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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