Description

Occasionally a paper reports a test's sensitivity and specificity but does not give the complete data used to derive these performance measures. The original data can be inferred if essential data is available.


 

Data required:

(1) sensitivity

(2) specificity

(3) total number of patients studied

(4) number of people with condition (or number of people without the condition)

 

total population =

= (TP) + (FP) + (TN) + (FN)

 

people with condition =

= (TP) + (FN)

 

people without condition =

= (total population) – (people with condition) =

= (TN) + (FP)

 

sensitivity =

= (TP) / ((TP) + (FN))

 

specificity =

= (TN) / ((TN) + (FP))

 

where:

• TP = true positives

• FP = false positives

• TN = true negatives

• FN = false negatives

 

If the above equations are rearranged:

 

TP =

= (sensitivity) * (people with condition)

 

FN =

= (TP) * (1 – (sensitivity)) / (sensitivity) =

= (people with condition) – (TP)

 

TN =

= (specificity) * ((total population) – (people with condition))

 

FP =

= (TN) * (1 – (specificity)) / (specificity) =

= ((total population) – (people with condition)) – (TN)

 


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