = Total Negatives-TN
FN = 1338-1302
FN = 36

Question 2:

What is the sensitivity of RST test for the diagnosis of strep throat?

  1. 98.1%
  2. 81.5%
  3. 95%
  4. 50%
Show answer >>

The correct answer is B.
Sensitivity = a / (a + c)
Sensitivity = TP / (TP + FN)
Sensitivity = 159 / (159 + 36)
Sensitivity = 159 / 195
Sensitivity = 0.815 = 81.5%

Question 3:

What is the specificity of RST for the diagnosis of strep throat?

  1. 7%
  2. 90%
  3. 81.5%
  4. 99.7%
Show answer >>

The correct answer is D.
Specificity = d / (b + d)
Specificity = TN / (FP + TN)
Specificity = 1302 / (3 + 1302)
Specificity = 1302 / 1305
Specificity = 0.997 = 99.7%

These data represent the actual sensitivity and specificity of most rapid strep tests. Because of this, in clinical practice, we trust a positive rapid strep and treat the patient based only on this result, but we do not completely trust a negative - a back up culture must be done to confirm that the patient truly does not have strep throat.