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Approaches to Likert-type Ordered Categorical Data Analysis
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Purpose: Ordinal variables are common pharmacodynamic responses, but when the number of categories reaches 11, current approaches to fit this type of data may not be suitable. This article aims at exploring modeling approach candidates for 11-point ordered categorical data.

Methods: The study consisted of two sets of 100 stochastic simulations and estimations in NONMEM VI. A first set was generated with a baseline response ordered categorical model, whose parameter values were derived from a real case study with 100 observations on average per individual. A second set included a linear drug effect observed in a 4 parallel dose arm treatment trial. Simulated data were analyzed with an ordered categorical (OC), a truncated generalized Poisson (PO), and a logit-transformed continuous (CO) models.

Results: The dose-response OC model needed 13 parameters, compared to 7 and 6 with the other models. Score distributions were closely mimicked by OC resimulations at all dose levels. The agreement with PO resimulated scores was best at low doses, in contrast to CO showing less discrepancy at high doses.

Conclusions: Truncated count (PO) or logit-transformed continuous (CO) models may be alternatives to ordered categorical models for Likert scores in case of sparse data or in presence of serial correlations.


Keyword [en]
Ordered categorical, count, Poisson, continuous, Likert, scale, score, NONMEM, power
National Category
Pharmaceutical Sciences
URN: urn:nbn:se:uu:diva-150922OAI: oai:DiVA.org:uu-150922DiVA: diva2:409327
Available from: 2011-04-07 Created: 2011-04-07 Last updated: 2013-08-20
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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