You are examined by an excellent screening test sensitivity

You are examined by an excellent screening test (sensitivity and specificity of 99%) for a rare disease (0.1% or 1/1000 of the population). Unfortunately, the test is positive. What is the probability that you have the disease?

Solution

a)

P(disease|positive) = P(positive and disease) / P(positive)

= [P(disease) P(true positive)] / [P(no disease) P(false positive) + P(disease) P(true positive)]

= [0.001*0.99] / [(1-0.001)*(0.01) + (0.001)*(0.99)]

= 0.090163934 [ANSWER]