We present a method for parameter estimation for nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs). It aims to regularize the estimation problem in the presence of model misspecification and practical identifiability issues, while avoiding the need to know or estimate initial conditions as nuisance parameters. To this end, we define our estimator as a minimizer of a cost function that incorporates a possible gap between the assumed population-level model and the specific individual dynamics. The computation of the cost function leads to formulate and solve optimal control problems at the subject level. Compared to the maximum likelihood method, we show through simulation examples that our method improves the 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-world application in which we model the antibody concentration after Ebola virus vaccination.

我们提出了一种基于常微分方程 (NLME-ODE) 的非线性混合效应模型参数估计方法。它的目的是在存在模型错误指定和实际可识别性问题的情况下规范估计问题，同时避免需要知道或估计初始条件作为干扰参数。为此，我们将估计量定义为成本函数的最小化器，其中包含假设的人口水平模型和特定个体动态之间可能存在的差距。成本函数的计算导致在主题层面上制定和解决最优控制问题。与最大似然法相比，我们通过仿真示例表明，我们的方法提高了在可能部分观测的系统中的估计精度，这些系统具有未知的初始条件或难以识别的参数，有或没有模型误差。我们通过实际应用来结束这项工作，其中我们对埃博拉病毒疫苗接种后的抗体浓度进行了建模。