Hoai-Thu Thai (1), France Mentré (1), Nicholas H.G. Holford (3), Christine Veyrat-Follet (2), Emmanuelle Comets (1)
(1) INSERM UMR738, University Paris Diderot, Sorbonne Paris Cité, Paris, France; (2) Drug Disposition Department, Sanofi, Paris, France; (3) Department of Pharmacology and Clinical Pharmacology, University of Auckland, Auckland, New Zealand
Objectives: Bootstrap methods are used for estimating uncertainty of parameters in multi-level or linear mixed-effects models with homoscedastic error [1-2]. Residual-based bootstrap methods which resample both random effects and residuals are an alternative approach to case bootstrap, which resamples the individuals. Residual bootstrap may be a good way to approach the data generating process [3]. However, most PKPD applications use the case bootstrap, for which software is available [4-5]. We propose to investigate the residual bootstrap for nonlinear mixed-effect models (NLMEM) with heteroscedastic error.
Methods: We implemented nonparametric and parametric versions of residual bootstrap, as well as the case bootstrap in R 2.14. In the nonparametric method, the standardized residuals and random effects were corrected for shrinkage [6-7]. In the parametric method, they were sampled from the estimated distributions. The performance of the three bootstraps was assessed by a simulation study based on clinical trials of aflibercept, an anti-VEGF drug, in cancer patients. We assumed that the PK of aflibercept follows a two-compartment infusion model with 1st order elimination. A frequent sampling design (30 subjects and 9 samples per subject) with two settings (1st order or Michaelis-Menten (MM) elimination) were investigated using 100 replicates and 1000 bootstrap samples per replicate for each bootstrap method. Each bootstrap dataset was fit with Monolix 4.1. The bootstrap approaches were compared in term of bias of parameters, standard errors (SE) and coverage rate of the 95% confidence interval of all parameter estimates. The bootstrap estimates were also compared to the asymptotic estimates.
Results: The asymptotic approach underestimated SE and gave low coverage rate for several parameters, especially for Km (parameter with highest nonlinearity) in design with MM elimination. The bootstrap approaches provided better estimates of SE and better coverage rate than the asymptotic approach, correcting the bias for most parameters, especially for Km.
Conclusion: The nonparametric residual bootstrap works as well as the case bootstrap for both settings in NLMEM with heteroscedasticity. The parametric residual bootstrap works slightly better than others but may not be as robust to model or distributional misspecifications. Bootstrap methods provide a better description of uncertainty for parameters, especially for nonlinear parameters compared to the asymptotic approach.
References:
[1] Van der Leeden R, Busing F. M. T. A., and Meijer E. Bootstrap methods for two-level models. Technical Report PRM 97-04, Leiden University, Department of Psychology, Leiden, 1997.
[2] Thai H-T, Veyrat-Follet C, Mentré F and Comets E. A comparison of bootstrap approaches for estimating standard errors of parameters in linear mixed effects models. 20th Population Group Approach in Europe, Athens, Greece, Juin 2011. Abstr 2271 [www.page-meeting.org/?abstract=2271].
[3] Chernick MR. Bootstrap methods: A guide for practitioners and researchers. Second edn., John Wiley & Sons: New Jersey, 2008.
[4] Parke J, Holford NHG, Charles BG. A procedure for generating bootstrap samples for the validation of nonlinear mixed-effects population models. Computer Methods and Programs in Biomedicine 1999; 59:19-29.
[5] Lindbom L, Pihlgren P, Jonsson EN. PsN-Toolkit-A collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Computer Methods and Programs in Biomedicine 2005; 79(3):241-257.
[6] Das S, Krishen A. Some bootstrap methods in nonlinear mixed-effects models. Journal of Statistical Planning and Inference 1999; 75: 237-245.
[7] Wang J, Carpenter JR and Kepler MA. Using SAS to conduct nonparametric residual bootstrap multilevel modeling with a small number of groups. Computer Methods and Programs in Biomedicine 2006; 82:130-143.
Reference: PAGE 21 () Abstr 2533 [www.page-meeting.org/?abstract=2533]
Poster: Model evaluation