Bayesian benchmark dose risk assessment with mixed-factor quantal data

Benchmark analysis is a general risk estimation strategy for identifying the benchmark dose (BMD) past which the risk of exhibiting an adverse environmental response exceeds a fixed, target value of benchmark response. Estimation of BMD and of its lower confidence limit (BMDL) is well understood for the case of an adverse response to a single stimulus. In many environmental settings, however, one or more additional, secondary, qualitative factor(s) may collude to affect the adverse outcome, such that the risk changes with differential levels of the secondary factor. Bayesian methods for estimation of the BMD and BMDL have grown in popularity, and a large variety of candidate dose–response models is available for applying these methods. This article applies Bayesian strategies to a mixed-factor setting with a secondary qualitative factor possessing two levels to derive two-factor Bayesian BMDs and BMDLs. We present reparameterized dose–response models that allow for explicit use of prior information on the target parameter of interest, the BMD. We also enhance our Bayesian estimation technique for BMD analysis by applying Bayesian model averaging to produce the BMDs and BMDLs, overcoming associated questions of model adequacy when multimodel uncertainty is present. An example from environmental carcinogenicity testing illustrates the calculations.