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J Biopharm Stat. 2006;16(5):657-77.

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

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Statistical Research and Consulting Center, Pfizer Inc, New London, Connecticut 06230, USA.


Application of a sigmoid Emax 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 Emax 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 Emax 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.

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