Zhe Huang (1), Tianwu Yang (1), Xiaomei Chen (1), Simon J. Carter (1), Rikard Nordgren (1), Stella Belin (1), Alzahra Hamdan (1), Shijun Wang (1), Andrew C. Hooker (1), Mats O. Karlsson (1)
(1) Department of Pharmacy, Uppsala University, Sweden
Introduction: Pharmacometric modelers usually choose on what form of data to use: normal scale or natural log-transformed data. While it is possible to objectively select between these two options using the likelihood [1], this is typically not done. The reason for the selection is typically not provided in publications, but residual analysis, run-time and/or stability differences have been mentioned. This poster addresses the performance comparison on the use of normal scaled data (untransformed data) and natural log scaled data (transformed data) with application to automatic model development (AMD) at different development stages. The most intuitive way to evaluate model performance is through the comparison of the objective function value (OFV), however, the OFVs for different datasets cannot be compared directly because the residual error assumption of normal scale data follows the independent normal distribution and the residual error of natural log-transformed data is assumed to be log-normal distributed. We used the dynamic transform both sides (dTBS) tool that makes it possible to compare the OFV between the two data forms [1].
Objectives: To compare the difference of model OFVs between untransformed and transformed data by the use of the dTBS method at different parts of the AMD process.
Methods: dTBS was applied for the transformation of the proportional residual error model on normal-scale data to the additive residual error model on log-transformed data. Models were transformed with lambda and zeta both fixed to 0 by PsN [2]. Five oral drugs (moxonidine, desmopressin, warfarin, lopinavir, melagatran) and five i.v. drugs (gentamicin, tobramycin, daunorubicin, factorVIII, pefloxacin) were evaluated in the AMD tool. The milestone models during AMD (starting model and models after selecting structural model and IIV model) were evaluated and the OFV was compared between untransformed and transformed data. To support the dTBS transformation result, the structural model was also built with the log scale dataset which was transformed manually and compared with the current model structure in AMD. The Bayesian information criterion (BIC) for mixed effect models was used to evaluate models with different structures because models are not nested [3].
Results: After the dTBS transformation, the OFVs of models for 7/10 drugs increased substantially (>12), supporting untransformed dataset at all stages of AMD. For 1/10 the OFV decreased at each stage of AMD supporting a transformed dataset. For 2/10 there was no difference or preference dependent on stage of development. For 7/10 datasets, the same structural model was selected with untransformed and transformed data. For 3/10 different structural models were selected and the BIC favoured the untransformed data models for two of them and for the third BIC was similar.
Conclusions: Most datasets explored here have better performance using untransformed data compared to the transformed data. These results also indicate consistency with the OFV difference of the same model with untransformed and transformed data at each model selection step. Therefore, it may suffice to compare the relative performance of untransformed and transformed data at one point during the model building scheme.
References:
[1] Dosne A, Bergstrand M, Karlsson MO. A strategy for residual error modeling incorporating scedasticity of variance and distribution shape. J Pharmacokinet Pharmacodyn. 2015;43(2):137–51. https://doi.org/10.1007/s10928-015-9460-y.
[2] Lindbom L, Pihlgren P, Jonsson EN. PsN-toolkit—a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Comput Methods Prog Biomed. 2005;79(3):241–57. https://doi.org/10.1016/j.cmpb.2005.04.005.
[3] Delattre M, Lavielle M, Poursat M-A. A note on BIC in mixed-effects models. Electronic journal of statistics 8 (1), 456-475.
Reference: PAGE 30 (2022) Abstr 10128 [www.page-meeting.org/?abstract=10128]
Poster: Methodology - Covariate/Variability Models