Overview :

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)

Braunwald E, Isselbacher KJ, et al (editors). Harrison's Principles of Internal Medicine, 11th edition. McGraw-Hill Book Publishers. 1987. page 7

Goldman L. Chapter 10: Quantitative aspects of clinical reasoning. pages 43-48. IN: Isselbacher KJ, Braunwald E, et al. Harrison's Principles of Internal Medicine, Thirteenth Edition. McGraw-Hill. 1994.

Panzer RJ, Black ER, Griner PF. Interpretation of diagnostic tests and strategies for their use in quantitative decision making. pages 17-28. IN: Panzer RJ, Black ER, et al. Diagnostic Strategies for Common Medical Problems. American College of Physicians. 1991.