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AAPS J. 2009 Sep;11(3):558-69. doi: 10.1208/s12248-009-9133-0. Epub 2009 Aug 1.

Importance of shrinkage in empirical bayes estimates for diagnostics: problems and solutions.

Author information

1
Division of Pharmacokinetics and Drug Therapy, Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Uppsala, Sweden. Rada.Savic@farmbio.uu.se

Abstract

Empirical Bayes ("post hoc") estimates (EBEs) of etas provide modelers with diagnostics: the EBEs themselves, individual prediction (IPRED), and residual errors (individual weighted residual (IWRES)). When data are uninformative at the individual level, the EBE distribution will shrink towards zero (eta-shrinkage, quantified as 1-SD(eta (EBE))/omega), IPREDs towards the corresponding observations, and IWRES towards zero (epsilon-shrinkage, quantified as 1-SD(IWRES)). These diagnostics are widely used in pharmacokinetic (PK) pharmacodynamic (PD) modeling; we investigate here their usefulness in the presence of shrinkage. Datasets were simulated from a range of PK PD models, EBEs estimated in non-linear mixed effects modeling based on the true or a misspecified model, and desired diagnostics evaluated both qualitatively and quantitatively. Identified consequences of eta-shrinkage on EBE-based model diagnostics include non-normal and/or asymmetric distribution of EBEs with their mean values ("ETABAR") significantly different from zero, even for a correctly specified model; EBE-EBE correlations and covariate relationships may be masked, falsely induced, or the shape of the true relationship distorted. Consequences of epsilon-shrinkage included low power of IPRED and IWRES to diagnose structural and residual error model misspecification, respectively. EBE-based diagnostics should be interpreted with caution whenever substantial eta- or epsilon-shrinkage exists (usually greater than 20% to 30%). Reporting the magnitude of eta- and epsilon-shrinkage will facilitate the informed use and interpretation of EBE-based diagnostics.

PMID:
19649712
PMCID:
PMC2758126
DOI:
10.1208/s12248-009-9133-0
[Indexed for MEDLINE]
Free PMC Article

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