2012 - Venice - Italy

PAGE 2012: Estimation Methods
Elin Svensson

Linear approximation methods for fast evaluation of random effects models

Elin Svensson, Mats O Karlsson

Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden

Objectives: To develop and assess a fast method for evaluation of IIV, IOV and residual variability (RV) model components.

Methods: The linear approximation used was based on a previously described first-order conditional estimates linearization [1]. Three real data analyses described elsewhere [2, 3, 4] were used to compare the results from nonlinear models with the corresponding linear version. Derivatives from a basic nonlinear model were used in the extended linear models.
The results were assessed based on the difference in objective function value (ΔOFV) between a basic model and extended models for the nonlinear and linear estimation methods respectively. The RV models evaluated were extensions to an additive, a proportional or a combined additive and proportional error model and included IIV on the RV, autocorrelation, a power model and time dependence. IIV and IOV variances and covariances, not estimated in the basic model, were added in the extended models. The analysis was carried out in NONMEM 7.2 [5] aided by PsN [6].

Results: The nonlinear and linear approaches gave the same results for models with additive RV. For models with proportional RV the ETA estimates sometimes got caught in local minimas which caused deviating results. Modelling the data on logarithmic scale and hence transforming the RV to additive solved the problem. For models with a combined RV a strategy including a dynamic scedasticity and transform-both-sides model [7] proved successful.
The ΔOFV from the linear and the conventional nonlinear models agreed well for all the evaluated RV models. For IIV and IOV evaluation the ΔOFV agreed well in the lower range but for large ΔOFV and when inclusion of variability resulted in a large change of typical values of the parameters some discrepancies were seen. The agreement was good also for IIV and IOV correlations. The linear analysis identified the same extended models as the conventional nonlinear analysis. The total runtime for estimating the four alternative RV models for one of the example data sets was 2.4 h and 3.7 min for the nonlinear and linear models respectively.

Conclusions: The linear approximation substantially decreases runtimes and has successfully been used for evaluation of a broad range of random effects models. The method can be implemented in PsN to further automate and speed up the model development process.

Acknowledgement: This work was performed as a part of the DDMoRe project.

References:
[1] Khandelwal et al., AAPS J. 2011;13(3):464-472
[2] Karlsson et al., J Pharmacokinet Biopharm. 1998;26(2):207-46
[3] Wählby et al., Br J Clin Pharmacol. 2004;58(4):367-77
[4] Jönsson et al., Antimicrob Agents Chemother. 2011;55(9):4230-7
[5] Beal et al., NONMEM user’s guides. Icon Development Solutions, Ellicott City, MD, USA; 1989-2009
[6] Lindbom et al., Comput Methods Programs Biomed. 2005;79(3):241-57
[7] Dosne et al., PAGE abstract, Venice, Italy; 2012.




Reference: PAGE 21 (2012) Abstr 2404 [www.page-meeting.org/?abstract=2404]
Poster: Estimation Methods
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