Selected Answers

Question on the study by Hoffman, Gillaland, et al. on page 6 regarding PSA screening

Subjects were 2,620 men 40 years and older undergoing (PSA) testing and biopsy.

Cancer was detected in 930 subjects (35%). The area under the ROC curve was 0.67 and the PSA cut point of 4 ng/ml had a sensitivity of 86% and a specificity of 33%. What was the positive predictive value in this study?


The area under the ROC curve is irrelevant. The question gives us the total number of subjects and the prevalence of biopsy-proven prostate cancer. It also gives us the sensitivity and specificity of the the PSA test that they used, so we can construct the contingency table from this information, and then compute the positive predictive value.

There were 930 men with confirmed prostate cancer, so this is the column total for cancer. If the sensitivity was 86%, then the number of diseased men with a positive test was 0.86 x 930 = 799.8 or 800 men. Therefore, the other 130 men with prostate cancer must have had a negative PSA test. If the study consisted of 2,620 men and 930 had cancer, then there must have been 2,620-930= 1690 men without cancer. And if the specificity was 33%, then there must have been 0.33 x 1690= 557.8 or 558 men without cancer who had negative PSA tests. Therefore, the number of men without prostate cancer who had positive tests must have been 1690-558=1132.

From this information we can now construct our screening contingency table as shown below. The last column was computed by adding the numbers in columns 2 and 3.

Table - Results of Screening for Prostate Cancer with Prostate-specific Antigen Test




No Cancer

Row Totals

PSA Screen +




PSA Screen -




Column Totals




Given these data, the positive predictive value is 800/1932 = 0.42, or 42%.

Interpretation: The probability of biopsy-proven prostate cancer among men with a positive PSA test was 42%.

The negative predictive value was 558/688 = 0.81, or 81%.

Interpretation: The probability of not having prostate cancer among men with a negative PSA test was 81%.


Answer to Question on Down Syndrome on page 9

Standard Test

Sensitivity = 5/5 = 100%

Specificity = 1835/1904 = 96.4%

Positive Predictive Value = 5/74 = 6.8%


DNA Sequencing

Sensitivity = 5/5 = 100% Specificity = 1898/1904= 99.7% Positive Predictive Value = 5/11 = 45.5%


Both tests had a sensitivity of 100%. However, as suggested by the NPR broadcast, the specificity of the new test that used DNA sequencing was better and resulted on only 6 false positive screening tests compared to 69 false positive tests with the older standard test. Since women with positive screening tests are recommended to undergo amniocentesis for definitive diagnosis, false positive tests in this setting represent cases in which unnecessary amniocentesis was done, placing the fetus at risk.

Note that amniocentesis is expensive and anxiety-producing, and it can cause a miscarriage (risk of 0.25-0.5%). Other rare complications of amniocentesis include Injury to the baby or mother, infection, and pre-term labor.