Question

1. Prostate-specific antigen (PSA) test is a common screening test used for detecting prostate cancer. From Harvard Medical School “Prostate Knowledge” webpage.

Is PSA reliable?

Although PSA testing can help catch prostate cancer at an early stage, having an elevated PSA (generally considered more than 4 ng/ml) doesn’t necessarily mean that a man has cancer. Noncancerous conditions, including benign prostatic hyperplasia (BPH), or an enlarged prostate, and prostatitis, can raise PSA levels. In fact, studies have shown that about 75% of men with an elevated PSA do not have cancer. However, many men undergo an ultrasound and prostate biopsy, to be certain.

Conversely, the PSA test doesn’t detect all cancers. About 20% of men who have cancer also have a normal PSA (less than 4 ng/ml), so the test may give some men a false sense of security.

An elevated PSA is considered testing positive, and “normal PSA” means testing negative. From information in article above, fill in the following table on screening measure values for the PSA test. If a value cannot be determined from information in the article, write “unknown”. Hint: 3 of the measures below can be determined from the paragraph above, and 3 cannot.

Sensitivity
Specificity
False Positive Rate
False Negative Rate
Positive predictive value
Negative predictive value

Answer 1

Given, elevated PSA, proportion of men do not have cancer = 75%

So, given elevated PSA, proportion of men having cancer = 100 - 75% = 25%

Given, men have cancer, proportion of men have a normal PSA = 20%

So, given, men have cancer, proportion of men have elevated PSA = 100 - 20% = 80%

Sensitivity = Given men have cancer, proportion of men have elevated PSA = 80%

Specificity = Given men do not have cancer, proportion of men have normal PSA = unknown

False Positive Rate = Given men do not have cancer, proportion of men have elevated PSA = unknown

False Negative Rate = Given men have cancer, proportion of men have normal PSA = 20%

Positive predictive value = Given elevated PSA, proportion of men having cancer = 25%

Negative predictive value = Given normal PSA, proportion of men not having cancer = unknown