Limitations to empirical extrapolation studies: the case of BMD ratios.

Extrapolation relationships are of keen interest to chemical risk assessment in which they play a prominent role in translating experimentally derived (usually in animals) toxicity estimates into estimates more relevant to human populations. A standard approach for characterizing each extrapolation relies on ratios of pre-existing toxicity estimates. Applications of this "ratio approach" have overlooked several sources of error. This article examines the case of ratios of benchmark doses, trying to better understand their informativeness. The approach involves mathematically modeling the process by which the ratios are generated in practice. Both closed form and simulation-based models of this "data-generating process" (DGP) are developed, paying special attention to the influence of experimental design. The results show the potential for significant limits to informativeness, and revealing dependencies. Future applications of the ratio approach should take imprecision and bias into account. Bootstrap techniques are recommended for gauging imprecision, but more complicated techniques will be required for gauging bias (and capturing dependencies). Strategies for mitigating the errors are suggested.