Bornkamp Björn
Novartis Pharma AG, WSJ-027.1.029, CH-4002 Basel, Switzerland.
Biometrics. 2012 Sep;68(3):893-901. doi: 10.1111/j.1541-0420.2012.01747.x. Epub 2012 Jul 27.
This article considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back-transform to obtain a prior distribution for the original model parameters. The primary application considered in this article is nonlinear regression, but the idea might be of interest beyond this case. For nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle, as opposed to uniform distributions on the parameters or the Jeffrey's prior, respectively. The utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose-finding trials, through a real data example and simulation.
本文探讨了在统计模型的主要组成部分依赖于非线性函数时寻找先验分布的主题。利用关于如何在一般度量空间中构建均匀分布的结果，我们提出了一种在先验非线性函数的函数形状空间中均匀的先验分布，然后通过逆变换获得原始模型参数的先验分布。本文考虑的主要应用是非线性回归，但该思想可能在这种情况之外也具有一定意义。对于非线性回归，如此构建的先验具有这样的优势，即它们是参数化不变的，并且不像分别在参数上的均匀分布或杰弗里斯先验那样违反似然原理。通过一个实际数据示例和模拟，在临床剂量探索试验中的非线性回归建模的设计和分析背景下证明了所提出先验的效用。
