Investigation of performances of FOCE and LAPLACE algorithms in NONMEM VI in population parameters estimation of PK and PD continuous data
E. Plan, M. C. Kjellsson, M. O. Karlsson
Division of Pharmacokinetics and Drug Therapy, Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Background: At PAGE 2005, P. Girard and F. Mentrť presented a study where the performance of several estimation methods used in nonlinear mixed effects modeling were compared. It was shown that FOCE using NONMEM VIbÍta did end in successful minimization in only 49% of the runs . In NONMEM VI, S. Beal had added a warning message making the covariance step abort when its estimate is equal to zero. It has been hypothesized that these warnings are the reason why FOCE in NONMEM VIbÍta shows such poor minimization properties. NONMEM VI includes a new estimation method, LAPLACE INTER, clearly intended for continuous type data. Therefore we also wanted to explore differences between FOCE and LAPLACE for such data.
Objective: The aim of this study was to compare the estimation performances of different methods available in NONMEM VI, with focus on FOCE and LAPLACE methods.
Methods: 100 datasets simulated by Girard et al were re-examined using NONMEM VI and a NONMEM VI version compiled without the warnings with methods FOCE, LAPLACE, SLOW, INTER, NUMERICAL, LIKE and -2LL. The model used to estimate these PK data was a one compartment model with a first order absorption and a first order elimination. Random effects exponentially added to all fixed effects with off-diagonal elements estimated and an exponential error completed the model. 100 other datasets were generated for further investigations in the difference in performance between FOCE and LAPLACE. PD data were then estimated using a sigmoÔd Hill model with a baseline and a correlation between the EMAX and the ED50. The model included also random effects multiplicatively affected to 3 of the 4 parameters and an additional error. Results were compared by computing bias and precision of the 100 estimated parameters and by plotting relative estimation errors.
Results and Discussion: 100% successful minimizations were obtained with NONMEM VI both with and without warnings; otherwise no evident difference was seen between the different algorithms in PK data estimations. Regarding PD data estimations, a trend of lower bias with LAPLACE than with FOCE was observed, whereas precisions were quite similar between these two methods. The difference in the bias increased with increasing complexity of the model. Moreover even though several estimations did not minimize successfully, the parameter estimates did seem to be similar to those obtained in a successful minimization.
 P. Girard and F. Mentrť. A comparison of estimation methods in nonlinear mixed effects models using a blind analysis. PAGE 14, Pampelona, Spain.