Question

A certain disease has an incidence rate of 0.4%. If the false negative rate is 4% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.

Answer 1

The question is explained and answered in the next 5 points--:

1) We can understand this with an example- Suppose there are 1,00,000 people who are tested, of these 100000 people, let 400 will be those who are impacted by the disease (since incidence rate is 0.4%, so 0.4% of 100000 will be 400).

2) Now the false negative rate is 4%, i.e. 4% people are those who are resulted negative after the test but they are actually positive, so out of the 400 people impacted from the disease,  16(4% of 400) will be those whose test will show negative test results and rest 384(400-16) will have positive test results.

3) Next, the false positive rate is 2% i.e. of the not impacted population of 99600(100000-400) people, 1992(2% of 99600) will show positive results.

4 )So, of (1992+384) 2376 people showing positive test results, only 384 will actually have the disease.

5) Hence, P(disease| positive results)= 384/2376 = 0.1616

Hope this helps!!