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Weighing the Positives

In medicine, as well as many other fields in life, the concept of conditional probability and posterior probability play major roles in decision making. These probabilities account for the likelihood of a particular outcome given two different paths, in a process called Bayes’ theorem. For example, in taking a HIV test one can either test positive because they have the disease and the test is accurate, or they can test positive because they don’t have the disease and the test is inaccurate. Bayes theorem weighs the likelihood of both events and analyzes how likely the outcome is given initial information. However, there is some pushback against the use of these tests and Bayes’ theorem, especially when it comes to rare diseases.

There are two potential problems with this process. First, is whether or not the information is actually useful. For example, researchers at Dartmouth proposed that just because a mammogram detects a cancer doesn’t mean it saves a life, and therefore the test isn’t helpful. Either the cancers were growing so slowly that they didn’t pose a serious problem (or they would have been successfully treated had they been discovered later), or the cancers were so aggressive that the early testing was useless and the patients died anyway. If the test doesn’t help change the outcome, then it serves very little purpose. The second issue is that if a disease is sufficiently rare, then the test will be a false positive more often than not, rendering the test useless as well. For example, if a disease is present in 0.4 % of the population and the test is 99.5% accurate when the disease is present, and 1% false positive, then Bayes’ theorem can be used to determine the likelihood of having the disease if the test is positive to be  = 0.286 or 28.6%. This means only 28.6% of the positive test results are accurate: the other 71.4% are all false positives. This renders the test effectively useless, since a positive result on the test isn’t actually representative of having the disease. Furthermore, it can even be harmful if the people who test positive start treatment for the disease (even if they don’t really have it), which can result in all sort of complications and dangerous, as well as unnecessary, side affects.

It is hard to say what to really do about the tests. Not doing anything isn’t really a better solution than testing with limited success, although the cost of the tests is certainly a consideration. In theory the best solution would be finding more accurate tests for these rare diseases, or at least secondary tests to run if the first test is positive.



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