There is a growing recognition among medical professionals that cancer screening is a
double-edged sword. While some individuals may benefit from early detection, others
may be falsely diagnosed and treated for cancer unnecessarily. To make good decisions
about screening, the public needs to know its potential benefits and harms.
The following two paragraphs are taken from a study to test physicians’ ability to
interpret clinical laboratory results.
To diagnose colorectal cancer, the hemoccult test is conducted to detect occult
blood in the stool. For symptom-free people over 50 years old who participate in
screening using the hemoccult test, the following information is available.
The probability that one of these people has colorectal cancer is 0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that he will have a
positive hemoccult test. If a person does not have colorectal cancer, the
probability is 3 percent that he will still have a positive hemoccult test. Imagine a
person (over age 50, no symptoms) who has a positive hemoccult test in your
screening. What is the probability that this person actually has colorectal
Your assignment is to use this hemoccult test scenario as an example to communicate the
nature of a medical test to a lay person. (Think of a family member or a friend who is not
familiar with statistics.) You need to incorporate three elements in your essay:
1. Identify the base rate (or prevalence in medical literature), sensitivity (the
percentage of individuals with a disease who are correctly classified as having the
disease), and false positive rate in this case. Provide a brief and clear description
of these terms using your own words.
2. Calculate the probability that this person actually has colorectal cancer given a
3. Based on your analysis, communicate your result to someone who thinks that
routine cancer screening tests for healthy persons are always a good idea.
Your essay will be scored based on your (1) interpretation, (2) calculation, and (3)
communication; see the attached rubric. But don’t simply do what the rubric tells you to
do. Be creative: up to 3 additional points are based on effort, originality, or insight.