Epidemiological Models and Spotty Statistics

Epidemiological models generate statistics that look like ordinary counts and percents of real things. But these statistics are anything but ordinary counts and percents. These statistics are generated by models – they are speculative statistics. And like all model-generated numbers, they depend critically on the assumptions involved – the choice of what to take into account. This paper reviews how these statistics are generated and shows how sensitive they are when taking into account confounders. These speculative statistics are described as “spotty statistics” for the same reason we might say a worker’s resume with big gaps between jobs is a “spotty work record.” We are not saying that anything is necessarily false. We are saying that what is not shown may be extremely relevant to the situation at hand. In the case of spotty statistics, their sensitivity to assumptions or confounders means they should definitely be handled with care. Introduction The focus of this paper is the presence of model-based statistics in the everyday media. Here are some examples involving linear models:  “the rate of [Alzheimer’s] decline unfolded 4 percent more quickly for each additional year of education.” Reuters 10/22/2007.  “For every can or glass of sugar-sweetened beverage a child drank [a day] ..., a child’s ... chance of becoming obese increased 60%.” The Lancet, 2001; 357:505-508.  “each hour of television watched per day at ages 1-3 increases the risk of attention problems, such as ADHD, by almost 10 percent at age 7.” Science Daily 4/6/2004. Statistics generated by epidemiological models appear even more frequently. Here are some examples. Figure 1: Smoking-Related Deaths A casual observer might think that these fivemillion deaths represent real deaths – deaths that are certifiable by a coroner. All deaths are coroner certified. So what is speculative about this statistic? It is the unstated claim that of all the actual deaths, 5 million of them are caused by cigarette smoking. That is the speculative claim, the model-based claim. Figure 2 illustrates more of these speculative statistics. Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session STS008) p.2114