  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.
