One-hit models of carcinogenesis: conservative or not?

One-hit formulas are widely believed to be "conservative" when used to analyze carcinogenesis bioassays, in the sense that they will rarely underestimate risks of cancer at low exposures. Such formulas are generally applied to the lifetime incidence of cancer at a specific site, with risks estimated from animal data at zero dose (control), and two or more additional doses that are appreciable fractions of a maximum tolerated dose. No empirical study has demonstrated that the one-hit formula is conservative in the sense described. The Carcinogenesis Bioassay Database System contains data on 1212 separate bioassays of 308 chemical substances tested at exactly three evaluable doses. These provided sufficient data to examine 8432 specific combinations of cancer site with sex, species, and chemical. For each of these we fitted a one-hit formula to the zero and maximum dose data points, then examined the relation of the fitted curve to the incidence rate observed at the mid-dose, with and without adjustment for intercurrent mortality. Both underestimates and overestimates of risk at mid-dose occurred substantially more often than expected by chance. We cannot tell whether such underestimates would occur at lower doses, but offer six biological reasons why underestimates might be expected. In a high percentage of animal bioassays, the one-hit formula is not conservative when applied in the usual way to animal data. It remains possible that the one-hit formula may indeed be conservative at sufficiently low doses (below the observational range), but the usual procedure, applied to the usual dose range, can be nonconservative in estimating the slope of the formula at such low doses. Risk assessments for regulation of carcinogens should incorporate some measure of additional uncertainty.