Feeling Sick or Unlucky

Let’s play doctor.Image result for doctor holding stethoscope

Let’s say you have a patient who shows signs of a disease that’s tricky to diagnose.  In fact, of the people who show these symptoms, only 1 in 100 have the disease.  The test is only successful in detecting the disease 90% of the time.  The test can also fail by incorrectly indicating a “false positive” (i.e., test results show you have the disease when in fact, you do not) 9% of the time.

How do you feel about them odds?

Since this case study is appearing on this blog, you are correct in thinking there is a trick.  In the real world, physicians are confronted with these type of odds all the time.  To make matters worse, the percentages are even murkier, for example, with overlapping or contradicting studies.  The neuroscientist Daniel Levitin, in his book ‘A Field Guide to Lies’ cites a study the indicates that 90% of physicians make the error of conducting the test.
What’s the error?  The odds are that about 9 in 10 positive results are actual false positives.  If the test shows that your patient has the disease, you are nine times more wrong than you are right.  This test, is therefore, useless, or worse than useless.
One thing I have learned is that maintaining one or two numbers and the relationship between them is relatively easy.  When you have to deal with three numbers, even if the math is easy, things get hard really fast.  To do the above math in your head, you have to do a few things.
  1. Track the “patient does not have the disease” part of the equation.  Using numbers from above, 99 do not have the disease, 9% false positive is about 9 people.
  2. Compare that to the “correct positive” of the 1 person who has the disease and gets a positive result”.  Let’s round up and say it’s one person.

Nine false positives to one correct positive.  Feeling lucky?

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