Suppose a test for a disease is 80% accurate for those who have the disease (true positives) and 80% accurate for those who do not have the disease (true negatives). Within a sample of 4,000 patients, the incidence rate of the disease matches the national average, which is 1.5%.

a. Of those with the disease, what percentage test positive?

b. Of those who test positive, what percentage have the disease? Compare this result to the one in part a and explain why they are different.

c. Suppose a patient tests positive for the disease. As a doctor using this table, how would you describe the patient's chance of actually having the disease? Compare this figure to the overall incidence rate of the disease.

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Test positive Test negative Total Disease No disease Total 836 3,164 4,000 48 12 60 788 3,152 3,940