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Improving The Estimation Of Parameter Uncertainty Distributions In Nonlinear Mixed Effects Models Using Sampling Importance Resampling
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.
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 6, 583-596 p.Article in journal (Refereed) Published
Abstract [en]

Taking parameter uncertainty into account is key to make drug development decisions such as testing whether trial endpoints meet defined criteria. Currently used methods for assessing parameter uncertainty in NLMEM have limitations, and there is a lack of diagnostics for when these limitations occur. In this work, a method based on sampling importance resampling (SIR) is proposed, which has the advantage of being free of distributional assumptions and does not require repeated parameter estimation. To perform SIR, a high number of parameter vectors are simulated from a given proposal uncertainty distribution. Their likelihood given the true uncertainty is then approximated by the ratio between the likelihood of the data given each vector and the likelihood of each vector given the proposal distribution, called the importance ratio. Non-parametric uncertainty distributions are obtained by resampling parameter vectors according to probabilities proportional to their importance ratios. Two simulation examples and three real data examples were used to define how SIR should be performed with NLMEM and to investigate the performance of the method. The simulation examples showed that SIR was able to recover the true parameter uncertainty. The real data examples showed that parameter 95 % confidence intervals (CI) obtained with SIR, the covariance matrix, bootstrap and log-likelihood profiling were generally in agreement when 95 % CI were symmetric. For parameters showing asymmetric 95 % CI, SIR 95 % CI provided a close agreement with log-likelihood profiling but often differed from bootstrap 95 % CI which had been shown to be suboptimal for the chosen examples. This work also provides guidance towards the SIR workflow, i.e.,which proposal distribution to choose and how many parameter vectors to sample when performing SIR, using diagnostics developed for this purpose. SIR is a promising approach for assessing parameter uncertainty as it is applicable in many situations where other methods for assessing parameter uncertainty fail, such as in the presence of small datasets, highly nonlinear models or meta-analysis.

Place, publisher, year, edition, pages
2016. Vol. 43, no 6, 583-596 p.
Keyword [en]
Sampling importance resampling, Parameter uncertainty, Confidence intervals, Asymptotic covariance matrix, Nonlinear mixed-effects models, Bootstrap
National Category
Pharmaceutical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-303629DOI: 10.1007/s10928-016-9487-8ISI: 000388634800003PubMedID: 27730482OAI: oai:DiVA.org:uu-303629DiVA: diva2:1038969
Funder
EU, European Research Council, 602552 115156
Available from: 2016-10-20 Created: 2016-09-21 Last updated: 2016-12-29Bibliographically 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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Dosne, Anne-GaëlleBergstrand, MartinHarling, KajsaKarlsson, Mats O.
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