Gunnar Yngman, Rikard Nordgren, Svetlana Freiberga, Mats O. Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Sweden
Objectives:
Full Random Effects Modeling (FREM) is a methodology for covariate modeling whereupon a covariate set of interest is prespecified before all covariate-parameter effects are estimated simultaneously (through parameter-covariate covariance estimation). It has been used with NONMEM, is implemented in PsN [1] and the technique and motivation has been described before [2,3,4].
Linearization is another methodology implemented in PsN allowing automatic linearization of a NONMEM model around the estimated typical population parameters, leaving only the random effects of the model to be estimated (conditional on the typical values) [5]. It has been shown to enable fast and relatively unbiased approximations of the nonlinear model in situations where the typical values are not expected to change, such as during covariate modeling [6]. Linearization is utilized by default in the new QA PsN script to speed up the entire procedure, of which FREM constitutes an important component [7].
The aim of this investigation was to explore the performance, characteristics and differences of linearized FREM in the context of automatic model assessment, where the full PsN functionality may be run on linearized models, with an implementation where the base model is linearized before FREM is executed.
Methods:
To investigate linearized FREM, 25 in-house NONMEM models with covariate data were subject to FREM estimation with and without linearization through the QA tool (PsN 4.7.13, NONMEM 7.3.0); Many of which were selected for fast nonlinear runtimes. Models were only excluded if linear-nonlinear base model evaluation absolute dOFV>3 (linearization may be imperfect), or the estimation terminated without a final OFV for either final FREM model.
Of the remaining models, linear and nonlinear FREM results were compared with respect to coefficients, estimation time and OFVs. The coefficients were standardized by the standard deviation of the covariates to compare strength of relation (i.e. remove the dependence on the spread of the covariates). Difference in coefficients (univariate and multivariate), runtimes (identical hardware and software) and correlations of OFVs and coefficients were explored.
Results:
20 of the 25 models were included (3 models showed dOFV>3 and 2 nonlinear FREM models terminated prematurely). This set thus had both linear and nonlinear full FREM results, from which 458+458 coefficients could be calculated.
Final FREM estimation times spanned a large range (0.38s, 8.0h). The mean runtime of linear and nonlinear FREM models were 12s (median: 3.3s) and 31min (median: 1.8min), respectively. On average, the linear variants of the final FREM models executed (not including the covariance step) 510 times faster.
The mean absolute univariate coefficient size was 0.107 and 0.0935 across all linear and nonlinear models, respectively. The mean absolute difference was 0.0418. No bias was observed. Similarly, multivariate means were 0.141 and 0.140 (mean difference: 0.0488). Only 5/20 models shared a successful covariance step. However, the success rate was higher for linear (11) than nonlinear (6) executions.
Linear-nonlinear correlation coefficients were 68% and 83% for all univariate and multivariate coefficients respectively, but 93% and 98% when excluding 5 pairs where the linearized base model dropped more than 3 units of OFV during estimation. OFV drop from the full block models, including the covariate observations without parameter-covariate covariances, to the final FREM minimization correlated 96% (but only 8.5% amongst the 5 models mentioned).
Conclusions:
Similar estimates of the coefficients of covariate-parameter relations are obtained when using a nonlinear and linearized implementation of the FREM model. Differences appear not to be systematic, but a higher degree of concordance can be seen when estimated nonlinear and linearized base models show similar OFVs. These results supports linearized FREM for time-efficient estimation of covariate effects in automatic model assessment.
References:
[1] Yngman, G, Joakim, N, Niclas, EN, Karlsson, MO. Practical considerations for using the full random effects modeling (FREM) approach to covariate modeling, PAGE 26 (2017) Abstr 7365 [http://www.page-meeting.org/?abstract=7365]
[2] Karlsson, MO. A full model approach based on the covariance matrix of parameters and covariates, PAGE 21 (2012) Abstr 2455 [http://www.page-meeting.org/?abstract=2455]
[3] Karlsson, MO, Hooker, AC, Nordgren, R, et al. PsN: Perl-speaks-NONMEM (2018) [https://github.com/UUPharmacometrics/PsN]
[4] Ivaturi, VD, Hooker, AC, Karlsson, MO. Selection Bias in Pre-Specified Covariate Models, PAGE 20 (2011) Abstr 2228 [http://www.page-meeting.org/?abstract=2228]
[5] Khandelwal et al. A fast method for testing covariates in population pk/pd models, AAPS J (2011); 13(3): 464-72
[6] Svensson et al. Linear approximation methods for fast evaluation of random effects models, PAGE 21 (2012) Abstr 2404 [www.page-meeting.org/?abstract=2404]
[7] Karlsson, MO, Freiberga, S, Yngman, G, Nordgren, R, Ueckert, S. Extensive and automatic assumption assessment of pharmacometric models, PAGE 27 (2018) Abstr 8754 [http://www.page-meeting.org/?abstract=8754]
Reference: PAGE 27 (2018) Abstr 8750 [www.page-meeting.org/?abstract=8750]
Poster: Methodology - Covariate/Variability Models