Background and Objective: Uncertainty in non-linear mixed effect models is often assessed using the Fisher information matrix to derive the standard errors of estimation. The bootstrap is an alternative to the asymptotic method, with different approaches to handle the different levels of individual and population variabilities. The simplest method is the Case bootstrap where the entire vector of individuals is resampled, but this approach does not take into account the hierarchical nature of non-linear mixed effect models (NLMEM). Methods: We propose here a non-parametric bootstrap, cNP, to preserve the structure of the original data. We resample interindividual random effects from the conditional distribution of the individual parameters, obtained as a by-product of the SAEM algorithm, and residuals from their distribution. cNP was implemented in the saemix package for R along with the case, parametric (Par), and non-parametric (NP) residual bootstraps. Coverage rates were compared in a simulation study using sigmoid Emax models, with rich, sparse and unbalanced designs, and 3 levels of residual variability. Results: The asymptotic method tended to produce lower than theoretical coverages for the variance terms. Bootstraps provided more adequate coverage, but none of the approaches maintained coverage when the residual error increased. Overall, the new cNP and the Case provided better coverage than the classical NP. Conclusion: The new conditional non-parametric bootstrap can be used when it is important to preserve the structure of the original dataset, such as the number of observations or the repartition of covariates as it does not require stratification.

翻译：背景与目的：非线性混合效应模型中的不确定性常通过Fisher信息矩阵推导估计标准误来评估。自助法作为渐近方法的替代方案，可采用不同方式处理个体与群体变异的多层次特性。最简单的方法是病例自助法（Case bootstrap），即对个体向量整体进行重抽样，但该方法未考虑非线性混合效应模型（NLMEM）的层次结构。方法：本文提出一种非参数自助法（cNP），以保持原始数据的结构。我们从个体参数的条件分布（作为SAEM算法的副产物获得）中重抽样个体间随机效应，并从残差的分布中重抽样残差值。cNP被集成至R语言的saemix包中，同时包含病例自助法、参数自助法（Par）及非参数残差自助法（NP）。通过模拟研究比较覆盖概率，采用S形Emax模型，设计包括密集、稀疏及非平衡方案，并设置三级残差变异水平。结果：对于方差项，渐近方法的覆盖概率低于理论值。自助法提供了更合适的覆盖概率，但所有方法在残差误差增大时均无法维持覆盖概率。总体而言，新提出的cNP与病例自助法的覆盖表现优于经典NP方法。结论：当需保持原始数据集结构（如观测次数或协变量的分布特征）且无需分层时，可采用新提出的条件非参数自助法。