标题： 基于一类由Emax模型和一室模型混合而成的组合模型的局部D-最优设计 显示英文标题

标题： Locally D-optimal designs based on a class of composed models resulted from blending Emax and one-compartment models

摘要： 引入了一类结合药代动力学房室模型和药效学Emax模型的非线性模型。 对于四参数组合模型，发现局部D最优（LD）设计是一个饱和的四个点均匀LD设计，且设计空间的两个边界点包含在LD设计的支持集中。 对于五参数组合模型，推导出了使LD设计所需的采样时间点数最少的一个充分条件。 同时，还研究了这两个模型的鲁棒LD设计。 研究发现，若两个组合模型中的线性参数均为无关参数，则具有$k$参数的LD设计等价于具有$k-1$参数的LD设计。 给出了多种LD设计的例子。 显示英文摘要

摘要： A class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic Emax model is introduced. The locally D-optimal (LD) design for a four-parameter composed model is found to be a saturated four-point uniform LD design with the two boundary points of the design space in the LD design support. For a five-parameter composed model, a sufficient condition for the LD design to require the minimum number of sampling time points is derived. Robust LD designs are also investigated for both models. It is found that an LD design with $k$ parameters is equivalent to an LD design with $k-1$ parameters if the linear parameter in the two composed models is a nuisance parameter. Assorted examples of LD designs are presented.