We present a parameter estimation method for nonlinear mixed effect models based on ordinary differential equations (NLME-ODEs). The method presented here aims at regularizing the estimation problem in presence of model misspecifications, practical identifiability issues and unknown initial conditions. For doing so, we define our estimator as the minimizer of a cost function which incorporates a possible gap between the assumed model at the population level and the specific individual dynamic. The cost function computation leads to formulate and solve optimal control problems at the subject level. This control theory approach allows to bypass the need to know or estimate initial conditions for each subject and it regularizes the estimation problem in presence of poorly identifiable parameters. Comparing to maximum likelihood, we show on simulation examples that our method improves estimation accuracy in possibly partially observed systems with unknown initial conditions or poorly identifiable parameters with or without model error. We conclude this work with a real application on antibody concentration data after vaccination against Ebola virus coming from phase 1 trials. We use the estimated model discrepancy at the subject level to analyze the presence of model misspecification.

翻译：我们为基于普通差异方程式的非线性混合效应模型(NLME-ODEs)提出了一个参数估计方法。这里介绍的方法旨在在模型误差、实际可识别问题和未知初始条件的情况下对估算问题进行常规化。为此,我们将我们的估算器定义为成本功能的最小化器,该功能包含假设模型在人口层面与特定个体动态之间可能存在的差距。成本函数计算导致在主题层面制定和解决最佳控制问题。这种控制理论方法可以避免了解或估计每个对象的初始条件的需要,并在存在可识别参数的情况下对估算问题进行规范化。我们用模拟实例比较了最大的可能性,表明我们的方法提高了可能部分观测到的系统的估计准确性,这些系统初始条件未知,或有或没有模型误差的参数。我们在完成这项工作时,在第一阶段试验的埃博拉病毒疫苗接种后对抗体浓度数据进行了实际应用。我们使用在主题层面的估计模型差异来分析模型的是否存在错误。