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Estimating bias in population parameters for some models for repeated measures ordinal data using NONMEM or NLMIXED
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences, Division of Pharmacokinetics and Drug Therapy. (Farmakometri)
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences, Division of Pharmacokinetics and Drug Therapy. (Farmakometri)ORCID iD: 0000-0003-3531-9452
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences, Division of Pharmacokinetics and Drug Therapy. (Farmakometri)
2004 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 31, no 4, 299-320 p.Article in journal (Refereed) Published
Abstract [en]

The application of proportional odds models to ordered categorical data using the mixed-effects modeling approach has become more frequently reported within the pharmacokinetic/pharmacodynamic area during the last decade. The aim of this paper was to investigate the bias in parameter estimates, when models for ordered categorical data were estimated using methods employing different approximations of the likelihood integral; the Laplacian approximation in NONMEM (without and with the centering option) and NLMIXED, and the Gaussian quadrature approximations in NLMIXED. In particular, we have focused on situations with non-even distributions of the response categories and the impact of interpatient variability. This is a Monte Carlo simulation study where original data sets were derived from a known model and fixed study design. The simulated response was a four-category variable on the ordinal scale with categories 0, 1, 2 and 3. The model used for simulation was fitted to each data set for assessment of bias. Also, simulations of new data based on estimated population parameters were performed to evaluate the usefulness of the estimated model. For the conditions tested, Gaussian quadrature performed without appreciable bias in parameter estimates. However, markedly biased parameter estimates were obtained using the Laplacian estimation method without the centering option, in particular when distributions of observations between response categories were skewed and when the interpatient variability was moderate to large. Simulations under the model could not mimic the original data when bias was present, but resulted in overestimation of rare events. The bias was considerably reduced when the centering option in NONMEM was used. The cause for the biased estimates appears to be related to the conditioning on uninformative and uncertain empirical Bayes estimate of interindividual random effects during the estimation, in conjunction with the normality assumption.

Place, publisher, year, edition, pages
2004. Vol. 31, no 4, 299-320 p.
Keyword [en]
NONMEM, NLMIXED, SAS, Laplacian, Gaussian quadrature, maximum likelihood estimation, ordered categorical, proportional odds model, bias in parameter estimates
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:uu:diva-91736DOI: 10.1023/B:JOPA.0000042738.06821.61PubMedID: 15563005OAI: oai:DiVA.org:uu-91736DiVA: diva2:164565
Available from: 2004-04-26 Created: 2004-04-26 Last updated: 2017-12-14
In thesis
1. Estimation of Dosing Strategies for Individualisation
Open this publication in new window or tab >>Estimation of Dosing Strategies for Individualisation
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

To increase the proportion of patients with successful drug treatment, dose individualisation on the basis of one or several patient characteristics, a priori individualisation, and/or on the basis of feedback observations from the patient following an initial dose, a posteriori individualisation, is an option. Efficient tools in optimising individualised dosing strategies are population models describing pharmacokinetics (PK) and the relation between pharmacokinetics and pharmacodynamics (PK/PD).

Methods for estimating optimal dosing strategies, with a discrete number of doses, for dose individualisation a priori and a posteriori were developed and explored using simulated data. The methods required definitions of (i) the therapeutic target, i.e. the value of the target variable and a risk function quantifying the seriousness of deviation from the target, (ii) a population PK/PD model relating dose input to the target variable in the patients to be treated, and (iii) distributions of relevant patient factors. Optimal dosing strategies, in terms of dose sizes and individualisation conditions, were estimated by minimising the overall risk. Factors influencing the optimal dosing strategies were identified. Consideration of those will have implications for study design, data collection, population model development and target definition.

A dosing strategy for a priori individualisation was estimated for NXY-059, a drug under development. Applying the estimated dosing strategy in a clinical study resulted in reasonable agreement between observed and expected outcome, supporting the developed methodology.

Estimation of a dosing strategy for a posteriori individualisation for oxybutynin, a drug marketed for the treatment of overactive bladder, illustrated the implementation of the method when defining the therapeutic target in terms of utility and responder probability, that is, as a combination of the desired and adverse effects.

The proposed approach provides an estimate of the maximal benefit expected from individualisation and, if individualisation is considered clinically superior, the optimal conditions for individualisation. The main application for the methods is in drug development where the methods can be generally employed in the establishment of dosing strategies for individualisation with relevant extensions regarding population model complexity and individualisation conditions.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2004. 62 p.
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 0282-7484 ; 312
Keyword
Pharmaceutical biosciences, Dosing strategy, Individualisation, Pharmacokinetic, Pharmacodynamic, Modeling, NONMEM, Decision making, Farmaceutisk biovetenskap
National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-4255 (URN)91-554-5960-9 (ISBN)
Public defence
2004-05-19, Room B21, BMC, Husargatan 3, Uppsala, 09:15
Opponent
Supervisors
Available from: 2004-04-26 Created: 2004-04-26Bibliographically approved
2. Methodological Studies on Models and Methods for Mixed-Effects Categorical Data Analysis
Open this publication in new window or tab >>Methodological Studies on Models and Methods for Mixed-Effects Categorical Data Analysis
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Effects of drugs are in clinical trials often measured on categorical scales. These measurements are increasingly being analyzed using mixed-effects logistic regression. However, the experience with such analyzes is limited and only a few models are used.

The aim of this thesis was to investigate the performance and improve the use of models and methods for mixed-effects categorical data analysis. The Laplacian method was shown to produce biased parameter estimates if (i) the data variability is large or (ii) the distribution of the responses is skewed. Two solutions are suggested; the Gaussian quadrature method and the back-step method. Two assumptions made with the proportional odds model have also been investigated. The assumption with proportional odds for all categories was shown to be unsuitable for analysis of data arising from a ranking scale of effects with several underlying causes. An alternative model, the differential odds model, was developed and shown to be an improvement, in regard to statistical significance as well as predictive performance, over the proportional odds model for such data. The appropriateness of the likelihood ratio test was investigated for an analysis where dependence between observations is ignored, i.e. performing the analysis using the proportional odds model. The type I error was found to be affected; thus assessing the actual critical value is prudent in order to verify the statistical significance level. An alternative approach is to use a Markov model, in which dependence between observations is incorporated. In the case of polychotomous data such model may involve considerable complexity and thus, a strategy for the reduction of the time-consuming model building with the Markov model and sleep data is presented.

This thesis will hopefully contribute to a more confident use of models for categorical data analysis within the area of pharmacokinetic and pharmacodynamic modelling in the future.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2008. 76 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 83
Keyword
Pharmacodynamics, Categorical data, Markov model, Modelling, NONMEM, NLMIXED, Laplace, Gaussian quadrature, Back-Step Method, Proportional odds model, Differential odds model
National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-9333 (URN)978-91-554-7316-7 (ISBN)
Public defence
2008-11-21, B42, BMC, Husargatan 3, Uppsala, 13:15
Opponent
Supervisors
Available from: 2008-10-30 Created: 2008-10-30 Last updated: 2012-06-01Bibliographically approved

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Jönsson, SivKjellsson, Maria C.Karlsson, Mats O.

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