Suppose a test for a disease is 85% accurate for those who have the disease (tru

Question

Suppose a test for a disease is 85% accurate for those who have the disease (true positives) and 85% accurate for those who do not have the disease (true negatives). Within a sample of 4000 patients, the incidence rate of the disease is Test Positive 51 395 446 the national average. Complete parts (a) through (c) below. Test Negative 9 3645 3554 Total 60 3940 4000 a. Use the entries in the table to determine the overall incident rate of the disease. The incident rate is Type an integer or decimal rounded to the nearest tenth as needed.) b. Of those with the disease, what percentage test positive? Type an integer or decimal rounded to the nearest tenth as needed.) c. Of those who test positive, what percentage have the disease? Type an integer or decimal rounded to the nearest tenth as needed.) Compare this result to the one in part (b) and explain why they are different. In part (b), the comparison is to Y and here the comparison is to disease? d. Suppose a tests positive for the disease. As a doctor using this you describe the patients chance of actually having the patient table, how would below. Compare this figure to the overall incidence rate of the disease. Choose the correct answer O A. chance of having the disease increases to that the test was positive, compared rate without the test. given to the incidence The was positive, compared to the incidence rate without the test. O B. The chance of having the disease decreases to given that the test

Explanation / Answer

a) Number of test positive having a disease = 0.85 * 60 = 51

Number of people with disease = Incident rate * 4000

60 = IR * 4000

IR = 1.5%

b) Percentage test positive = 51*100/60 = 85%

c) Total test positive = 446

Percentage who have the disease = 51*100/446 = 11.43%

In part b the comparison is to those who have the disease and in c the comparison is to who test positive.

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