Question

A test has a true positive rate of 100% and false positive rate of 5%. There is a population with a 1/1000 rate of having the condition the test identifies. Considering a positive test, what is the probability of having that condition?

Answer 1

We will use the following formulae :

(incidence rate × true positive rate) / {(True positive rate × incidence rate) + (False positive rate × (1 - incidence rate)
Incidence rate = 1/1000 = 0.001

True positive rate = 1

False positive rate = 0.05

Doing the substitution :

(0.001 × 1)/{(1 × 0.001) + (0.05 × (1 - 0.001)}

(0.001) / (0.001 + 0.04995)

= 0.001 / 0.05095

= 0.01963

Convert this to percentage :

= 0.01963 × 100 = 1.963%

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