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Modelling overdispersion and Markovian features in count data.
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 5, 461-477 p.Article in journal (Refereed) Published
Abstract [en]

The number of counts (events) per unit of time is a discrete response variable that is generally analyzed with the Poisson distribution (PS) model. The PS model makes two assumptions: the mean number of counts (lambda) is assumed equal to the variance, and counts occurring in non-overlapping intervals are assumed independent. However, many counting outcomes show greater variability than predicted by the PS model, a phenomenon called overdispersion. The purpose of this study was to implement and explore, in the population context, different distribution models accounting for overdispersion and Markov patterns in the analysis of count data. Daily seizures count data obtained from 551 subjects during the 12-week screening phase of a double-blind, placebo-controlled, parallel-group multicenter study performed in epileptic patients with medically refractory partial seizures, were used in the current investigation. The following distribution models were fitted to the data: PS, Zero-Inflated PS (ZIP), Negative Binomial (NB), and Zero-Inflated Negative Binomial (ZINB) models. Markovian features were introduced estimating different lambdas and overdispersion parameters depending on whether the previous day was a seizure or a non-seizure day. All analyses were performed with NONMEM VI. All models were successfully implemented and all overdispersed models improved the fit with respect to the PS model. The NB model resulted in the best description of the data. The inclusion of Markovian features in lambda and in the overdispersion parameter improved the fit significantly (P < 0.001). The plot of the variance versus mean daily seizure count profiles, and the number of transitions, are suggested as model performance tools reflecting the capability to handle overdispersion and Markovian features, respectively.

Place, publisher, year, edition, pages
2009. Vol. 36, no 5, 461-477 p.
Keyword [en]
Count data, population pharmacodynamic modelling, NONMEM, epilepsy, Gabapentin
National Category
Pharmaceutical Sciences
URN: urn:nbn:se:uu:diva-122144DOI: 10.1007/s10928-009-9131-yISI: 000271673000005PubMedID: 19798550OAI: oai:DiVA.org:uu-122144DiVA: diva2:308493
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.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 145
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
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)
Available from: 2011-04-28 Created: 2011-04-07 Last updated: 2011-05-05Bibliographically approved

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