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Development and Evaluation of Nonparametric Mixed Effects Models
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
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
Keyword [en]
nonparametric, model, pharmacometrics, pharmacokinetics, pharmacodynamic, imprecision, covariate analysis, parameter distribution
National Category
Computer and Information Sciences Pharmacology and Toxicology
Research subject
Biopharmaceutics; Clinical Pharmacology; Computer Systems; Pharmacology; Statistics
URN: urn:nbn:se:uu:diva-144583ISBN: 978-91-554-7995-4 (print)OAI: diva2:393670
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: 2018-01-12Bibliographically approved
List of papers
1. Evaluation of the Nonparametric Estimation Method in NONMEM VI: Application to Real Data
Open this publication in new window or tab >>Evaluation of the Nonparametric Estimation Method in NONMEM VI: Application to Real Data
2009 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 36, no 4, 297-315 p.Article in journal (Refereed) Published
Abstract [en]

The aim of the study was to evaluate the nonparametric estimation methods available in NONMEM VI in comparison with the parametric first-order method (FO) and the first-order conditional estimation method (FOCE) when applied to real datasets. Four methods for estimating model parameters and parameter distributions (FO, FOCE, nonparametric preceded by FO (FO-NONP) and nonparametric preceded by FOCE (FOCE-NONP)) were compared for 25 models previously developed using real data and a parametric method. Numerical predictive checks were used to test the appropriateness of each model. Up to 1000 new datasets were simulated from each model and with each method to construct 90% and 50% prediction intervals. The mean absolute error and the mean error of the different outcomes investigated were computed as indicators of imprecision and bias respectively and formal statistical tests were performed. Overall, less imprecision and less bias were observed with nonparametric methods than with parametric methods. Across the 25 models, t-tests revealed that imprecision and bias were significantly lower (P < 0.05) with FOCE-NONP than with FOCE for half of the NPC outcomes investigated. Improvements were even more pronounced with FO-NONP in comparison with FO. In conclusion, when applied to real datasets and evaluated by numerical predictive checks, the nonparametric estimation methods in NONMEM VI performed better than the corresponding parametric methods (FO or FOCE).

Nonparametric estimation method, Numerical predictive check (NPC), Simulation properties, Imprecision, Bias
National Category
Pharmaceutical Sciences
urn:nbn:se:uu:diva-97513 (URN)10.1007/s10928-009-9122-z (DOI)000269079600001 ()
Available from: 2008-09-12 Created: 2008-09-12 Last updated: 2018-01-13Bibliographically approved
2. Predictive performance of internal and external validation procedures
Open this publication in new window or tab >>Predictive performance of internal and external validation procedures
(English)Article in journal (Other academic) Submitted
Abstract [en]

Purpose: To compare estimates of predictive performance between internal (IV) and external data-splitting (EV) validation procedures. Methods: Datasets of different study size (n=6, 12, 24, 48, 96, 192, or 384 individuals) were simulated from a one compartment, first-order absorption, pharmacokinetic model and both parametric (FOCE), and nonparametric (NONP) parameter estimates were obtained in NONMEM. From these, three different validation procedures (IV, EV, and a population validation (PV)) were undertaken by means of numerical predictive checks (NPCs) to provide estimates of predictive performance, the PV procedure serving as a reference to assess performance of IV and EV. The predictive performance of NONP versus FOCE estimates was further assessed. Results: Estimates of predictive performance for predicting the median of the population distribution had in general significantly lower imprecision for IV than EV, with little bias for both procedures. For small study sizes, n=6-12 (FOCE) or n=6-24 (NONP), the tails of the population distribution were significantly more biased with IV than EV, but similar imprecision was obtained. The predictive performance for FOCE was similar or superior to that of NONP. Conclusions: Data-splitting is inferior to IV when evaluating predictive models to retain sufficient precision both in predictions and in estimates of predictive performance.

urn:nbn:se:uu:diva-132776 (URN)
Available from: 2010-11-02 Created: 2010-10-26 Last updated: 2011-04-11Bibliographically approved
3. Two bootstrapping routines for obtaining imprecision estimates for nonparametric parameter distributions in nonlinear mixed effects models
Open this publication in new window or tab >>Two bootstrapping routines for obtaining imprecision estimates for nonparametric parameter distributions in nonlinear mixed effects models
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.

Bias, Bootstrap, Imprecision, Nonparametric estimation methods, Nonparametric probability density
National Category
Pharmaceutical Sciences
urn:nbn:se:uu:diva-141392 (URN)10.1007/s10928-010-9177-x (DOI)000286409300004 ()21076858 (PubMedID)
Available from: 2011-01-27 Created: 2011-01-11 Last updated: 2018-01-12Bibliographically approved
4. A novel covariate search method intended for PKPD models with nonparametric parameter distributions
Open this publication in new window or tab >>A novel covariate search method intended for PKPD models with nonparametric parameter distributions
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Objective. To develop a new covariate modeling approach adapted for nonparametric parameter distributions and to evaluate its statistical properties in terms of power and type-I error rate of covariate inclusion.

Methods. The proposed methodology is articulated around the decomposition of the nonparametric joint density obtained in NONMEM into a set of unique individual probability density distributions. These individual probabilities are then exported into R and used as weighting factors of a generalized additive model (GAM) regressing support points on covariate distributions. A calibration of the method is undertaken by means of 1000 randomization tests automated with GAM analyses to derive a decision criterion based on the Akaike’s information criterion (AIC) given the null hypothesis and a user-defined confidence level α. Statistical properties of the proposed methodology were then evaluated through Monte-Carlo simulations with α=5%. Eight scenarios of 1000 stochastic simulations followed by estimations (SSEs) were performed under FOCE-NONP given a 1-compartment pharmacokinetic model and an informative design. Estimates of the statistical power of inclusion of both a continuous and a categorical covariates with varying correlation strengths on CL were obtained with associated estimates of type-I error rate. A comparison was then intended with likelihood ratio test statistics (LRTs) given FOCE parameter distributions. Errors in estimates of correlation coefficients were further assessed.

Results. The methodology was successfully implemented by means of a Perl script calling PsN, NONMEM and R. Estimates of statistical power and type-I error rate of the proposed method were in close agreement with LRT statistics under ideal conditions of hypothesis-testing for the latter, and this, regardless of the correlation strengths and of the attributes of the covariate distribution investigated. Estimates of regression coefficients presented negligible bias and were as precise as the ones obtained with parametric models.

Conclusions. The set of covariate analysis tools is extended with a new, calibrated, covariate identification technique intended for nonparametric population models.

urn:nbn:se:uu:diva-144098 (URN)
Available from: 2011-01-27 Created: 2011-01-27 Last updated: 2013-09-04

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