One of the common cribs about the medical profession is that most doctors don’t have enough grounding in mathematics and statistics (subjects they typically don’t study beyond high school). Given the role of mathematics and statistics in medicine, in terms of gathering evidence, medical testing, etc. the lack of mathematical or statistical knowledge can have serious consequences in terms of interpretation of techniques and symptoms and all that.
In the field of statistics we have this adage that goes that we should “treat the disease and not the symptom”. This is no less true in the medical profession – let’s say that you have a bacterial infection which causes a fever, a poor doctor would diagnose your fever by taking your temperature, assume that it is the fever thanks to which you are sick and give you medication to lower the fever without realising that there is a “third variable” that might be causing both – your fever and your sickness. Thus, your fever might come down and consequently your sickness but both would presently appear.
I’ve had chronic pain in my heels for a few months now. It’s especially severe whenever I put my feet on the ground from a raised position. Someone had told me that it occurs due to calcification near the Achilles Tendon, and I must take medication for that. Having pushed it for a few months now I finally went to see my uncle who is an orthopaedic yesterday (this is the same guy who told me about my Boxer’s Fist).
He promptly diagnosed me with Plantar Fasciitis, and wrote down some medication, and told me what I need to do in order to reduce the pain in my feet. After a short conversation on what else I need to do, and any precautions, and all such, I asked him about the calcification thingy – whether he had ruled out that calcification of the Achilles Tendon was causing this problem.
“I’m sure there will be some calcification”, he said, “and I’m not sending you for an X-ray because I have a very good idea of what it will show and it won’t add much value”. And then he proceeded to explain that calcification is a “result” of plantar fasciitis and not a cause of it. He didn’t use the terms “correlation” or “causation” but he explained that when you suffer from plantar fasciitis you end up with both calcification of your Achilles Tendon and also shooting pain in your heels, especially immediately after waking up. The two are thus related, he said, but neither causes the other, but there is a third factor (fasciitis) that causes both, and that is the one that he is treating me for!
I was doubly impressed with him – first for understanding “information theory” in terms of understanding that the X-ray wouldn’t add much information, and secondly for recognising that there was a third factor and that correlation should not be mistaken for causation. Or perhaps I had a particularly low prior for mathematical and statistical skills of doctors!
He refused to charge me a fee, since I’m his nephew. While on my way out I was thinking about it and wondering on what circumstances I would waive my professional fees for my consulting. And I realised it would be hard to do so for anyone! It made me wonder what made my uncle waive his medical fees, while I’m extremely unlikely to do that.
I realised it has to do with the investment. He spent about five to ten minutes with me (perhaps a bit longer), but essentially his marginal cost of treating me was quite low. And this was a marginal cost that he was willing to sacrifice in return for the goodwill he gets for treating the extended family for free. Considering the size of my engagements, though, the marginal cost is usually high and is seldom justified by goodwill!