Question

Suppose that a certain HIV test has both a sensitivity and specificity of 99.9%. This test is applied to a population of 1,000,000 people.

Consider a population of drug rehabilitation patients for which 10% of the population is actually infected with HIV.

(a) Calculate the PPV. Suggestion: First make a table as seen below. (Round your answer to one decimal place.)
%

	Has disease	Does not have disease	Totals
Test positive
Test negative
Totals

(b) Calculate the NPV. (Round your answer to two decimal places.)
%

(c) How many people will test positive who are, in fact, disease-free?

Answer 1

(a) PPV = True positives / (true positives + false positives) = 99900/100800
= 0.991 = 99.1%

	disease	no disease	Total
positive	99900	900	100800
negative	100	899100	899200
Total	100000	900000	1000000

b)
NPV = True negatives / (true negatives + false negatives) = 100/899220
= 0.0001 = 0.01%

c)
900