Improvements and New Estimation Methods in NONMEM 7 for PK/PD Population Analysis
Robert J. Bauer and Thomas M. Ludden
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Objective: To demonstrate NONMEM 7's improvements and additional estimation methods for population analysis
Methods: The NONMEM 7 software has been significantly upgraded to meet the demands of population PK/PD modeling needs. The classical NONMEM algorithm first order conditional estimation method (FOCE) has been improved by reducing the occurrence of computational errors that result in abnormal termination, and allowing users to specify gradient precision, which improves the efficiency of optimization and increases the incidence of successful completion of the problem. In addition, exact likelihood Monte Carlo algorithms for non-linear mixed effects optimizations have been incorporated, such as importance sampling expectation maximization (EM) [1], and Markov chain Monte Carlo (MCMC) stochastic approximation EM (SAEM) [2]. A three hierarchical stage MCMC Bayesian method using Gibbs and Metropolis-Hastings algorithms is also available [3,4]. All set-up parameters for these new methods may be specified in the standard NMTRAN control stream file format. NONMEM 7 has the ability to handle more data file items, longer labels, and initial parameters may be expressed in any numerical format. Output files that are readily transferred to post-processing software are also produced, and the number of significant digits reported may be specified by the user. Diagnostic results such as inter-subject and residual variance shrinkage, conditional weighted residuals, Monte Carlo assessed exact weighted residuals, and normalized probability distribution errors [2], are also outputted. The source code has been upgraded from Fortran 77 to Fortran 95, and the internal precision of all variables involved in computation have been increased to 15 significant digits (double precision). Error handling of multiple problem runs have been improved to allow continuation despite abnormal termination of a given problem, and there is interactive control of NONMEM 7 batch processes.
Results: Three examples of simulated data sets were created to test NONMEM 7's EM and Bayesian algorithms. The first example consisted of a simple two compartment PK problem with few data points per subject. The second example was a two compartment first-order and receptor-mediated clearance PK and indirect response PD model, with 46 population parameters, variances/covariances, and intra-subject error coefficients to be estimated, requiring numerical integration of three mass transfer differential equations. NONMEM 7 population parameter estimates from these data were very similar to the expected values. In the third example, estimation performance of the Monte Carlo EM methods were compared to that of the FOCE method using data simulated for a two compartment model with first-order input from the depot compartment into the central compartment and zero-order input directly into the central compartment. Between subject variability was estimated for all parameters including the rate or duration of the zero-order input. Out of 100 replicate data sets, none of the FOCE analyses resulted in successful completion of both the estimation and covariance steps. For the Monte Carlo EM methods, successful completion of both steps occurred for 88% or more of the problems. Comparison of objective function values indicated that FOCE generally failed to achieve the minimum value based on comparisons with the EM methods.
Conclusions: The additional analysis methods, and expanded format of control stream input files and output files in NONMEM 7 provide users with a flexible, powerful, and accurate tool for population analysis of PK/PD models.
References:
[1] Bauer, RJ. Technical Guide on the Population Analysis Methods in the S-ADAPT Program, Appendix H, Version 1.56.
[2] Lavielle, M. Monolix Users Manual [computer program]. Version 2.4. Orsay, France: Laboratoire de Mathematiques, U. Paris-Sud; 2008.
[3] Benet, Racine-Poone, and Wakefield. MCMC for non linear hierarchical models. In: Markov Chain Monte Carlo in Practice. W.R. Gilks et al., Chapman & Hall (1996), chapter 19, pp 341-342.
[4]Gilks, Richardson and Spiegelhalter. Introducing Markov chain Monte Carlo. In: Markov Chain Monte Carlo in Practice. W.R. Gilks et al., Chapman & Hall (1996), chapter 1, pp 5-8.
