The prostate-specific antigen (PSA) test measures blood concentrations of PSA, a protein produced by the prostate...

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The prostate-specific antigen (PSA) test measures blood concentrations of PSA, a protein produced by the prostate gland. Higher PSA levels can occur in the presence of prostate cancer, but definitive diagnosis of prostate cancer requires biopsies of the prostate gland. Suppose that 500 men over 50 years of age who are considered at high risk for prostate cancer have both the PSA screening test and a biopsy of their prostate gland. Their PSA and biopsy results are reported in the following table. PSA Test: PSA Level < < 2.5 2.5-5.4 5.5-7.4 7.5-9.4 9.5 -11.4 11.5 - 13.4 13.5 15.4 15.5-17.4 17.5 -19.4 19.5-21.4 21.5 23.4 23.5-25.4 25.5 27.4 27.5 29.4 29.5-31.4 231.5 Total PSA Test: PSA Level 25.5 <25.5 Reference Standard: Biopsy Prostate No Prostate Cancer Cancer 66 56 0 0 Total 0 0 0 0 0 4 3232 13 12 11 15 21 19 100 63 42 35 23 22 26 Prostate Cancer 18 17 Although PSA levels are higher for men with prostate cancer, no PSA level clearly separates the two groups. In the following questions, you will be asked to consider three different cutoff levels. For each cutoff, you can consider those who fall above the cutoff as "positive" for prostate cancer and those who fall below the cutoff as "negative" for prostate cancer 10 13 a. Use the data in the table above to fill in the 2x2 table below assuming men with PSA levels of 25.5 or higher are considered to have prostate cancer. 9 0 0 0 400 Gold Standard: Biopsy No Prostate Cancer b. What is the sensitivity (as a percent) of the PSA test when men with PSA levels of 25.5 or higher are considered to have prostate cancer? Show your work. c. What is the specificity (as a percent) of the PSA test when men with PSA levels of 25.5 or higher are considered to have prostate cancer? Show your work. d. Use the data in the table above to fill in the 2x2 table below assuming men with PSA levels of 21.5 or higher are considered to have prostate cancer. PSA Test: PSA Level 221.5 <21.5 Gold Standard: Biopsy Total e. What is the sensitivity (as a percent) of the PSA test when men with PSA levels of 21.5 or higher are considered to have prostate cancer? PSA Test: PSA Level Prostate Cancer f. What is the specificity (as a percent) of the PSA test when men with PSA levels of 21.5 or higher are considered to have prostate cancer? 217.5 <17.5 No Prostate Cancer g. Use the data in the table above to fill in the 2x2 table below assuming men with PSA levels of 17.5 or higher are considered to have prostate cancer. Total Gold Standard: Biopsy Prostate Cancer 96 4 100 No Prostate Cancer 67 333 400 h. What is the sensitivity of the PSA test when men with PSA levels of 17.5 or higher are considered to have prostate cancer? i. What is the specificity of the PSA test when men with PSA levels of 17.5 or higher are considered to have prostate cancer? j. How does raising the PSA level cutoff when screening for prostate cancer change the sensitivity and specificity of the PSA test? Select your answer with an "X" below. Sensitivity: Decreases Increases Specificity: Decreases Increases k. How does lowering the PSA level cutoff when screening for prostate cancer change the sensitivity and specificity of the PSA test? Select your answer with an "X" below. Sensitivity: Specificity: Does not change Does not change Decreases Increases Decreases Increases Does not change Does not change 1. Which cutoff (would you use to minimize the number of men subjected to more invasive tests (i.e., biopsy) or treated unnecessarily for prostate cancer, and why? m. Which cutoff would you use to minimize the number of men with prostate cancer who are missed by the PSA test, and why? The prostate-specific antigen (PSA) test measures blood concentrations of PSA, a protein produced by the prostate gland. Higher PSA levels can occur in the presence of prostate cancer, but definitive diagnosis of prostate cancer requires biopsies of the prostate gland. Suppose that 500 men over 50 years of age who are considered at high risk for prostate cancer have both the PSA screening test and a biopsy of their prostate gland. Their PSA and biopsy results are reported in the following table. PSA Test: PSA Level < < 2.5 2.5-5.4 5.5-7.4 7.5-9.4 9.5 -11.4 11.5 - 13.4 13.5 15.4 15.5-17.4 17.5 -19.4 19.5-21.4 21.5 23.4 23.5-25.4 25.5 27.4 27.5 29.4 29.5-31.4 231.5 Total PSA Test: PSA Level 25.5 <25.5 Reference Standard: Biopsy Prostate No Prostate Cancer Cancer 66 56 0 0 Total 0 0 0 0 0 4 3232 13 12 11 15 21 19 100 63 42 35 23 22 26 Prostate Cancer 18 17 Although PSA levels are higher for men with prostate cancer, no PSA level clearly separates the two groups. In the following questions, you will be asked to consider three different cutoff levels. For each cutoff, you can consider those who fall above the cutoff as "positive" for prostate cancer and those who fall below the cutoff as "negative" for prostate cancer 10 13 a. Use the data in the table above to fill in the 2x2 table below assuming men with PSA levels of 25.5 or higher are considered to have prostate cancer. 9 0 0 0 400 Gold Standard: Biopsy No Prostate Cancer b. What is the sensitivity (as a percent) of the PSA test when men with PSA levels of 25.5 or higher are considered to have prostate cancer? Show your work. c. What is the specificity (as a percent) of the PSA test when men with PSA levels of 25.5 or higher are considered to have prostate cancer? Show your work. d. Use the data in the table above to fill in the 2x2 table below assuming men with PSA levels of 21.5 or higher are considered to have prostate cancer. PSA Test: PSA Level 221.5 <21.5 Gold Standard: Biopsy Total e. What is the sensitivity (as a percent) of the PSA test when men with PSA levels of 21.5 or higher are considered to have prostate cancer? PSA Test: PSA Level Prostate Cancer f. What is the specificity (as a percent) of the PSA test when men with PSA levels of 21.5 or higher are considered to have prostate cancer? 217.5 <17.5 No Prostate Cancer g. Use the data in the table above to fill in the 2x2 table below assuming men with PSA levels of 17.5 or higher are considered to have prostate cancer. Total Gold Standard: Biopsy Prostate Cancer 96 4 100 No Prostate Cancer 67 333 400 h. What is the sensitivity of the PSA test when men with PSA levels of 17.5 or higher are considered to have prostate cancer? i. What is the specificity of the PSA test when men with PSA levels of 17.5 or higher are considered to have prostate cancer? j. How does raising the PSA level cutoff when screening for prostate cancer change the sensitivity and specificity of the PSA test? Select your answer with an "X" below. Sensitivity: Decreases Increases Specificity: Decreases Increases k. How does lowering the PSA level cutoff when screening for prostate cancer change the sensitivity and specificity of the PSA test? Select your answer with an "X" below. Sensitivity: Specificity: Does not change Does not change Decreases Increases Decreases Increases Does not change Does not change 1. Which cutoff (would you use to minimize the number of men subjected to more invasive tests (i.e., biopsy) or treated unnecessarily for prostate cancer, and why? m. Which cutoff would you use to minimize the number of men with prostate cancer who are missed by the PSA test, and why?

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a Using the given data the 2x2 table assuming men with PSA levels of 255 or higher are considered to ... View the full answer