PDF of presentation

Background: In 1994, a blind evaluation of several estimation algorithms on one population PK simulated data set was presented American Statistical Association meeting[1]. Since this date NONMEM software and nlme function in SplusÔ and R have allowed large diffusion of population PK-PD in industry and academic research. At the same period, several new methods based on maximum (approximate or not) likelihood (ML) for non-linear mixed effect models were developed[2], in particular the use of Gauss Hermitte quadrature[3]and stochastic approximation EM algorithm[4,5]. Given those developments it was interesting to perform a new comparison between gold standard and newly developed methods using several simulated data sets that would be serially, automatically and blindly analysed (i.e. ignoring the true value of the parameters).

Objectives: To compare various "newly" developed and classical algorithms for non-linear mixed effect models using ML parametric estimate according to bias, precision and standard error estimates.

Methods: Simulate 100 population PK data sets using a one compartment model with first order absorption and first order elimination, the parameters being volume of distribution, elimination rate constant (Ke) and absorption rate constant (Ka). To avoid flip-flop during simulation, Ka is expressed as Ke+q, q being the parameter to be estimated. Three random effects, a full covariance matrix and an exponential error model complete the model. Each data set contains approximately one hundred patients receiving one single dose and having 1 to 4 concentration points. Proportion of patients having 3 or 4 points is on average 74% dataset. These datasets were proposed to several statisticians or pharmacometricians who are well-known for their skills or have developed algorithms for non-linear mixed effect models. The exact true pharmaco-statistical model was also provided as well as rough estimates of fixed effect parameters. Each participant is supposed to fit each of the one hundred data sets, using an automated fitting procedure in order to avoid the potential effect of the analyst’s skills and experience on the results. Results will be analyzed by computing relative bias and RMSE as well as by comparing standard errors with empirical SE defined as SD of the 100 estimated parameters. A crude comparison of CPU times will also be provided.

Results: Following statisticians or pharmacometricians have accepted to participate into this blind comparison (algorithm or software in parenthesis): Niclas Jonsson (NONMEMÔ V & VI); José Pinheiro and Chyi-Hung Hsu (nlme SplusÔ function); J. Hans Proost (Iterative Two-Stage Bayesian method); Bob Leary (PEM); Serge Guzy (MCPEM); Marc Lavielle (SAEM); Russ Wolfinger (SASÔ proc nlmixed). Extensive results will be presented at PAGE 2005 meeting. 

References:
[1]. D. J. Roe. Comparison of population pharmacokinetic modeling methods using simulated data: results from the population modeling workgroup. Stat.Med. 16:1241-1262, 1997.
[2]. F. Mentré. History and new developments in estimation methods in nonlinear mixed effects models. PAGE 2005, Pampelona, Spain.
[3]. Q. Liu & D.A. Pierce. A note on Gauss Hermitte quadrature, Biomerika, 81, 624-629.
[4]. Gu & Kong (1998). A stochastic approximation algorithm with MCMC for incomplete data estimation problems. PNAS, 95: 7270-4.
[5]. Delyon, Laveille & Moulines (1999). Convergence of a stochastic approximation version of the EM procedure. Ann Stat, 27: 94-128.