Schneier on Security

Roger • November 10, 2012 11:33 PM

I have several problems with this:

1. The examples suggest that it is defined in terms of 1 millionth of the subject’s residual life expectancy, not total. This produces confusing and counter-intuitive results when addressed to older people. For example, for many types of risk exposures, an exposure at 22 years causes several times greater reduction in mean life expectancy than an identical exposure does at 80. (This is the case for cigarettes.) However if it reduces the life expectancy of the 22 year old by 1½ hours, and that of an 80 year old by ½ hour, these would be quoted as 3 umt and 7½ umt, incorrectly making it sound much more dangerous for the older person.
2. Some of the claims for actual values are nonsense. For example, for cigarettes Prof. Spiegelhalter … [makes] the simplifying assumption that each cigarette contributes equally to the risk. This is not simplifiction, it is wrong. There does not exist a simple linear relationship between number of cigarettes consumed and reduced life expectancy. This isn’t to say that people shouldn’t be warned that it is very unwise to smoke and a good idea to quit; but it is false to say that “each cigarette loses 15 minutes of your life”, and stating falsehoods doesn’t help the argument.
3. The one for BMI is even worse. To force it into this proportionality model, he ignores several key features of the paper he cites. In particular, he grinds his microlife values out of a reported hazard ratio using a calculation based on Gompertz’ appromximation; all the while missing that the cited article’s figures (especially Fig.7) give the result directly. Those figures, however, would have been a little unsatisfactory: they show that i) the relationship is not remotely linear; ii) for BMI ranges below 22, it is negative i.e. losing weight shortens life expectancy; and iii) most importantly, for BMI below 35 (the supposed boundary between “moderately obese” and “severely obese”), the relationship is weak with both a small slope and weak correlation; nearly all the upswing is actually in the severely obese zone. To characterise this as “each 5 kg of overweight reduces life expectancy by 1 umt” is a completely false representation of the results in the cited paper.
4. Presumably this sentence is a typo: “This means he is losing around 350 days life-expectancy, 16,500 microlives, for every day he is overweight.” (If that was the case he would be dead in two months.)
5. But my worst gripe by far: The real problem — and a perennial problem in many epidemiological studies — is that there is large uncertainty in the results and it is rarely reported to the public nor to policy makers. In this BMI data, the 95% confidence intervals for the two BMI zones used by Prof. Spiegelhalter actually overlap by around 60%. Based on this data, we cannot state with confidence that a 1.75 m tall man who lowers his mass from 78 to 73 kg will thereby probably live 350 days longer. On the contrary, we do not even have very high confidence that he will increase his life expectancy at all; in fact there’s even about a 10% chance that losing weight will actually lower his life expectancy. This is one of the a perennial bug-bears of epidemiology: results are published at very low confidence levels, or with confidence intervals that overlap “no effect”, or without even calculating confidences; and are then made to seem important by multiplying a large “exposed” population by a highly uncertain number that is close to zero and may in fact be zero. The result is that people have learned to ignore epidemiological Cassandras not because they do not understand risk; but because they are fed up with an endless series of contradictory proclamations that are rarely substantiated.