False Positives: Unneeded Negativity in Your Life
https://www.newscientist.com/article/2100273-why-do-we-fall-for-false-positives-even-though-theyre-common/
False positives don’t quite get the same bad rep as false negatives, their beloved counterparts, which is fair. In most cases, the false negative, a result that indicates that a particular condition is absent when in fact it is not, is more serious. But false positives can still be a pain to deal with. We often hear about false positives in medicine when dealing with the probability of developing various diseases or ailments. Let’s look at a potential real-life example, mentioned in the article above. False positives that result from cancer screening can prove to be time-consuming, expensive, and potentially harmful. People who do not actually have cancer will be misled into believing that they require surgery and/or chemotherapy in order to survive. After weeks of stress and thousands of dollars spent on hospital-related fees, the declared “cancer patients” can let out “sighs of relief” after they find out they were cancer-free the whole time. Over time, more and more people have realized that the overwhelming majority of “positive” results that arise during cancer screening are actually “harmless” false alarms. As a result of this, many people are starting to claim that broad cancer screening is unethical and that patients should only be tested if they exhibit symptoms indicative of cancer.
I thought this article was interesting as it could directly be tied into Question #1 of Problem Set #6. For part (a) of this question, we had to apply Bayes’ rule to determine the probability that a randomly selected patient who tested positive for a particular disease actually had the disease. I had calculated this probability to be 0.99%, an overwhelmingly small figure. While it appears that false negative rates are low, it boggles my mind that it is possible that fewer than 1 out of every 100 people who test positive for a given disease may actually have it. Perhaps hypochondriacs should “loosen up” a bit, and stress out a little less about the pettiest of aches and pains. False positives appear to haunt many, and in most instances, unnecessarily so.