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Performance in population models for count data, part I: maximum likelihood approximations.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Farmakometri)
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Farmakometri)
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Farmakometri)
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Farmakometri)
2009 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 36, no 4, 353-366 p.Article in journal (Refereed) Published
Abstract [en]

There has been little evaluation of maximum likelihood approximation methods for non-linear mixed effects modelling of count data. The aim of this study was to explore the estimation accuracy of population parameters from six count models, using two different methods and programs. Simulations of 100 data sets were performed in NONMEM for each probability distribution with parameter values derived from a real case study on 551 epileptic patients. Models investigated were: Poisson (PS), Poisson with Markov elements (PMAK), Poisson with a mixture distribution for individual observations (PMIX), Zero Inflated Poisson (ZIP), Generalized Poisson (GP) and Negative Binomial (NB). Estimations of simulated datasets were completed with Laplacian approximation (LAPLACE) in NONMEM and LAPLACE/Gaussian Quadrature (GQ) in SAS. With LAPLACE, the average absolute value of the bias (AVB) in all models was 1.02% for fixed effects, and ranged 0.32-8.24% for the estimation of the random effect of the mean count (lambda). The random effect of the overdispersion parameter present in ZIP, GP and NB was underestimated (-25.87, -15.73 and -21.93% of relative bias, respectively). Analysis with GQ 9 points resulted in an improvement in these parameters (3.80% average AVB). Methods implemented in SAS had a lower fraction of successful minimizations, and GQ 9 points was considerably slower than 1 point. Simulations showed that parameter estimates, even when biased, resulted in data that were only marginally different from data simulated from the true model. Thus all methods investigated appear to provide useful results for the investigated count data models.

Place, publisher, year, edition, pages
2009. Vol. 36, no 4, 353-366 p.
Keyword [en]
NONMEM, LAPLACE, Laplacian approximation, SAS, Gaussian quadrature, Maximum likelihood approximation, Count data, Poisson model
National Category
Pharmaceutical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-122145DOI: 10.1007/s10928-009-9126-8ISI: 000269079600004PubMedID: 19653080OAI: oai:DiVA.org:uu-122145DiVA: diva2:308492
Available from: 2010-04-06 Created: 2010-04-06 Last updated: 2013-08-20Bibliographically approved
In thesis
1. Pharmacometric Methods and Novel Models for Discrete Data
Open this publication in new window or tab >>Pharmacometric Methods and Novel Models for Discrete Data
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Pharmacodynamic processes and disease progression are increasingly characterized with pharmacometric models. However, modelling options for discrete-type responses remain limited, although these response variables are commonly encountered clinical endpoints. Types of data defined as discrete data are generally ordinal, e.g. symptom severity, count, i.e. event frequency, and time-to-event, i.e. event occurrence. Underlying assumptions accompanying discrete data models need investigation and possibly adaptations in order to expand their use. Moreover, because these models are highly non-linear, estimation with linearization-based maximum likelihood methods may be biased.

The aim of this thesis was to explore pharmacometric methods and novel models for discrete data through (i) the investigation of benefits of treating discrete data with different modelling approaches, (ii) evaluations of the performance of several estimation methods for discrete models, and (iii) the development of novel models for the handling of complex discrete data recorded during (pre-)clinical studies.

A simulation study indicated that approaches such as a truncated Poisson model and a logit-transformed continuous model were adequate for treating ordinal data ranked on a 0-10 scale. Features that handled serial correlation and underdispersion were developed for the models to subsequently fit real pain scores. The performance of nine estimation methods was studied for dose-response continuous models. Other types of serially correlated count models were studied for the analysis of overdispersed data represented by the number of epilepsy seizures per day. For these types of models, the commonly used Laplace estimation method presented a bias, whereas the adaptive Gaussian quadrature method did not. Count models were also compared to repeated time-to-event models when the exact time of gastroesophageal symptom occurrence was known. Two new model structures handling repeated time-to-categorical events, i.e. events with an ordinal severity aspect, were introduced. Laplace and two expectation-maximisation estimation methods were found to be performing well for frequent repeated time-to-event models.

In conclusion, this thesis presents approaches, estimation methods, and diagnostics adapted for treating discrete data. Novel models and diagnostics were developed when lacking and applied to biological observations.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2011. 80 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 145
Keyword
Pharmacometrics, pharmacodynamics, disease progression, modelling, discrete data, count, ordered categorical, repeated time-to-event, RTTCE, RCEpT, NONMEM, FOCE, LAPLACE, SAEM, AGQ, pain scores, epilepsy seizures, gastroesophageal symptoms, statistical power, simulations, diagnostics
National Category
Pharmaceutical Sciences
Research subject
Pharmacokinetics and Drug Therapy
Identifiers
urn:nbn:se:uu:diva-150929 (URN)978-91-554-8064-6 (ISBN)
Public defence
2011-05-20, B41, BMC, Husargatan 3, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2011-04-28 Created: 2011-04-07 Last updated: 2011-05-05Bibliographically approved
2. Optimal (Adaptive) Design and Estimation Performance in Pharmacometric Modelling
Open this publication in new window or tab >>Optimal (Adaptive) Design and Estimation Performance in Pharmacometric Modelling
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The pharmaceutical industry now recognises the importance of the newly defined discipline of pharmacometrics. Pharmacometrics uses mathematical models to describe and then predict the performance of new drugs in clinical development. To ensure these models are useful, the clinical studies need to be designed such that the data generated allows the model predictions to be sufficiently accurate and precise. The capability of the available software to reliably estimate the model parameters must also be well understood. 

This thesis investigated two important areas in pharmacometrics: optimal design and software estimation performance. The three optimal design papers progressed significant areas of optimal design research, especially relevant to phase II dose response designs. The use of exposure, rather than dose, was investigated within an optimal design framework. In addition to using both optimal design and clinical trial simulation, this work employed a wide range of metrics for assessing design performance, and was illustrative of how optimal designs for exposure response models may yield dose selections quite different to those based on standard dose response models. The investigation of the optimal designs for Poisson dose response models demonstrated a novel mathematical approach to the necessary matrix calculations for non-linear mixed effects models. Finally, the enormous potential of using optimal adaptive designs over fixed optimal designs was demonstrated. The results showed how the adaptive designs were robust to initial parameter misspecification, with the capability to "learn" the true dose response using the accruing subject data. The two estimation performance papers investigated the relative performance of a number of different algorithms and software programs for two complex pharmacometric models.

In conclusion these papers, in combination, cover a wide spectrum of study designs for non-linear dose/exposure response models, covering: normal/non-normal data, fixed/mixed effect models, single/multiple design criteria metrics, optimal design/clinical trial simulation, and adaptive/fixed designs. 

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 76 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 166
Keyword
Phase II, dose response, optimal design, adaptive design, exposure response, count data
National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-182284 (URN)978-91-554-8491-0 (ISBN)
Public defence
2012-11-30, B41, Biomedicinskt Centrum, Husargatan 3, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2012-11-02 Created: 2012-10-08 Last updated: 2013-01-23Bibliographically approved

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Plan, Elodie L.Karlsson, Mats O.

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