Question:

Over the past few years, there has been controversy about the age at which to start routine breast cancer screening. In November of 2009, a federally appointed task force recommended starting mandatory breast cancer screening at 50 rather than at 40.2 Republicans suggested that this was the first step toward healthcare rationing, and the Obama administration quickly distanced itself from the recommendations as a result.

This problem explores the probabilities behind the controversy.

Suppose you have a 40-year-old female friend who has just gone to UHS to be screened for breast cancer. Roughly one out of 229 forty-year-old women will have developed cancer, so we'll take this as the baseline rate. The doctor uses a mammogram procedure that is very accurate by medical standards: 90% of the people who have breast cancer will test positive for it, and 94% of the people who do not have cancer will test negative.

1. Suppose your friend takes the test and it comes out positive. You decide to calculate the probability that she actually has breast cancer. What is it? Explain your reasoning and state the applicable formulas and probabilities. How worried should you be?
2. Instead, suppose your friend takes the test and it comes out negative. You still want to know the probability that she actually has cancer. What is it?
3. Now, imagine that your friend is 50, rather than 40. The rate of breast cancer among 50-year-olds is roughly 1 out of 68. Also, the mammogram is more accurate for older women. Let's assume that this improves the accuracy enough that 93% of the people who have breast cancer will test positive for it, and 96% of the people who do not have cancer will test negative. Recalculate the probability that your friend has cancer if she tests positive. Then recalculate the probability that she has cancer if she tests negative.

How do the results for your 40-year-old and 50-year-old friend relate to the debate about the age at which to recommend universal cancer screening?

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document