Statistical evaluation of the dose--response function in lead epidemiology is rarely attempted. Economic evaluation of health benefits of lead reduction usually assumes a linear dose-response function, regardless of the outcome measure used. We reanalyzed a previously published study, an international pooled data set combining data from seven prospective lead studies examining contemporaneous blood lead effect on IQ (intelligence quotient) of 7-year-old children (n = 1,333). We constructed alternative linear multiple regression models with linear blood lead terms (linear-linear dose response) and natural-log-transformed blood lead terms (log-linear dose response). We tested the two lead specifications for nonlinearity in the models, compared the two lead specifications for significantly better fit to the data, and examined the effects of possible residual confounding on the functional form of the dose-response relationship. We found that a log-linear lead-IQ relationship was a significantly better fit than was a linear-linear relationship for IQ (p = 0.009), with little evidence of residual confounding of included model variables, We substituted the log-linear lead-IQ effect in a previously published health benefits model and found that the economic savings due to U.S. population lead decrease between 1976 and 1999 (from 17.1 [micro]g/dL to 2.0 [micro]g/dL) was 2.2 times ($319 billion) that calculated using a linear-linear dose-response function ($149 billion). The Centers for Disease Control and Prevention action limit of 10 [micro]g/dL for children fails to protect against most damage and economic cost attributable to lead exposure. Key words: child IQ, dose response, health benefit, health policy, lead.

Few researchers doubt that lead exposure has significant health consequences at levels below those considered medically acceptable just decades ago, although there is still debate over what levels of lead exposure, if any, can be considered harmless. Key to this debate is determining the form of the dose-response function describing how the amount of exposure is related to the magnitude of the health effect.

There are two basic forms of the dose-response function for lead: a simple linear model, in which the increase in health effect is a linear function of increasing blood lead concentration (BPb), and a nonlinear model, in which the amount of health effect change attributable to lead changes according the region of the dose-response curve studied. A special case of the nonlinear dose-response function is a threshold model in which the response to lead decreases as a function of decreasing dose until it reaches a lead dose below which there is no further detectable change in health. An alternative threshold model is one in which the response to lead changes as a function of increasing dose until an upper lead bound is reached, at which point the increase in health damage exceeds predictions, as in cases of high doses producing organ damage.

Although epidemiologists have become increasingly sophisticated in construction and diagnosis of models describing their data, as a whole, we generally pay much less attention to systematically and rigorously addressing the specification of the dose-response function. A number of public health issues depend on adequately specifying the form of the dose-response function for lead, chief among them regulatory action.

Cost-benefit analyses should form the backbone of regulatory decisions regarding permissible exposures or background concentrations of toxic substances in both population and occupational settings. In such an ideal world, the savings in health care, disability, and productivity gain realized from reducing exposure to a particular substance are compared to the cost required to achieve that reduction in exposure. Policy analysts seek the "sweet spot," where the marginal costs of lead reduction equal the marginal benefits (i.e., where the slopes of the cost function and benefits function are equal) (Pacala et al. 2003). Even if in the real world less easily quantifiable factors affect regulatory decisions, all parties to regulation have some notion of costs and benefits in mind when presenting their cases to regulatory agencies.

One recent publication (Grosse et al. 2002) presented data on the economic benefits of nationwide lead reduction due to childhood IQ (intelligence quotient) loss attributable to lead over the last 25 years. These authors conservatively used a linear dose-response function of lead-IQ as part of their model, stating that there was insufficient evidence to determine the shape of the dose-response function. The economic savings predicted by their model were in the range of hundreds of billions of dollars over the lifetime of a yearly birth cohort.

The lead-health dose-response function selected for the benefits model has clear implications for policy decisions based on it. A threshold model suggests that once reductions of population level of lead reach the threshold, further lowering of lead would have no beneficial health or economic consequences. The current Centers for Disease Control and Prevention (CDC) action limit of > 10 [micro]g/dL for children (CDC 1991) would be justifiable on health grounds alone if there were a threshold somewhere near that limit. A linear model suggests that equal reduction in population BPb is accompanied by equal reduction in health consequence from any starting level of lead. Under a linear dose-response model, even though the health benefit would continue to increase with further population lead reduction, the present CDC action limit might be justifiable on economic grounds if the cost of further population BPb reduction far exceeded the recoverable economic benefits. A nonlinear model, especially one in which health benefits are greater for lead reduction nearer the population's zero lead point than farther from it, would argue for further reduction in population lead levels and CDC action limits if the accelerated health benefit at lower lead levels exceeded the increased costs of lead reduction to those levels.