Abstract
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 non-linear regression models are well represented in the literature. The biggest drawback of parametric approaches is the need to specify the adequate 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 imposes two constraints on the nonparametric approach: the dose-response function must be monotonic and always positive. Here, we propose a Bayesian solution to this problem using a novel class of non-parametric models. A set of basis functions developed in this research is Alamri Monotonic spline (AM-spline). Our approach is illustrated using two simulated datasets and two experimental datasets from pesticide related research at the US Environmental Protection Agency.