Bayesian Benchmark Dose Analysis

TL;DR

This paper develops Bayesian models for estimating Benchmark Doses in environmental risk assessment, incorporating prior information and using Monte Carlo methods for improved inference of BMDs and BMDLs.

Contribution

It introduces reparameterized Bayesian models for BMD analysis that explicitly target the BMD and BMDL, enhancing estimation accuracy with prior information.

Findings

Bayesian approach provides credible limits for BMDs.

Monte Carlo adaptive Metropolis algorithm effectively approximates posterior distributions.

Application to carcinogenicity testing demonstrates practical utility.

Abstract

An important objective in environmental risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs) that induce a pre-specified Benchmark Response (BMR) 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 employing quantifiable prior belief to represent parameter uncertainty in the statistical model. Implementation is facilitated via a Monte Carlo-based adaptive Metropolis (AM) algorithm to approximate the posterior distribution. An example from environmental carcinogenicity testing illustrates the calculations.