Answered: 2.1 The PSA blood test is designed to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2.1 The PSA blood test is designed to detect prostate cancer. Suppose that of men who have this disease, the test fails to detect prostate cancer in 1 in 4, and of men who do not have it, 1 in 10 have positive test results (so-called false-positive results). Let C ( ¯ C) denote the event of having (not having) prostate cancer and let + (−) denote a positive (negative) test result. a. Which is true: P(− | C) = 1/4 or P(C | −) = 1/4? P( ¯ C | +) = 1/10 or P(+ | ¯ C) = 1/10? b. Find the sensitivity and specificity of this test. c. Of men who take the PSA test, suppose P(C) = 0.04. Find the cell probabilities in the 2×2 table for the joint distribution that cross-classifies Y = diagnosis with X = true disease status. d. Using (c), find the marginal distribution for the diagnosis and show that P(C | +) = 0.238. (In fact, the National Cancer Institute estimates that only about 25% of men who have a slightly elevated PSA level, 4–10 ng/mL, actually have prostate cancer.18)

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