## Yearly mammograms increase false alarm risk

A new study has found that most women who have annual mammograms over a period of ten years will be incorrectly diagnosed (false positive) at least once, while 7-9% will go on to do a breast biopsy but not be diagnosed with breast cancer (false positive biopsy recommendation). The results of the study, detailed in “Yearly mammograms increase false alarm risk” (http://www.cbc.ca/news/health/story/2011/10/17/mammogram-breast-cancer-screening-false.html), have sparked discussion about the impact of false alarms on anxiety levels. Moreover, some now wonder whether annual mammograms are even necessary, and whether less frequent testing would be beneficial by lowering the false alarm rate.

In class, we discussed the application of probability, specifically Bayes’ Rule, to medical testing. The rule states that the probability of one event, A, given that event B has occurred, is as follows:

Pr (A | B) = [Pr (A) · Pr (B | A)] / Pr (B)

In terms of medical testing, event A corresponds to having a particular condition – in this case, breast cancer – while event B corresponds to a positive test. According to the article, Pr (A | B), or the probability that one has breast cancer given that one has tested positive, will increase with a decrease in mammograms. This makes sense, as fewer screenings will lead to fewer false positives. However, the opposite side brings up an even more valid argument, which is that false positives are more desirable than false negatives. While fewer screenings decreases the chance that healthy women will test positive for the disease, it also decreases the chance that women with cancer will receive a diagnosis. The former can certainly cause anxiety, but the latter is life-threatening.

It would also be interesting to know how these findings are interpreted by readers. As we learned in class, people can easily misunderstand the data that is presented to them – for example, a 1% error rate does not mean that someone who tests positive has a 1% chance of being healthy, but that is often how such statistics are perceived. The article does not report specific error rates, but it does say that, for every 10,000 women between the ages of 40 and 49, digital mammograms produce 2 more accurate tests and 170 more false positive tests than do traditional mammograms. It’s difficult to evaluate these in depth without a more detailed comparison to traditional mammogram results, but such numbers can very easily lead readers to misinterpret them, and a practical implication of the findings is that it’s important for people to have a greater understanding of what the numbers mean. This is especially true given the article’s already-clear emphasis on the anxiety caused by false positives – a false interpretation of probabilities can also cause harm.