Question

Approximately 1 in 14 men over the age of 50 has prostate cancer. The level of 'prostate specific antigen' (PSA) is used as a preliminary screening test for prostate cancer.

7% of men with prostate cancer do not have a high level of PSA. These results are known as 'false negatives'.

75% of those men with a high level of PSA do not have cancer. These results are known as 'false positives'.

If a man over 50 has a normal level of PSA, what are the chances that he has prostate cancer?

A. 7%
B. 25%
C. 5%
D. 0.7%
E. 0.5%

Answer 1

Given the data on PSA levels and prostate cancer incidence, the probability that a man over 50 with a normal level of PSA has prostate cancer is close to 7%, reflecting the false-negative rate of men who have prostate cancer but normal PSA levels.

Step-by-step explanation:

To calculate the probability that a man over 50 with a normal level of PSA has prostate cancer, we need to look at the given statistics. Approximately 1 in 14 men over the age of 50 has prostate cancer, which is roughly 7.14%. According to the information provided, 7% of these men will have a false-negative PSA test, implying a normal PSA level despite having cancer. Therefore, for every 100 men with prostate cancer, 7 will have a normal PSA level. Utilizing conditional probability and the base rate, the chances of a man having prostate cancer given a normal PSA test can be calculated.

To provide a specific answer here, we should acknowledge the lack of express information on the overall incidence rates of normal PSA among all tested males with or without cancer. However, considering the false-negative rate, the chances of having prostate cancer with a normal PSA level would be close to 7%, as that's the percentage of people with the disease who will not display elevated PSA levels.