PSA is a screening test used to detect patients who may be at a higher risk of d

ID: 209164 • Letter: P

Question

PSA is a screening test used to detect patients who may be at a higher risk of developing prostate cancer. A PSA value > 4.0 ng/mL is typically a value that physicians would use to further recommend a prostate biopsy. Statistics show that only 25% of men with a PSA > 4.0 actually have prostate cancer. The cost of a prostate biopsy is expensive but the cost of missing a case could be fatal.

a. Based on the above information, what factors would you consider when recommending a PSA screening test to a patient? Would you err on the side of having a false positive or false negative? Explain your rationale.

b. Based on the above information, what is the false positive rate for a PSA test?

c. Suppose you sample 35 men with prostate cancer and 35 without prostate cancer. Among the 35 with prostate cancer, 7 have a PSA > 4.0. Among the 35 without prostate cancer, 3 have a PSA greater than 4.0. Based on this data, calculate the sensitivity, specificity, positive predictive value and negative predictive value. HINT – It may be helpful to draw out the 2 by 2 grid. Show calculations

Explanation / Answer

The presence of low levels of prostate specific antigen, less than PSA of 4 ngms/ml indicate that the man does not have prostate cancer. But, if PSA is present in higher quantities than 4ngms/ml considering age and race, it means that the man has prostate cancer. As age progresses, PSA also increases.

A single test is not sufficient to diagnose prostate cancer. If there are higher PSA levels, the doctor has to suggest for a biopsy or other tests to establish the presence of cancer.

Sometimes, if prostate gland is swollen or is recently ejaculated or it is infected, PSA levels can get elevated. All those mentioned above are not connected to prostate cancer. In this case, the doctor will first treat any infection and then suggest for a PSA test. In this case, without treating infection, the PSA test can result in false positives.

AS PSA test will be followed by other tests and biopsy, it is fine if there is any false positive as the results will be out even in the next stage. But, in the case of false negatives, there is no chance of going to the next stage. There is a higher risk expected in false negatives although the test does not detect it primarily and the disease progresses further without proper diagnosis.

As only 25% of men with PSA greater than 4ngms/ml were having prostate cancer, it can be understood that the rate of false positives is 75percent.

According to the literature review conducted by American cancer society, the sensitivity of PSA cutoff at 4ng/ml was estimated as 21% for detecting prostate cancer and 51% for detecting other kinds of cancers. The cutoff at 3ng/ml has estimated that the sensitivity of this test was 32% for prostate cancer and 68% for other cancers.

The specificity of the PSA cutoff at 4ng/ml was estimated to be as 91% and 85% at 3ng/ml.

7 out of 35 men in the first category has PSA >4ng/ml. It means 20% had PSA positive test.

3 out of 35 men in the second category has PSA >4ng/ml. It means 10% had PSA positive test.

Sensitivity of 100% people with prostate cancer having PSA>4 is 21%. Then sensitivity of 20% people is (20*21)/100=21/5=4.2%

Similarly, Sensitivity of 100% people without prostate cancer having PSA>4 is 21%. Then sensitivity of 10% people is (10*21)/100=21/10=2.1%

Specificity was 91% for all the 35 people, for 7 it is 91/5=1.82%

Specificity was 91% for all the 35 people, for 3 it is 91/5=18.2%

The positive predictive value for PSA level >4ng/ml is nearly 30% for the person to have prostate cancer.

The negative predictive value for PSA level <4ng/m is nearly 85% for those who had normal PSA levels.

Positive predictive value in the first category is (30*7)/35=6%

Positive predictive value in the second category is (30*3)/35=2.57%

Negative predictive value in the first category is (85*7)/35 = 17%

Negative predictive value in the second category is (85*3)/35 = 7.29%

35 men with prostate cancer

35 men without prostate cancer

Sensitivity

4.2

2.1

Specificity

1.82

18.2

Positive predictive value

2.57%

Negative predictive value

17%

7.29%