9.50 Decision errors in prostate cancer detection In the year 2016, approximately 181,000 new prostate cancer cases were expected to be diagnosed in the United States and approximately 26,100 deaths were linked to prostate cancer (www.uptodate.com/contents/screening-for-prostate-

cancer). The prostate-specific antigen (PSA) test is used to detect the presence of prostate cancer. Define the null hypothesis as the patient does not have prostate cancer. See the table for a summary of the possible outcomes:

a. When an oncologist interprets a PSA test result, explain why a Type I error is a false positive, predicting that a man has prostate cancer when actually he does not.

b. A Type II error is a false negative. What does this mean, and what is the consequence of such an error to the man?

c. An oncologist wants to reduce the chance of telling a man that he may have prostate cancer when actually he does not. Consequently, a positive test result will be reported only when there is extremely strong evidence that prostate cancer is present. What is the disadvantage of this approach?

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Prostate Cancer Detection Cancer Detection Cancer No (H0) Yes (Ha) Negative Positive Correct Type II error Type I error Correct