Laboratory Testing
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) |
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| Gehlback, S. H. (2006). Interpreting the Medical Literature. Columbus, OH, McGraw-Hill Companies. | ||||
Question 1:
Question:
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:
Question 1:
What is the sensitivity of RST test for the diagnosis of strep throat?
Question 3:
Question 1:
What is the specificity of RST for the diagnosis of strep throat?
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.