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## 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. 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: 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. Calculate the probability that this person actually has colorectal cancer given a positive test. Based on your analysis, communicate your result to someone who thinks that routine cancer screening tests for healthy persons are always a good idea.

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.

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 positive test.

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.

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