  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.
