Bayesian benchmark dose analysis

An important objective in environmental risk assessment is the estimation of minimum exposure levels called benchmark doses (BMDs), which induce a pre-specified benchmark response in a target population. Established inferential approaches for BMD analysis typically involve one-sided, frequentist confidence limits, leading in practice to what are called benchmark dose lower Limits (BMDLs). Appeal to Bayesian modeling and credible limits for building BMDLs is far less developed, however. Indeed, for the few existing forms of Bayesian BMDs, informative prior information is seldom incorporated. We develop reparameterized quantal-response models that explicitly describe the BMD as a target parameter. Our goal is to obtain an improved estimation and calculation archetype for the BMD and for the BMDL by quantifying prior beliefs representing parameter uncertainty in the statistical model. Implementation is facilitated via a Monte Carlo-based adaptive Metropolis algorithm to approximate the posterior distribution. An example from environmental carcinogenicity testing illustrates the methodology.