Unhealthful News 10 – time trends are often not trends

Paul Bergen suggested this pretty funny story for today's post.  It seems that an investment bank financial analyst in Great Britain looked at historical smoking rates and predicted that smoking in that country would drop to approximately zero in 30-50 years.  The prediction was apparently based on a linear extrapolation from smoking prevalence from the 1960s to today, extending it into the future.  The story attributes a drop in the share prices of two British-based tobacco companies to the report.

Oh where to start?

As I presented at greater length a couple of days ago, in the context of intentional junk science, apparent time trends depend a lot on what time period you choose.  If we extrapolate smoking prevalence based on a linear trend since 1911, we would predict an increase in use.  From 2001 we would predict little change for the foreseeable future.  I do not think the present example rises to the level of junk science, however, because it is really too simplistic to qualify.

There have been about a zillion studies of predicted future smoking prevalence.  Most of them are political and all have major limitations, but some (not all) are better than just extrapolating a line.  If the new report had charted and extrapolated the decline in the use of, say, staplers, predicting their disappearance, that might have been news.  But adding one bit of simplistic analysis about smoking (that anyone familiar with the topic can do in their head in seconds) adds nothing.  Thus it seems particularly amusing to attribute the days change in stock prices to the report; only news that is new can change people's beliefs.  Also, a quick calculation using reasonable discount rates (a topic for another day) shows that what is happening that many decades in the future should barely affect current share prices, particularly for British American Tobacco which, despite the name and headquarters location, does very little of its business in Britain.  Indeed, it turns out that the attributed price drop was such a tiny fraction of 1% of share value that it should have been rounded to "unchanged".

This story is an illustration of one way that econometrics does much better than epidemiology (and apparently financial analysis), explaining changes as variables in themselves.  That is, epidemiology almost always looks only at the particular value of interest (e.g., smoking prevalence), trying to explain it in terms of other variables (e.g., time trend), but not at changes in prevalence or changes in the rate of change in the prevalence (also called the first and second derivatives of the prevalence by those who prefer to think that way).  Econometrics quite often looks for explanatory variables that predict changes or changes-in-changes in themselves, rather than just the value itself.  When epidemiologists do it, they usually bungle the job.  Anyone who is serious about studying smoking prevalence changes should try to estimate the effects of particular shocks (like everyone learning about the risk, which explains the sharp decrease in smoking from the peak in the 1960s) rather than naively attributing it to time trend.  Understanding this is critical because that downward shock is an event that is completed and cannot be duplicated.

Poor understanding of changes per se, particularly the effect of one-off events, may contribute to many anti-smoking political actors' misreading of history.  They seem to think that since telling people about the risks reduced smoking by half, continuing to tell them even more loudly can reduce it to zero.  This leads them to claim (and perhaps even to actually believe) that smoking will soon be eliminated and there is no benefit from pursuing tobacco harm reduction.  Needless to say this is obviously wrong, since people can only learn a particular fact only once.  Claiming that further warnings will reduce smoking is exactly the same as claiming that the stock market reacted to the "news" about what happens if we linearly extrapolate smoking prevalence.  

Of course it is possible that smoking in Britain will indeed drop to near zero within 30 years.  Indeed, many of us predict as much, and hope it will happen much sooner, but not because what happened in the 1970s will happen again.  Instead, there will be an equally important shock:  People will eventually get honest information about how smokeless nicotine products are about 99% less harmful, the products will become as legal and socially acceptable as cigarettes, and most smokers will switch to them.  (Tomorrow I will attribute the days' change in tobacco share prices to the fact that I wrote that sentence – and no one will be able to prove me wrong.)