Chained Fagan's Nomograph

A fresh look at the Bayesian inference medical tool known as the Fagan's nomograph.

Every once in a while a profession or trade reinvents something known for hundreds of years, albeit to another area of expertise, and by cultural aversion or simple ignorance never associates their thinking with the very old (often mathematical) tradition. Perhaps my favorite example is the Fagan’s Nomogram (or Nomograph) which is almost exclusively described without mention of Bayes’ Theorem (although you’ll note the theorem does appear, uncredited, in the explanation).

On one hand, it says something troublesome that doctors feel they need specialized, if archaic, equipment to perform a multiplication. But on the other hand, the fact that it is somewhat archaic leads me to think that determining how likely it is someone actually has a disease before you treat them is not something they care to do well or frequently, which is much more concerning that the math trouble!

Aside from essentially not having a web-implementation, the obvious way of building it sucks. With the physical item, you can use multiple tests without going mad. But if you put it on a computer, you could very easily ask people to do error-prone and boring data entry, and to keep the running probabilities in their head. 

I think the digital version should be easier, and it occurred to me that if you reverse the tool every new datum, the geometric property still works and you get visual continuity for your updating probability. It makes perfect sense when you see it. 

Chained Fagan’s Nomograph