Purpose

Non-linear mixed effect models are widely used and increasingly integrated into decision-making processes. Propagating uncertainty is an important element of this process, and while standard errors (SE) on pa- rameters are most often computed using asymptotic approaches, alternative methods such as the bootstrap are also available. In this article, we propose a modified residual parametric bootstrap taking into account the different levels of variability involved in these models.

Methods

The proposed approach uses samples from the individual conditional distribution, and was implemented in R using the saemix algorithm. We performed a simulation study to assess its performance in different scenarios, comparing it to the asymptotic approximation and to standard bootstraps in terms of coverage, also looking at bias in the parameters and their SE.

Results

Simulations with an Emax model with different designs and sigmoidicity factors showed a similar coverage rate to the parametric bootstrap, while requiring less hypotheses. Bootstrap improved coverage in several scenarios compared to the asymptotic method especially for the variance param-eters. However, all bootstraps were sensitive to estimation bias in the original datasets.

Conclusions

The conditional bootstrap provided better coverage rate than the traditional residual bootstrap, while preserving the structure of the data generating process.

中文翻译：

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非线性混合效应模型的条件非参数 Bootstrap

目的

非线性混合效应模型被广泛使用并越来越多地融入决策过程。传播不确定性是这个过程的一个重要元素，虽然参数的标准误差 (SE) 最常使用渐近方法计算，但也可以使用其他方法，例如引导程序。在本文中，我们提出了一种改进的残差参数引导程序，考虑到这些模型中涉及的不同程度的可变性。

方法

所提出的方法使用来自个体条件分布的样本，并使用 saemix 算法在 R 中实现。我们进行了一项模拟研究以评估其在不同场景中的性能，将其与渐近近似和标准引导程序在覆盖范围方面进行比较，同时查看参数及其 SE 的偏差。

结果

使用具有不同设计和 sigmoidity 因子的 Emax 模型进行的模拟显示出与参数引导程序相似的覆盖率，同时需要较少的假设。与渐近方法相比，Bootstrap 改进了几种场景的覆盖率，尤其是对于方差参数。然而，所有引导程序都对原始数据集中的估计偏差敏感。

结论

条件引导程序提供了比传统残差引导程序更好的覆盖率，同时保留了数据生成过程的结构。