Nonlinear Mixed Effects Estimation Algorithms: A Performance Comparison for Continuous Pharmacodynamic Population Models
Elodie L. Plan (1), Alan Maloney (1,2), France Mentré (3), Mats O. Karlsson (1), Julie Bertrand (3)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden, (2) Exprimo NV, Mechelen, Belgium, (3) UMR738, INSERM, Université Paris Diderot, Paris, France
Background: Nonlinear mixed-effects modelling has enabled substantial advances in the learning-and-confirming process during drug development. It has been accompanied by considerable improvements of the statistical softwares. Although algorithms were tested with PD data for categorical  and count models [2,3], and communications done for continuous models [4,5], a thorough study remains to be performed.
Objectives: To compare estimation performances of FOCE in NONMEM VII and R 2.9.1 nlme (FOCE_NM and FOCE_R), LAPLACE in NONMEM VII and SAS 9.2 (LAP_NM and LAP_SAS), adaptive Gaussian quadrature in SAS 9.2 (AGQ_SAS), and SAEM in NONMEM VII and MONOLIX 3.1 (SAEM_NM and SAEM_MLX) for a set of PD models.
Methods: Six models were considered, all derived from a sigmoid Emax model including baseline, multiplicative interindividual variability (IIV) on each parameter and correlation between Emax and ED50. The Hill factor successively was 1, 2 and 3 and the residual error was either additive or proportional. The design adopted for the datasets counted 100 individuals having an observation at 4 dose levels.
This stochastic simulations-estimation study was performed as follows, 100 datasets were generated in NONMEM and subsequently analyzed using each of the 7 algorithms. All algorithms started from initial estimates set to, firstly, the values used to simulate parameters, secondly, values set far away from the truth (higher fixed effects, lower random effects).
Results were examined through relative root mean square error (RRMSE) of the 100 estimates, in order to assess both accuracy and variability. A rank based on RRMSE was attributed to each algorithm for each parameter within each model; these ranks were then averaged across models, to allow the algorithms to be ordered.
Results: Parameter estimates could be obtained for all data sets with all algorithms, except FOCE_R. Considering all population parameters, from the best RRMSEs to the poorest, results were SAEM_NM (2.28), AGQ_SAS (3.13), LAP_SAS (3.65), LAP_NM (3.91), FOCE_NM (4.02), SAEM_MLX (4.15), and FOCE_R (6.83). For the parameter of interest ED50 (IIV), the average RRMSE was around 13.5 % (28.5 %) for all algorithms except FOCE_R: 30 % (70.5 %). Altering initial conditions made the picture more complex as properties did not change in a parallel manner for all algorithms.
Conclusions: All algorithms but FOCE_R performed with bias and precision of reasonable order of magnitude for these settings. Runtimes and the impact of the design are currently under study.
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