How A 2,500-Year-Old Math Proof Can Help Determine When A Patient Improves

...A while back a colleague and I were having lunch and looking over some data resulting from something called an ROC curve. These curves were initially developed in World War II to help "diagnose" allied aircraft and submarines so that Allied forces shot at the right things and didn't unnecessarily reduce a population of large, water-bound mammals. Later, in the 1980s, the curves were adopted by epidemiologists to help them decide at what point an individual can be said to have recovered from a health complaint. I won't bore you with all the techy details, in case statistics isn't your passion, but basically it all comes down to choosing a point on a curve to determine when recovery has occurred. For many chronic conditions epidemiologists agree that the correct point to choose is the point closest to the top-left corner of this curve. As we stopped to think about it, it struck us as obvious that the way to choose this point is by using Pythagoras' theorem. We had a point in two-dimensional space, with coordinates that describe two sides of a right-angled triangle. The distance to the top-left corner is then the hypotenuse.

This wasn't really a "eureka" moment -- not by any stretch -- but what concerned us was that this was not what our epidemiologist peers and colleagues were doing. None of them was. For example, methods of defining the point based on drawing a tangent line had crept into research articles and were being repeated by those applying the work in new settings...