an investigator develops a new diagnostic test for prostate cancer. the sensitivity of this test is 80% and the specificity is 75%. suppose that the prevalence of prostate cancer who seek testing is 10%. what proportion of men would show positive on the test?

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16-12-2022
Mathematics

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an investigator develops a new diagnostic test for prostate cancer. the sensitivity of this test is 80% and the specificity is 75%. suppose that the prevalence of prostate cancer who seek testing is 10%. what proportion of men would show positive on the test?

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-12-21T08:59:24-05:00

The proportion of men would show positive on the test is 28.

In the given question, an investigator develops a new diagnostic test for prostate cancer. the sensitivity of this test is 80% and the specificity is 75%.

Suppose that the prevalence of prostate cancer who seek testing is 10%.

We have to find proportion of men would show positive on the test.

p (cancer)=10/100

p (cancer)=0.10

p (true positive)=80/100

p (true positive)=0.80

p (false positive)=1-75/100

p (false positive)=0.25

p (positive)=[0.10*0.80+0.80*0.25]*100

p (positive)=28

Hence, the proportion of men would show positive on the test is 28.

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