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Sensitivity and Specificity Calculations for Health Science

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The prevalence of prostate cancer is 16% among men. Out of 20,000 men screened with the prostate specific antigen (PSA) test, 400 men with prostate cancer had a negative test results and 800 of the men without prostate cancer had positive test results.

i. Determine the specificity of the PSA test.
ii. Determine the sensitivity of the PSA test.
iii. What is the accuracy of this diagnostic test?

The prevalence of breast cancer is 12% among women. Out of 100,000 women screened for breast cancer, 11,000 women with breast cancer had a positive test result and 4,000 women without breast cancer had a positive test result.

i. Determine the specificity of the breast cancer screen.
ii. Determine the sensitivity of the breast cancer screen.
iii. What is the accuracy of this diagnostic screening?

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Solution Summary

This response includes complete, worked through solutions for sample problems related to prostate and breast cancer. Explanations are provided to aid in calculating sensitivity, specificity and accuracy.

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True Disease Status
Present Not Present Total
Test Result

Positive TP FP

Negative FN TN


Where TP is true positive, FP is false positive, FN is false negative and TN is true negative

To determine the values that will go into the table, we need to use the prevalence data as well as the sample number.

Prevalence of disease = (number of people with disease/total of people in sample)*100

The prevalence was given at 16%, meaning that we would expect 3, 200 of the 20, 000 screened individuals to have the disease and 16, 000 to be disease free. These can be used as ...

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