A Lower Confidence Limit for the Benchmark Dose Using Higher Order Inference
Year of Publication
Joint Statistical Meeting
Asymptotic Normality; Benchmark Dose; Coverage Probability; Likelihood; Logistic Model
In dose-response studies, the benchmark dose (BMD) is defined as the dose level that produces a specified increase in the probability of an adverse outcome, compared to background. Animal toxicity studies are usually used to estimate the BMD, and to compute a lower confidence limit (denoted by BMDL) for the BMD. The BMDL is typically calculated using the Wald statistic or the likelihood ratio test (LRT) statistic. Both of these rely on asymptotic normality, and are known to be accurate to the first order. In many applications, due to the cost involved in the experiment, or due to the toxicity of the chemical agent, the number of animals per dose and/or the number of dose levels is small, and thus the Wald and LRT statistics may yield inaccurate results. In the talk, we propose a higher order likelihood based procedure to obtain BMDL under the logistic regression model. Simulation results on the coverage probability show the improved performance of the proposed method over the existing procedures. Joint work with John Fox and Leonid Kopylev at EPA and Thomas Mathew and Anindya Roy at UMBC.