Erroneous Interpretation of the Results of Mammogram Readings

Low base rates of disease occurrences can lead to drastic misinterpretations of test results. The following is taken from Gerd Gigerenzer’s Calculated Risks: How to Know When the Numbers Deceive You.1 I highly recommend this book. The probability that a woman 40 years old has breast cancer is about one percent. So of 10,000 women, it is expected that 100 will have breast cancer. The probability that the readout of a mammogram will miss a cancer is 0.05. The probability that a woman who does not have breast cancer will test positive is 0.09. So let’s consider how these 10,000 women break down.

Of the 10,000 women, about 100 will have breast cancer. About 95 of these cases will be detected by the mammogram, 5 will not. So a negative mammogram does not guarantee a women that she does not have breast cancer.

Of the 9,900 women who do not have breast cancer, about 891 will test positive. So about 891 women who do not have breast cancer will leave the diagnosis thinking that they have breast cancer. They will be miserable, perhaps terrified. One would hope that physicians would be able to set their minds at ease and tell them that even though they tested positive, it is highly likely that subsequent tests would reveal them to be cancer free. Although one would hope that this is the case, apparently it is not so. The answer given by most physicians was that there was a 0.90 probability that a woman whose mammagrom was positive actually had cancer. This ignorance, defective mindware (see “Mindware” blog poast), among physicians is truly appalling. One should bear this in mind when consulting one’s physician. It is possible, perhaps probable, or maybe even likely that the information supplied by the physician will be in error.

1Gigerenzer, G. (2002). Calculated Risks: How to Know When Numbers Deceive You. New York: Simon & Schuster

© Douglas Griffith and healthymemory.wordpress.com, 2009. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Douglas Griffith and healthymemory.wordpress.com with appropriate and specific direction to the original content.

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