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Likert Pain Scores Modeling: A Markov Integer Model and an Autoregressive Continuous Model
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
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2012 (English)In: Clinical Pharmacology and Therapeutics, ISSN 0009-9236, E-ISSN 1532-6519, Vol. 91, no 5, 820-828 p.Article in journal (Refereed) Published
Abstract [en]

Pain intensity is principally assessed using rating scales such as the 11-point Likert scale. In general, frequent pain assessments are serially correlated and underdispersed. The aim of this investigation was to develop population models adapted to fit the 11-point pain scale. Daily Likert scores were recorded over 18 weeks by 231 patients with neuropathic pain from a clinical trial placebo group. An integer model consisting of a truncated generalized Poisson (GP) distribution with Markovian transition probability inflation was implemented in NONMEM 7.1.0. It was compared to a logit-transformed autoregressive continuous model with correlated residual errors. In both models, the score baseline was estimated to be 6.2 and the placebo effect to be 19%. Developed models similarly retrieved consistent underlying features of the data and therefore correspond to platform models for drug effect detection. The integer model was complex but flexible, whereas the continuous model can more easily be developed, although requires longer runtimes.


Place, publisher, year, edition, pages
2012. Vol. 91, no 5, 820-828 p.
Keyword [en]
Pain, Likert, Score, Poisson, Markov, Underdispersion, Correlation, Placebo, NONMEM
National Category
Medical and Health Sciences
URN: urn:nbn:se:uu:diva-150926DOI: 10.1038/clpt.2011.301ISI: 000303047400015OAI: oai:DiVA.org:uu-150926DiVA: diva2:409330
Available from: 2011-04-07 Created: 2011-04-07 Last updated: 2012-05-28Bibliographically 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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Plan, Elodie LKarlsson, Mats O
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