Truth, damn truth, and statistics

It's just unavoidable when we're talking about public health, medicine, or for that matter physics and cosmology that we spend a lot of time speaking the language of probability and statistics. People generally feel that they have an intuitive grasp of probabilistic concepts, and that they handle the idea of risk and odds with facility. On the other hand those scientific types go off on less familiar ideas like confidence intervals and correlation coefficients, and really impenetrable concepts like multivariate modeling.

I have tried to present some of the basic ideas as accessibly as I could, here, and another important idea here. But today I don't want to get deeply into the higher mathematics, I just want to ponder probabilistic thinking in general.

As I say, we feel we graps the idea of probability -- odds -- intuitively. But it's actually a very slippery concept. In fact, although scientists rely heavily on probabilistic thinking, the philosophical underpinnings of science have great difficulty with it. The modern philosophy of science has its footings pounded deeply into the positivist idea that the meaning of a statement is equivalent to the method needed to verify its truth. But it isn't entirely clear how statements about probability are verified. If your TV weatherbot says there is a 50% chance of rain tomorrow, she will have been right. Rain or no rain, there was a 50% chance. Or maybe not.

So, when we say that risk factors for stroke include family history, smoking, high LDL cholesterol, obesity, high blood pressure, and diabetes, we don't mean that fat, lazy, french fry gobbling, chain smoking uncle Larry whose parents both had strokes is going to have one; whereas slim, abstemious, vegetarian triathlete brother-in-law Fred whose parents are both 100 years old and compete annually in the world Scrabble championship definitely won't. Out of a thousand Fred's and a thousand Larrys, more Larrys than Freds will have strokes by the age of 50, 60, 70, etc. On the other hand, since a higher percentage of Freds will live to any given age, they will have more time to have strokes and in the end, as we see in the Framingham cohort, about equal numbers will get it in the end.

Social scientists, and the religious cult known as economists, are always trying to analyze such proabilities in terms of "rationality" or "rational choice." Somehow they think they can figure out in objective, unassailable terms, whether the pleasure you get from that french fry is really worth the risks. Then they will give you the relevant information and if you don't do what they say, you're irrational -- a sort of derangement. I even use some of these ideas at times -- such as cost per Quality Adjusted Life Year -- because they offer a convenient metric for making comparisons. But always remember -- shit happens.