Dose–Response Modeling Under Simple Order Restrictions Using Bayesian Variable Selection Methods

Bayesian modeling of dose–response data offers the possibility to establish the relationship between a clinical or a genomic response and increasing doses of a therapeutic compound and to determine the nature of the relationship wherever it exists. In this article, we focus on an order-restricted one-way ANOVA model which can be used to test the null hypothesis of no dose effect against an ordered alternative. Within the framework of the dose–response modeling, a model uncertainty can be addressed using model averaging techniques. In this setting, the uncertainty is related to the number of all possible models that can be fitted to the data and should be taken into account for both inference and estimation. In this article, we propose an order-restricted Bayesian variable selection model that addresses the model uncertainty and can be used for both inference and estimation. The proposed method is applied to two case studies and is compared to the likelihood ratio test and the multiple contrast tests in both the analyses of the case studies and a simulation study. This article has online supplementary material.