Overview :

How well a test with a given sensitivity and specificity identifies affected and unaffected persons is affected by the prevalence of disease in the population being studied. This approach assumes that the sensitivity and specificity for the test are constant.

total population =

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

sensitivity =

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

specificity =

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

prevalence =

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

where:

• TP = true positives

• FP = false positives

• TN = true negatives

• FN = false negatives

• sensitivity, specificity and prevalence are expressed as decimal fractions

If the above equations are rearranged:

(TP) + (FN) =

= (prevalence) * (total)

sensitivity =

= (TP) / ((prevalence) * (total))

TP =

= (sensitivity) * (prevalence) * (total)

FN =

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

(TN) + (FP) =

= (total) * (1 – (prevalence))

TN =

= (specificity) * (total) * (1 – (prevalence))

specificity =

= (TN) / ((total) * (1 – (prevalence)))

FP =

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

If the sensitivity, specificity, prevalence and total population size are given, then the distribution of true and false positives and negatives can be determined.

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.