Benchmark Dose Estimation using a Family of Link Functions

Abstract: This article proposes a method of estimating benchmark dose (BMD) using a family of link functions in binomial response models dealing with model uncertainty problems. Researchers usually estimate the BMD using binomial response models with a single link function. Several forms of link function have been proposed to fit dose response models to estimate the BMD and the corresponding benchmark dose lower bound (BMDL). However, if the assumed link is not correct, then the estimated BMD and BMDL from the fitted model may not be accurate. To account for model uncertainty, model averaging (MA) methods are proposed to estimate BMD averaging over a model space containing a finite number of standard models. Usual model averaging focuses on a pre-specified list of parametric models leading to pitfalls when none of the models in the list is the correct model. Here, an alternative which augments an initial list of parametric models with an infinite number of additional models having varying links has been proposed. In addition, different methods for estimating BMDL based on the family of link functions are derived. The proposed approach is compared with MA in a simulation study and applied to a real data set. Simulation studies are also conducted to compare the four methods of estimating BMDL.