Toxicologists are often concerned with determining the dosage to which an individual can be exposed with an acceptable risk of adverse effect. These types of studies have been conducted widely in the past, and many novel approaches have been developed. Parametric techniques utilizing ANOVA and nonlinear regression models are well represented in the literature. The biggest drawback of parametric approaches is the need to specify the correct model. Recently, there has been an interest in nonparametric approaches to tolerable dosage estimation. In this work, we focus on the monotonically decreasing dose response model where the response is a percent to control. This poses two constraints to the nonparametric approach. The doseresponse function must be one at control (dose = 0), and the function must always be positive. Here we propose a Bayesian solution to this problem using a novel class of nonparametric models. A basis function developed in this research is the Alamri Monotonic spline (AM-spline). Our approach is illustrated using both simulated data and an experimental dataset from pesticide related research at the US Environmental Protection Agency.
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