Duffull Stephen B, Hooker Andrew C
School of Pharmacy, University of Otago, 18 Frederick St, Dunedin, New Zealand.
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden.
J Pharmacokinet Pharmacodyn. 2017 Dec;44(6):611-616. doi: 10.1007/s10928-017-9552-y. Epub 2017 Oct 24.
Optimal designs for nonlinear models are dependent on the choice of parameter values. Various methods have been proposed to provide designs that are robust to uncertainty in the prior choice of parameter values. These methods are generally based on estimating the expectation of the determinant (or a transformation of the determinant) of the information matrix over the prior distribution of the parameter values. For high dimensional models this can be computationally challenging. For nonlinear mixed-effects models the question arises as to the importance of accounting for uncertainty in the prior value of the variances of the random effects parameters. In this work we explore the influence of the variance of the random effects parameters on the optimal design. We find that the method for approximating the expectation and variance of the likelihood is of potential importance for considering the influence of random effects. The most common approximation to the likelihood, based on a first-order Taylor series approximation, yields designs that are relatively insensitive to the prior value of the variance of the random effects parameters and under these conditions it appears to be sufficient to consider uncertainty on the fixed-effects parameters only.
非线性模型的最优设计取决于参数值的选择。已经提出了各种方法来提供对参数值先验选择中的不确定性具有鲁棒性的设计。这些方法通常基于在参数值的先验分布上估计信息矩阵行列式（或行列式的变换）的期望。对于高维模型，这在计算上可能具有挑战性。对于非线性混合效应模型，随机效应参数方差的先验值中的不确定性的重要性问题随之而来。在这项工作中，我们探讨了随机效应参数的方差对最优设计的影响。我们发现，近似似然期望和方差的方法对于考虑随机效应的影响可能具有重要意义。基于一阶泰勒级数近似的最常见似然近似产生的设计对随机效应参数方差的先验值相对不敏感，在这些条件下，似乎仅考虑固定效应参数的不确定性就足够了。
