Question

A test for measurement of level of Prostate Specific Antigen (PSA) is a commonly used screening procedure for prostate cancer. Men with PSA levels greater than 10 nanograms per millilitre (ng/ml) (S) have 60% chance of prostate cancer (C), men whose PSA levels are between 4 ng/ml and 10 ng/ml (S) have 25% chance of having prostate cancer (C) and for men whose PSA levels are less than 4ng/ml (S), the risk of developing prostate cancer is 10% (C) Suppose that l 8% of men have PSA levels greater than 10 ng/ml, 15% of men have PSA levels between 4 ng/ml and 10 ng/ml, 67% of men have PSA levels below 4 ng/ml. (1) Draw a probability tree diagram incorporating the suggested notation S1, S2. S3 and C for the relevant events. prevalence of prostate cancer? (3) What is the probability that a randomly selected man has a PSA level greater than 10 ng/ml, given that he has prostate cancer? Let T be the test for detecting prostate cancer based on PSA level with cut ofT 4 ng/ml. Denote T+-(The test T is positive) (4) Find the positive predictive value of the test p (CIT+). (5) Find the sensitivity of the test P(T IC).

Answer 1

S1 S2 $3

SC, S2C, S3C

0.60 (0.18)0.25 (0.15)0.10*0.67 0.2125 0.10 0.67/0.2125-0.3153 PC0.10 0.67/0.2125-02 P(C) (4) P(T+)P(S3)0.67, P(T) P(The test T is negative) -1 - P(T+)0.33 P(C|T*) = 0.10 0.10 * 0.67/0.2125-0.3153. P(C)