The incidence of prostate cancer among men in the US over 65 years of age is 60% (!). A blood test for elevated levels of prostate-specific antigen (PSA) is used as one indicator of prostate cancer. The accuracy of this test is tabulated below where the entries are the conditional probabilities P [test result | state] for the two states S1-have prostate cancer and S2 - do not have prostate cancer. P [test result | state] State S1 - have prostate cancer State S2 - do not have prostate cancer Test: positive Test: negative 0.95 0.05 0.78 0.22 A PSA test has been run on a man over 60 and the result is negative. What is the revised probability that he does NOT have prostate cancer? Be sure to show your work.
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Step 1: Calculate the revised probability that the man does not have prostate cancer given a negative test result. Show more…
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One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSA) test. However, this test is known to have a high false-positive rate (tests that come back positive for cancer when no cancer is present). Suppose there is a 0.04 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is 0.85, and the probability of a false-negative (no indication of cancer when cancer is actually present) is 0.30. Let C = event male patient has prostate cancer + positive PSA test for prostate cancer - negative PSA test for prostate cancer. What is the probability that the male patient has prostate cancer and the PSA test comes back false negative? 0.843 0.012 0.124 0.363
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Prostate cancer There has been debate among doctors over whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. Recently, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer, compared with 31 of the 348 men who did not have surgery. a) Was this an experiment or an observational study? Explain. b) Create a 95% confidence interval for the difference in rates of death for the two groups of men. c) Based on your confidence interval, is there evidence that surgery may be effective in preventing death from prostate cancer? Explain.
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