Multiplicity-adjusted inferences in risk assessment: Benchmark analysis with quantal response data

A primary objective in quantitative risk or safety assessment is characterization of the severity and likelihood of an adverse effect caused by a chemical toxin or pharmaceutical agent. In many cases data are not available at low doses or low exposures to the agent, and inferences at those doses must be based on the high-dose data. A modern method for making low-dose inferences is known as benchmark analysis, where attention centers on the dose at which a fixed benchmark level of risk is achieved. Both upper confidence limits on the risk and lower confidence limits on the "benchmark dose" are of interest. In practice, a number of possible benchmark risks may be under study; if so, corrections must be applied to adjust the limits for multiplicity. In this short note, we discuss approaches for doing so with quantal response data.