Thomas Neal
Statistical Research and Consulting Center, Pfizer Inc, New London, Connecticut 06230, USA.
J Biopharm Stat. 2006;16(5):657-77. doi: 10.1080/10543400600860469.
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.
描述了一种S形Emax模型的应用，用于评估包含少量剂量（通常为三到六个）的设计中的剂量反应。扩展模型是一个常见的Emax模型，其中幂（希尔）参数应用于剂量和ED50参数。该模型将按照Bretz等人（2005年）提出的策略进行评估。S形Emax模型用于创建几个具有高功效的对比，以检测与安慰剂相比的递增趋势。使用应用于从对比中获得的p值的多重比较方法来控制无剂量反应假设的α水平。在确定药物活性之后，使用贝叶斯方法从稀疏给药设计中估计剂量反应曲线。应用于S形模型的贝叶斯估计代表了模型选择中的不确定性，而当从一组非嵌套模型中选择单个更简单的模型时，这种不确定性就会被忽略。目标是基于对剂量反应关系的实质性知识和广泛经验来进行模型选择，而不是基于为确保估计量收敛而选择的标准。当一些参数确定得很差时，贝叶斯估计还解决了基于渐近最大似然估计得出的置信区间和检验中的缺陷，这对于常见剂量反应设计的数据来说是典型的。
