Baayen C, Hougaard P
Biometrics Division, H. Lundbeck A/S, Ottiliavej 9, 2500 Valby, Denmark.
Section of Biostatistics, University of Copenhagen, Øster Farimagsgade 5, 1014 Copenhagen, Denmark.
Stat Med. 2015 Nov 30;34(27):3546-62. doi: 10.1002/sim.6566. Epub 2015 Jun 25.
An important aim of drug trials is to characterize the dose-response relationship of a new compound. Such a relationship can often be described by a parametric (nonlinear) function that is monotone in dose. If such a model is fitted, it is useful to know the uncertainty of the fitted curve. It is well known that Wald confidence intervals are based on linear approximations and are often unsatisfactory in nonlinear models. Apart from incorrect coverage rates, they can be unreasonable in the sense that the lower confidence limit of the difference to placebo can be negative, even when an overall test shows a significant positive effect. Bootstrap confidence intervals solve many of the problems of the Wald confidence intervals but are computationally intensive and prone to undercoverage for small sample sizes. In this work, we propose a profile likelihood approach to compute confidence intervals for the dose-response curve. These confidence bounds have better coverage than Wald intervals and are more precise and generally faster than bootstrap methods. Moreover, if monotonicity is assumed, the profile likelihood approach takes this automatically into account. The approach is illustrated using a public dataset and simulations based on the Emax and sigmoid Emax models.
药物试验的一个重要目标是刻画新化合物的剂量-反应关系。这样的关系通常可以用一个在剂量上单调的参数（非线性）函数来描述。如果拟合了这样一个模型，了解拟合曲线的不确定性是很有用的。众所周知，Wald置信区间基于线性近似，在非线性模型中往往不尽人意。除了覆盖率不正确之外，从与安慰剂差异的置信下限可能为负这一意义上来说，它们可能是不合理的，即使总体检验显示有显著的正效应。自助置信区间解决了Wald置信区间的许多问题，但计算量大，并且对于小样本量容易出现覆盖率不足的情况。在这项工作中，我们提出一种轮廓似然方法来计算剂量-反应曲线的置信区间。这些置信区间比Wald区间有更好的覆盖率，并且比自助法更精确且通常更快。此外，如果假设单调性，轮廓似然方法会自动考虑这一点。使用一个公共数据集以及基于Emax和Sigmoid Emax模型的模拟来说明该方法。
