Performance in population models for count data, part II: A new SAEM algorithm
- 204 Downloads
Analysis of count data from clinical trials using mixed effect analysis has recently become widely used. However, algorithms available for the parameter estimation, including LAPLACE and Gaussian quadrature (GQ), are associated with certain limitations, including bias in parameter estimates and the long analysis runtime. The stochastic approximation expectation maximization (SAEM) algorithm has proven to be a very efficient and powerful tool in the analysis of continuous data. The aim of this study was to implement and investigate the performance of a new SAEM algorithm for application to count data. A new SAEM algorithm was implemented in MATLAB for estimation of both, parameters and the Fisher information matrix. Stochastic Monte Carlo simulations followed by re-estimation were performed according to scenarios used in previous studies (part I) to investigate properties of alternative algorithms (Plan et al., 2008, Abstr 1372 [http://wwwpage-meetingorg/?abstract=1372]). A single scenario was used to explore six probability distribution models. For parameter estimation, the relative bias was less than 0.92% and 4.13% for fixed and random effects, for all models studied including ones accounting for over- or under-dispersion. Empirical and estimated relative standard errors were similar, with distance between them being <1.7% for all explored scenarios. The longest CPU time was 95 s for parameter estimation and 56 s for SE estimation. The SAEM algorithm was extended for analysis of count data. It provides accurate estimates of both, parameters and standard errors. The estimation is significantly faster compared to LAPLACE and GQ. The algorithm is implemented in Monolix 3.1, (beta-version available in July 2009).
KeywordsNonlinear mixed effects model Count data Maximum likelihood estimation Fischer information matrix SAEM algorithm MONOLIX
Radojka Savic was financially supported by a Postdoc grant from the Swedish Academy of Pharmaceutical Sciences (Apotekarsocieteten). We thank Dr. Shasha Jumbe for valuable comments on the manuscript.
- 2.Troconiz IF, Plan EL, Miller R, Karlsson MO (2008) Modelling overdispersion and Markovian features in count data. American Conference on Pharmacometrics, Tucson, AZGoogle Scholar
- 3.Beal SL, Sheiner LB, Boeckmann AJ (1989–2006) NONMEM users guides, icon development solutions, Ellicott City, Maryland, USAGoogle Scholar
- 4.Ette EI, Williams PJ (2007) Pharmacometrics: the science of quantitative pharmacology. Wiley, HobokenGoogle Scholar
- 6.SAS Institute Inc SAS Online Doc. SAS/STAT User’s Guide, The NLMIXED Procedure. http://statdist.its.uu.se/sas/SASOnlinedocV8/sasdoc/saspdf/
- 7.Plan EL, Maloney A, Troconiz IF, Karlsson MO (2008) Maximum likelihood approximations: performance in population models for count data, p. 17, Abstr 1372 [http://wwwpage-meetingorg/?abstract=1372]. Accessed January 2009
- 8.Clausen WHO, Ronn BB, Skoovgard IM (2009) Maximum likelihood estimation in nonlinear mixed effect models: Adaptive Gaussian Quadrature by sparse grid sampling, p 18, Abstr 1584 [http://wwwpage-meetingorg/?abstract=1584]. Accessed June 2009
- 10.Verbeke G (2006) Mixed models for the analysis of categorical repeated measures, p 15, Abstr 930 [http://wwwpage-meetingorg/?abstract=930]. Accessed June 2009
- 13.MONOLIX 2.4 User Guide, Vol. http://software.monolix.org. Accessed January 2009
- 14.Girard P, Mentre F (2005) A comparison of estimation methods in nonlinear mixed effects models using a blind analysis, p 14, Abstr 834 [http://wwwpage-meetingorg/?abstract=834], Pamplona, Spain
- 16.Karlsson MO, Holford N (2008) A tutorial on visual predictive checks, p 17, Abstr 1434 [http://wwwpage-meetingorg/?abstract=1434], Marseille. Accessed January 2009
- 17.Savic RM, Karlsson MO (2009) Importance of shrinkage in empirical bayes estimates for diagnostics: problems and solutions. AAPS J (in press)Google Scholar