Hypothesis testing and Bayesian estimation using a sigmoid Emax model applied to sparse dose-response designs

Application of a sigmoid E-max model is described for the assessment of dose-response with designs containing a small number of doses (typically, three to six). The expanded model is a common E-max model with a power (Hill) parameter applied to dose and the ED50 parameter. The model will be evaluated following a strategy proposed by Bretz et al. (2005). The sigmoid E-max model is used to create several contrasts that have high power to detect an increasing trend from placebo. Alpha level for the hypothesis of no dose-response is controlled using multiple comparison methods applied to the p-values obtained from the contrasts. Subsequent to establishing drug activity, Bayesian methods are used to estimate the dose-response curve from the sparse dosing design. Bayesian estimation applied to the sigmoid model represents uncertainty in model selection that is missed when a single simpler model is selected from a collection of non-nested models. The goal is to base model selection on substantive knowledge and broad experience with dose-response relationships rather than criteria selected to ensure convergence of estimators. Bayesian estimation also addresses deficiencies in confidence intervals and tests derived from asymptotic-based maximum likelihood estimation when some parameters are poorly determined, which is typical for data from common dose-response designs.