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The impact of misspecification of residual error or correlation structure on the type I error rate for covariate inclusion
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)ORCID iD: 0000-0003-3531-9452
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 1, 81-99 p.Article in journal (Refereed) Published
Abstract [en]

It has been shown that when using the FOCE method in NONMEM, the likelihood ratio test (LRT) can be sensitive to the use of an inappropriate estimation method in that ignoring an existing eta-epsilon interaction leads to actual significance levels for type I errors being higher than the nominal levels. The objective of this study was to assess through simulations the LRT sensitivity to various types of residual error model misspecifications in both continuous and categorical data. The study contained two parts, simulations based on continuous and categorical data. Data sets containing 250 individuals with up to 24 observations per individual were simulated multiple times (1000) with different types of residual error models for the continuous data and different strength of correlation between observations for the categorical data. The data sets were analyzed using either the correct or a simpler (incorrect) model with or without addition of a covariate. The type I error rate of inclusion of the non-informative covariate on the 5% level was calculated as the number of runs where the drop in the objective function value (OFV) was larger than 3.84 when the covariate relationship was included in the model using the correct or the incorrect model. The difference in OFV between the model with the correct and the incorrect structure was also calculated as a measure of the residual error model misspecification. For continuous data the FOCE method was used in most cases (with interaction when appropriate). The Laplacian estimation method was used for one of the continuous models and for categorical data. The results showed that the residual error model misspecifications when the erroneous model was used were pronounced, as indicated by the OFV being substantially higher than for the corresponding correct models. The significance levels of the LRT with the incorrect model were appropriate in all cases but ignoring (serial) correlations between observations (continuous and categorical data) as well as when the eta-epsilon interaction was ignored (which has previously been shown, continuous data). When ignoring correlation, the type I error rates were shown to be sensitive to the correlation strength, the number of observations per individual and the magnitude of the inter-individual variability on clearance. We conclude that the LRT appears robust towards all tested cases, but ignoring (serial) correlations between observations and eta-epsilon interaction.

Place, publisher, year, edition, pages
2009. Vol. 36, no 1, 81-99 p.
Keyword [en]
Residual error, Model misspecification, Continuous data, Categorical data, NONMEM, Markov model, Proportional odds model, Simulation, Likelihood ratio test
National Category
Pharmaceutical Sciences
Research subject
Pharmacokinetics and Drug Therapy
Identifiers
URN: urn:nbn:se:uu:diva-99064DOI: 10.1007/s10928-009-9112-1ISI: 000263797800005PubMedID: 19219538OAI: oai:DiVA.org:uu-99064DiVA: diva2:202206
Available from: 2009-03-09 Created: 2009-03-06 Last updated: 2017-12-13
In thesis
1. Integrated Modeling of Glucose and Insulin Regulation Following Provocation Experiments
Open this publication in new window or tab >>Integrated Modeling of Glucose and Insulin Regulation Following Provocation Experiments
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Blood glucose is controlled by a complex system of insulin and other hormones to assure a constant supply of glucose to the tissues. Type 2 diabetes is a metabolic disorder which is characterized by progressively worsening glycemic control due to a relative deficiency of insulin secretion and a decreased response to insulin. Numerous mathematical models have been developed with the aim of describing glucose and insulin regulation. A drawback with most previously presented models is that they use an open-loop approach which simplifies the model development but at the same time limits the possible use for predictive purposes.

The integrated glucose-insulin model presented in this thesis is a semi-mechanistic model which describes glucose and insulin simultaneously. The model has been used to analyze both intravenous and oral provocations and has been shown to describe and predict healthy and diabetic individuals well. Important differences between healthy and diabetic individuals were identified in insulin secretion and sensitivity. The model was used for design optimization of the intravenous glucose tolerance test and it was shown that the design could be improved and simplified by reduction of the number of samples and by change of glucose and insulin dose. Two methodological aspects which were of importance for model development were evaluated. These were (i) comparison of methods for incorporation of baseline data, and (ii) evaluation of the effects of model misspecification on hypothesis testing for covariate inclusion. Baseline information should be included in the model using either of three presented methods and normalization or subtraction of baseline should be avoided. The likelihood ratio test performed well in most cases except when serial correlation was present.

In conclusion, a new model for glucose and insulin regulation has been proposed which is expected to play an important role in clinical development of anti-diabetic drugs.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2009. 71 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 92
Research subject
Pharmacokinetics and Drug Therapy
Identifiers
urn:nbn:se:uu:diva-99195 (URN)978-91-554-7463-8 (ISBN)
Public defence
2009-04-24, B21, BMC, Husargatan 3, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2009-04-03 Created: 2009-03-10 Last updated: 2011-05-11Bibliographically 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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Kjellsson, Maria CKarlsson, Mats O

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