Statistics, Voodoo, and Medical Misadventures

Dr. Kildare, washing his d*mn hands!

People don’t become doctors because they are good at or even interested in science. They become doctors because they want to help people. Some may be good at science and math, but that’s almost a coincidence, when it happens. It’s possible for a motivated but untalented person to cram enough biology and chemistry to get by without every really understanding any of it.* This disjunction between medicine and science is evident in the history of medicine. See, for example, the story of what it took, and how long it took, for doctors to accept that they needed to wash their hands.

That said, I for one am very grateful to doctors – like many if not most people, I have had a couple occasions in my life where, without expert medical intervention, I would have ended up crippled or possibly dead. So, thanks, doctor-persons!

But we would do well to remember that doctors, as doctors, are not, in fact, scientists. In fact, a brief look at the vast panorama of quackery at large today reveals doctors are behind a depressing amount of it – fad diets and treatments that make bloodletting and bell-ringing sound pretty reasonable by comparison. (Look up Dr. Kellogg sometimes.) The drive and ambition that gets one through medical school has very little to do with a love for science and logic.

There’s this thing let’s call mathematical or perhaps scientific intuition. It is the ability to look at something represented with numbers, and understand what it is trying to tell you and, more important, what it can and can’t tell you.

Like just about any talent, mathematical intuition seems to have both nature and nurture components. I’ve got it to some minor degree, but I’ve also nurtured it for decades now, so I seem to be pretty good at, I think. Note that this has little to do with mathematical skills: The hardest math I can do is the Black – Scholes calculations, which, at the level I can do them, would entail *very* light derivative calculus and super-easy multiple regression analysis – stuff you can do in Excel. I’ve been too lazy to get very good at math. But I made a career out of well-honed mathematical intuition.

In the finance world, it’s a huge, as in HUGE, advantage to be able to look at some numbers and quickly figure out what they’re telling you. In this field, it’s a common, but by no means ubiquitous, talent. Suffice it to say that a lot of finance numbers don’t quite mean what they seem, and that, without an understanding of what goes into them, they can easily lead you very far astray.

But doctors are very unlikely to have any mathematical intuition, and less likely to hone it over time – it’s just not what they do. Except when they do, such as in developing or applying protocols based on statistical analysis.

Having doctors develop and apply protocols based on their understanding of what statistics mean is not a formula from which we should expect happy results. Two example, and these are from memory and a decade or more out of date, current situation may be better, etc., but since they are illustrative, I going to be lazy and not look them up:

Blood pressure: we’ve all heard 120/80 as the Holy Grail, and those are good numbers. However, turns out that 120/80 is not measurably more healthy than 135/85 – the actual statistics don’t show the dreaded uptick in problems associated with high blood pressure until you get above those numbers. Also, there is an alarming assumption of homogeneity: that everybody within a group, usually and age or weight group, with the same blood pressure is equally likely to have the same reaction. Are they? It would be surprising if, in fact, blood pressure had the same meaning across all people – maybe it does, could be, but when I looked into this, I didn’t see anything but wide bands assembled for analysis. People were just grouped – male, 50-55, with a BMI of something, etc.

The science guy in me – my mathematical intuition – really wants to know about other details for these people thus grouped: Any body-builder or distance runners in there? How about couch potatoes, or people with other health problems? Are we really assuming everyone in this group is effectively ‘the same’? Really?

Now doctors are going to follow protocols based on their understanding of what all this means: the protocol is (or, at least was as of a few years ago) that adult males under a certain age must have a 120/80 reading, or drugs will be prescribed as needed to get them there.** Now, there is a certain amount of wisdom in shooting for numbers that are a) very common in healthy people, and b) providing a little buffer beneath the danger zone, but there should also be some wiggle room in there, it seems to me. Knowing what constitutes acceptable wiggle room would require not just understanding the medical issues, but some *mathematical intution* about what the numbers are telling you.

Also, if you follow the protocols, it makes it harder for you to get sued. So, what might have started as guidelines end up as laws carved in stone.

Second example: salt intake. Take a thousand people with high blood pressure, say, an average of 140/90. Have them all cut their salt intake. It is very likely that the average will drop, maybe to 135/85. Conclusion: salt intake causes blood pressure to go up; reducing salt intake causes blood pressure to go down. Therefore, the protocol is developed to tell people with high blood pressure to cut salt intake.

Anybody see the obvious problem in here? Beuler?

Turns out that salt intake really does affect blood pressure – for around 30% of people with high blood pressure. For the other 70%, no amount of salt that any person with functioning taste buds would ever put on their food in real life has any effect at all. But, if you just see the results – we had a thousand people cut salt, and their average blood pressure dropped – and had no mathematical intuition, the conclusion as expressed in a protocol is obvious: people with high blood pressure should cut their salt intake.

Thus, doctors waste their social capital by telling people to make a very difficult change – cutting salt for somebody with a lifetime of eating habits can be very difficult and miserable – on recommendations that only help a minority of people. (There’s also a deficit in some doctors’ understanding how their orders affect the people getting them, that people generally trust and even love their doctors, and when they fail, as they generally do, in making the changes the doctor tells them to make, they feel bad about it, want to stay away from the doctor, don’t even try to follow his next recommendation, and in general do more harm than good.)

This general and demonstrable lack of mathematical intuition in the medical world is another contributing factor in my insistence on looking at the COVID 19 models and numbers myself: they have been processed by doctors, and therefore, almost certainly fundamentally misunderstood.

And, yes, they have been.

One final tragedy here, the one that will haunt and curse us for years to come: If you lack mathematical intuition, reality will almost always seem to back you up! 120/80 really is a good blood pressure! Few people with it die from heart trouble! On average, reducing salt really does lower blood pressure!

And the spread of infections really does drop when you do a bunch of reasonable-sounding things all at the same time across entire populations. That 95% of those things don’t do anything for 95% of the people will be masked by looking at the big numbers only, and refusing to consider the heterogeneity of the underlying situations. Add emotions flamed white-hot by incessant panic-mongering, and – well, here we are.

The transition to voodoo is all but invisible, and has already taken place: the medicine man must perform the ritual before dawn, or the sun will not rise! Ignore those heretics with their telescopes and astrolabes! We can’t take the risk! Pay up the offering! Or else!

We will be told, over and over and over again, how we were only spared DOOOOOM by doing what our betters told us to do: wearing masks, social distancing, shuttering millions of businesses, and discarding the constitutionally-guaranteed right to free assembly; and that, if we don’t want DOOOOM this fall, we’ll have to – HAVE TO!!!! – do it all over again. Any who say anything against this are heretics, and want people to die.

*For what it’s worth (hint: not much) read somewhere, years ago, that doctors have an average IQ of about 105 – very slightly above the general average. So, just a little smarter than the average bear. But: doctors have very large ambition and drive. So, you tend to end up with people who are justifiably proud of their achievement – medical school is hard – but really not all that smart. They then have to tell people what to do in emotionally intense situations. And they don’t understand science. So, if you push back (as I have, on occasion,very politely) it’s hard for them to process. Not all, by any means, and to greatly varying degrees – but I’d be surprised to meet very many people who have not run across a doctor or two with delusions of godhead.

** I learned all this because, of course, I developed high blood pressure some years ago, and was prescribed a bunch of drugs, some of which really messed with my sleep and general well-being. Getting the doctor to cut the meds made him uncomfortable, although he’s a great guy and all that, because there’s a *protocol* for how much and in what order different drugs are prescribed. When I told him I’d be happy to accept the (non-existent) risk of shooting for a 135/85 reading, he wasn’t too enthusiastic.