Statistics with Real World Consequences
Lead poisoning has been identified as a major public health problem that disproportionately affects poor children. High lead levels in children's blood are associated with serious declines in IQ, but several investigators have reported a puzzling observation: IQ appears to decrease faster at low blood lead levels (less than 10 micrograms/dl) than at high levels. This is called a supra-linear dose-response curve. It is hard to understand the biological basis for such an effect, but it has led to strenuous and costly efforts to remove even trace amounts of lead from children's environments.
Two researchers [1] have now shown that that the effect is likely a statistical artifact. It arises from the fact that IQ is distributed according to a symmetrical bell-shaped curve, while lead burden is distributed in a log-normal fashion, with a peak at low values and a long tail to high lead concentrations. If the assumption is made that the 50th percentile of IQ is associated with the 50th percentile of lead concentration, the 5th percentile of IQ with the 95th percentile of lead concentration, and so forth, the supra-linear dose-response relationship is the inexorable result. It shows that the apparent strong effect of low lead levels on IQ is simply a consequence of the two statistical distributions, and probably has no biological or public health significance.
I've written about this paper not because I'm a statistics aficionado, or a skeptic about the deleterious effects of high lead levels in children's blood. Rather, I feel the paper is important because it shows how careful we must be to examine experimental data and its statistical treatment when it is used as the basis for expensive public policy. The money spent to remediate low-level lead exposures could very likely have been spent more productively on other public health measures for poor children.
[1] "What is the meaning of non-linear dose-response relationships between blood lead concentrations and IQ?", T.S. Bowers and B.D. Beck, NeuroToxicology 27 (2006) 520-524.