Mammograms are a very widely used screening tool for breast cancer. However, cer

Question

Mammograms are a very widely used screening tool for breast cancer. However, certain types of findings are notorious for being difficult to interpret. In order to be on the safe side, when a radiologist decides that a finding on the mammogram is suspicious, they will indicate this and the patient might then be referred to a surgeon for possible biopsy.

Part a: Suppose that a certain type of suspicious mammogram finding called a “microcalcification” has a false positive rate of 12%. That is, 12% of microcalcifications are not actually pre-cancerous. If a physician sees 8 patients every week with microcalcifications, what is the likelihood of a false positive? That is, what is the likelihood that at least 1 person of those 8 will be told incorrectly that they need to see a surgeon for possible biopsy?

NOTE: The 12% figure quoted in this problem is an entirely made-up number. Please do not apply this number to real-life situations!

Part b: Real world application: When interpreting statistics, it is often important to try to interpret statistical scenarios without necessarily have expertise in the particular area. Try to do so here: Why do you think false positive findings are problematic? Wouldn’t it be better to send any patient with an even slightly suspicious mammogram to a surgeon “just to be on the safe side”?

Explanation / Answer

X no of false positives is binomial with p =0.12

n =8

P(X>=1) = 0.6404

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False positive findings are problematic because the person diagnosed with positive may fell panicky and may get some other health problems due to fear of cancer.

Also the test would become a ridicule in the media, if 2 or 3 persons report they were tested positive and not. Thus prople may lose confidence in the test and patients would be reluctant to undergo the test.

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