  This paper describes several approaches for estimating the benchmark dose
(BMD) in a risk assessment study with quantal dose-response data and when there
are competing model classes for the dose-response function. Strategies
involving a two-step approach, a model-averaging approach, a focused-inference
approach, and a nonparametric approach based on a PAVA-based estimator of the
dose-response function are described and compared. Attention is raised to the
perils involved in data "double-dipping" and the need to adjust for the
model-selection stage in the estimation procedure. Simulation results are
presented comparing the performance of five model selectors and eight BMD
estimators. An illustration using a real quantal-response data set from a
carcinogenecity study is provided.
