History and new developments in estimation methods in nonlinear mixed-effects models
France Mentré
INSERM U738, Department of Epidemiology and Biostatistics, University Hospital Bichat, Paris, France
NONMEM software, which included FO and then FOCE methods, was developed in the late 70’s before statistician got really involved in linear mixed-effects models and before any other software was available in that area. NONMEM is the software the most used in population PK/PD and is defined as the reference in drug industry.
Since the 80’s, various developments in statistical methods for linear and nonlinear models were performed, which can roughly be grouped in 4 periods. In the 80’s, developments in linear mixed effects models were performed, as well as, for nonlinear models, the apparition of the EM algorithm, nonparametric (i.e. NPML, …) or Bayesian methods (i.e. MCMC, …). The 90’s was certainly the period of increased used of NONMEM FOCE and of growing interest among statisticians. Several other methods were published based on linearisation and other functions were developed (i.e. SAS, Splus, …). New Bayesian and nonparametric methods were also developed and incorporated in software (i.e. NPEM, PKBUGS, …). Since 2000, several papers have discussed the non-consistency of estimators based on FOCE and several simulations have illustrated some of the drawbacks of this approach. Better approximation methods have been developed, and especially, methods for Maximum Likelihood Estimation based on stochastic algorithms appeared recently (i.e. SPML, PEM, MCPEM, SAEM, …).
With the increased used of nonlinear mixed effects models and of their results both in drug development and for drug use, these new methods are promising because they should provide results with better statistical properties.