基于常微分方程的非线性混合效应模型的参数估计：一种最优控制方法
Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach
摘要：
提出了一种基于常微分方程的非线性混合效应模型（NLME-ODEs）的参数估计方法。这里提出的方法的目的是正则化的估计问题存在的模型误设定，实际的可识别性问题和未知的初始条件。为此，我们将估计量定义为成本函数的最小值，该成本函数包含了在总体水平上假设的模型与特定个体动态之间可能存在的差距。成本函数的计算导致制定和解决最优控制问题的主题水平。这种控制理论的方法允许绕过需要知道或估计每个主题的初始条件，它正则化的估计问题，在存在难以识别的参数。仿真结果表明，与极大似然方法相比，该方法在初始条件未知或参数辨识性差的情况下，无论有无模型误差，都能提高估计精度.我们结束这项工作的实际应用对埃博拉病毒疫苗接种后的抗体浓度数据来自1期试验。我们使用估计的模型差异，在主题水平上分析模型误设的存在。
英文摘要：
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.
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