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A strategy for residual error modeling incorporating scedasticity of variance and distribution shape
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
2016 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 43, no 2, 137-151 p.Article in journal (Refereed) Published
Resource type
Text
Abstract [en]

Nonlinear mixed effects models parameters are commonly estimated using maximum likelihood. The properties of these estimators depend on the assumption that residual errors are independent and normally distributed with mean zero and correctly defined variance. Violations of this assumption can cause bias in parameter estimates, invalidate the likelihood ratio test and preclude simulation of real-life like data. The choice of error model is mostly done on a case-by-case basis from a limited set of commonly used models. In this work, two strategies are proposed to extend and unify residual error modeling: a dynamic transform-both-sides approach combined with a power error model (dTBS) capable of handling skewed and/or heteroscedastic residuals, and a t-distributed residual error model allowing for symmetric heavy tails. Ten published pharmacokinetic and pharmacodynamic models as well as stochastic simulation and estimation were used to evaluate the two approaches. dTBS always led to significant improvements in objective function value, with most examples displaying some degree of right-skewness and variances proportional to predictions raised to powers between 0 and 1. The t-distribution led to significant improvement for 5 out of 10 models with degrees of freedom between 3 and 9. Six models were most improved by the t-distribution while four models benefited more from dTBS. Changes in other model parameter estimates were observed. In conclusion, the use of dTBS and/or t-distribution models provides a flexible and easy-to-use framework capable of characterizing all commonly encountered residual error distributions.

Place, publisher, year, edition, pages
2016. Vol. 43, no 2, 137-151 p.
Keyword [en]
Residual error, Transform-both-sides, Skewness, Heteroscedasticity, Heavy tails, t-Distribution
National Category
Pharmaceutical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-297131DOI: 10.1007/s10928-015-9460-yISI: 000374704100002PubMedID: 26679003OAI: oai:DiVA.org:uu-297131DiVA: diva2:941121
Funder
EU, European Research Council
Available from: 2016-06-22 Created: 2016-06-21 Last updated: 2017-11-28Bibliographically approved
In thesis
1. Improved Methods for Pharmacometric Model-Based Decision-Making in Clinical Drug Development
Open this publication in new window or tab >>Improved Methods for Pharmacometric Model-Based Decision-Making in Clinical Drug Development
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Pharmacometric model-based analysis using nonlinear mixed-effects models (NLMEM) has to date mainly been applied to learning activities in drug development. However, such analyses can also serve as the primary analysis in confirmatory studies, which is expected to bring higher power than traditional analysis methods, among other advantages. Because of the high expertise in designing and interpreting confirmatory studies with other types of analyses and because of a number of unresolved uncertainties regarding the magnitude of potential gains and risks, pharmacometric analyses are traditionally not used as primary analysis in confirmatory trials.

The aim of this thesis was to address current hurdles hampering the use of pharmacometric model-based analysis in confirmatory settings by developing strategies to increase model compliance to distributional assumptions regarding the residual error, to improve the quantification of parameter uncertainty and to enable model prespecification.

A dynamic transform-both-sides approach capable of handling skewed and/or heteroscedastic residuals and a t-distribution approach allowing for symmetric heavy tails were developed and proved relevant tools to increase model compliance to distributional assumptions regarding the residual error. A diagnostic capable of assessing the appropriateness of parameter uncertainty distributions was developed, showing that currently used uncertainty methods such as bootstrap have limitations for NLMEM. A method based on sampling importance resampling (SIR) was thus proposed, which could provide parameter uncertainty in many situations where other methods fail such as with small datasets, highly nonlinear models or meta-analysis. SIR was successfully applied to predict the uncertainty in human plasma concentrations for the antibiotic colistin and its prodrug colistin methanesulfonate based on an interspecies whole-body physiologically based pharmacokinetic model. Lastly, strategies based on model-averaging were proposed to enable full model prespecification and proved to be valid alternatives to standard methodologies for studies assessing the QT prolongation potential of a drug and for phase III trials in rheumatoid arthritis.

In conclusion, improved methods for handling residual error, parameter uncertainty and model uncertainty in NLMEM were successfully developed. As confirmatory trials are among the most demanding in terms of patient-participation, cost and time in drug development, allowing (some of) these trials to be analyzed with pharmacometric model-based methods will help improve the safety and efficiency of drug development.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2016. 91 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 223
Keyword
pharmacometrics, nonlinear mixed-effects models, confirmatory trials, residual error modeling, parameter uncertainty, sampling importance resampling, model-averaging
National Category
Health Sciences
Research subject
Pharmaceutical Science
Identifiers
urn:nbn:se:uu:diva-305697 (URN)978-91-554-9734-7 (ISBN)
Public defence
2016-12-09, B/A1:107a, Biomedicinskt Centrum, Husargatan 3, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2016-11-18 Created: 2016-10-20 Last updated: 2016-11-28

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