  Parametric nonlinear mixed effects models (NLMEs) are now widely used in
biometrical studies, especially in pharmacokinetics research and HIV dynamics
models, due to, among other aspects, the computational advances achieved during
the last years. However, this kind of models may not be flexible enough for
complex longitudinal data analysis. Semiparametric NLMEs (SNMMs) have been
proposed by Ke and Wang (2001). These models are a good compromise and retain
nice features of both parametric and nonparametric models resulting in more
flexible models than standard parametric NLMEs. However, SNMMs are complex
models for which estimation still remains a challenge. The estimation procedure
proposed by Ke and Wang (2001) is based on a combination of log-likelihood
approximation methods for parametric estimation and smoothing splines
techniques for nonparametric estimation. In this work, we propose new
estimation strategies in SNMMs. On the one hand, we use the Stochastic
Approximation version of EM algorithm (Delyon et al., 1999) to obtain exact ML
and REML estimates of the fixed effects and variance components. On the other
hand, we propose a LASSO-type method to estimate the unknown nonlinear
function. We derive oracle inequalities for this nonparametric estimator. We
combine the two approaches in a general estimation procedure that we illustrate
with simulated and real data.
