uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Two bootstrapping routines for obtaining imprecision estimates for nonparametric parameter distributions in nonlinear mixed effects models
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.
2011 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 38, no 1, 63-82 p.Article in journal (Refereed) Published
Abstract [en]

When parameter estimates are used in predictions or decisions, it is important to consider the magnitude of imprecision associated with the estimation. Such imprecision estimates are, however, presently lacking for nonparametric algorithms intended for nonlinear mixed effects models. The objective of this study was to develop resampling-based methods for estimating imprecision in nonparametric distribution (NPD) estimates obtained in NONMEM. A one-compartment PK model was used to simulate datasets for which the random effect of clearance conformed to a (i) normal (ii) bimodal and (iii) heavy-tailed underlying distributional shapes. Re-estimation was conducted assuming normality under FOCE, and NPDs were estimated sequential to this step. Imprecision in the NPD was then estimated by means of two different resampling procedures. The first (full) method relies on bootstrap sampling from the raw data and a re-estimation of both the preceding parametric (FOCE) and the nonparametric step. The second (simplified) method relies on bootstrap sampling of individual nonparametric probability distributions. Nonparametric 95% confidence intervals (95% CIs) were obtained and mean errors (MEs) of the 95% CI width were computed. Standard errors (SEs) of nonparametric population estimates were obtained using the simplified method and evaluated through 100 stochastic simulations followed by estimations (SSEs). Both methods were successfully implemented to provide imprecision estimates for NPDs. The imprecision estimates adequately reflected the reference imprecision in all distributional cases and regardless of the numbers of individuals in the original data. Relative MEs of the 95% CI width of CL marginal density when original data contained 200 individuals were equal to: (i) -22 and -12%, (ii) -22 and -9%, (iii) -13 and -5% for the full and simplified (n = 100), respectively. SEs derived from the simplified method were consistent with the ones obtained from 100 SSEs. In conclusion, two novel bootstrapping methods intended for nonparametric estimation methods are proposed. In addition of providing information about the precision of nonparametric parameter estimates, they can serve as diagnostic tools for the detection of misspecified parameter distributions.

Place, publisher, year, edition, pages
2011. Vol. 38, no 1, 63-82 p.
Keyword [en]
Bias, Bootstrap, Imprecision, Nonparametric estimation methods, Nonparametric probability density
National Category
Pharmaceutical Sciences
URN: urn:nbn:se:uu:diva-141392DOI: 10.1007/s10928-010-9177-xISI: 000286409300004PubMedID: 21076858OAI: oai:DiVA.org:uu-141392DiVA: diva2:385545
Available from: 2011-01-27 Created: 2011-01-11 Last updated: 2011-03-09Bibliographically approved
In thesis
1. Development and Evaluation of Nonparametric Mixed Effects Models
Open this publication in new window or tab >>Development and Evaluation of Nonparametric Mixed Effects Models
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

A nonparametric population approach is now accessible to a more comprehensive network of modelers given its recent implementation into the popular NONMEM application, previously limited in scope by standard parametric approaches for the analysis of pharmacokinetic and pharmacodynamic data.

The aim of this thesis was to assess the relative merits and downsides of nonparametric models in a nonlinear mixed effects framework in comparison with a set of parametric models developed in NONMEM based on real datasets and when applied to simple experimental settings, and to develop new diagnostic tools adapted to nonparametric models.

Nonparametric models as implemented in NONMEM VI showed better overall simulation properties and predictive performance than standard parametric models, with significantly less bias and imprecision in outcomes of numerical predictive check (NPC) from 25 real data designs. This evaluation was carried on by a simulation study comparing the relative predictive performance of nonparametric and parametric models across three different validation procedures assessed by NPC. The usefulness of a nonparametric estimation step in diagnosing distributional assumption of parameters was then demonstrated through the development and the application of two bootstrapping techniques aiming to estimate imprecision of nonparametric parameter distributions. Finally, a novel covariate modeling approach intended for nonparametric models was developed with good statistical properties for identification of predictive covariates.

In conclusion, by relaxing the classical normality assumption in the distribution of model parameters and given the set of diagnostic tools developed, the nonparametric approach in NONMEM constitutes an attractive alternative to the routinely used parametric approach and an improvement for efficient data analysis.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2011. 68 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 136
nonparametric, model, pharmacometrics, pharmacokinetics, pharmacodynamic, imprecision, covariate analysis, parameter distribution
National Category
Computer and Information Science Pharmacology and Toxicology
Research subject
Biopharmaceutics; Clinical Pharmacology; Computer Systems; Pharmacology; Statistics
urn:nbn:se:uu:diva-144583 (URN)978-91-554-7995-4 (ISBN)
Public defence
2011-03-22, Room B21, BMC, Husarg. 3, Uppsala, 09:15 (English)
Available from: 2011-03-09 Created: 2011-01-31 Last updated: 2011-05-04Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textPubMed

Search in DiVA

By author/editor
Baverel, Paul G.Savic, Radojka M.Karlsson, Mats O.
By organisation
Department of Pharmaceutical Biosciences
In the same journal
Journal of Pharmacokinetics and Pharmacodynamics
Pharmaceutical Sciences

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 280 hits
ReferencesLink to record
Permanent link

Direct link