Extended NPDE diagnostics for the between-subject variability and residual error model
Ron J Keizer, Kajsa Harling, Mats O Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Introduction: NPDEs allow comparison of each observation (DV) to its own predictive distribution based on simulation.[1] Thereby, NPDEs offers a model diagnostic tool, but it does not separate misspecification at the various levels of random effects. For diagnosis of misspecification of the between-subject (BSV) and residual error (RE) models, summaries of empirical Bayes estimates (EBE) and individual weighted residuals (IWRES) are commonly employed. However, these diagnostics are very sensitive to η- and ε-shrinkage.[2]
As extension and improvement to the above diagnostics, we propose to construct NPDE’s for EBE and IWRES. These new NPDEs would have two main advantages:
a) the decomposition of the NPDE diagnostic to the BSV model (EBE-NPDE), and the RE model (IWRES-NPDE)
b) the proposed NPDE diagnostics would not be subjective to shrinkage
Objectives: To evaluate the ability of EBE-NPDE and IWRES-NPDE to diagnose model misspecification.
Methods: Calculation of the proposed NPDEs requires iterated re-estimation of EBEs (but not population parameter values) based on simulated data. Algorithms for this were implemented in PsN (versions 3.5.3 and up).[3] A previously developed model for a PK dataset (prazosin, n=65, 11 obs.) was used. Several misspecifications in the BSV model and the RE model were implemented, such as Box-Cox transformations and t-distributions vs normal distributions[4], and heteroscedastic vs homoscedastic RE models. DV-NPDE, EBEs, IWRES, EBE-NPDE and IWRES-NPDE were then calculated for the base model. The analysis was repeated at varying levels of shrinkage. Several diagnostic plots were evaluated for their diagnostic ability.
Results: IWRES-NPDE were more sensitive to detect misspecification in the RE model than DV-NPDE or IWRES, at both high and low levels of ε-shrinkage. EBE-NPDEs were able to detect misspecification of the η-distribution (Box-Cox transformed), which could not be detected using diagnostic plots of EBE or DV-NPDE, and were also informative in diagnosing appropriateness of covariance structure. Diagnostic plots for the NPDEs that were most informative included distribution plots, qq-plots, correlation plots, and plots of NPDE vs individual predictions.
Conclusion: EBE-NPDE and IWRES-NPDE offer valuable diagnostic tools, and allow decomposition of the NPDE-DV diagnostic to the BSV and RE level. The new NPDEs were more sensitive to detect model misspecification than the DV-NPDE or diagnostics based on EBE or IWRES.
Acknowledgements: This research was performed as part of the DDMoRe project
References
[1] Comets E et al., Comput Methods Programs Biomed 2008
[2] Savic R and Karlsson MO, Clin Pharmacol Therapeut 2007
[3] Harling et al., http://psn.sourceforge.net
[4] Dosne AG et al., PAGE 2012, Abstract 2527, http://www.page-meeting.org/default.asp?abstract=2527
