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Simultaneous estimation of parameters in the bivariate Emax model
Stockholm University, Faculty of Social Sciences, Department of Statistics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper we explore inference in multi-response, nonlinear models. By multi-responsewe mean models with m>1 response variables and accordingly m relations. Each parameter/explanatory variable may appear in one or more of the relations. We study a system estimation approach for simultaneous computation and inference of the model and (co)variance parameters. For illustration we fit a bivariate Emax model to diabetes dose response data. Further the bivariate Emax model is used in a simulation study that compares the system estimation approach to equation-by-equation estimation. We conclude that overall the system estimation approach performs better for the bivariate Emax model when there are dependencies among relations. The stronger the dependencies the more we gain in precision by using system estimation rather than equation-by-equation estimation.

Keyword [en]
multi-response nonlinear models; system estimation; clinical trials; Emax model
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-102866OAI: oai:DiVA.org:su-102866DiVA: diva2:713851
Available from: 2014-04-24 Created: 2014-04-23 Last updated: 2014-04-24
In thesis
1. Estimation and optimal designs for multi-response Emax models
Open this publication in new window or tab >>Estimation and optimal designs for multi-response Emax models
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns optimal designs and estimation approaches for a class of nonlinear dose response models, namely multi-response Emax models. These models describe the relationship between the dose of a drug and two or more efficacy and/or safety variables. In order to obtain precise parameter estimates it is important to choose efficient estimation approaches and to use optimal designs to control the level of the doses administered to the patients in the study.

We provide some optimal designs that are efficient for estimating the parameters, a subset of the parameters, and a function of the parameters in multi-response Emax models. The function of interest is an estimate of the best dose to administer to a group of patients. More specifically the dose that maximizes the Clinical Utility Index (CUI) which assesses the net benefit of a drug taking both effects and side-effects into account. The designs derived in this thesis are locally optimal, that is they depend upon the true parameter values. An important part of this thesis is to study how sensitive the optimal designs are to misspecification of prior parameter values.

For multi-response Emax models it is possible to derive maximum likelihood (ML) estimates separately for the parameters in each dose response relation. However, ML estimation can also be carried out simultaneously for all response profiles by making use of dependencies between the profiles (system estimation). In this thesis we compare the performance of these two approaches by using a simulation study where a bivariate Emax model is fitted and by fitting a four dimensional Emax model to real dose response data. The results are that system estimation can substantially increase the precision of parameter estimates, especially when the correlation between response profiles is strong or when the study has not been designed in an efficient way.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2014. 38 p.
Keyword
multi-response Emax models, Clinical Utility Index (CUI), optimal designs, system estimation, dose-response studies.
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-102888 (URN)978-91-7447-909-6 (ISBN)
Public defence
2014-05-30, Nordenskiöldsalen, Geovetenskapens hus, Svante Arrhenius väg 12, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defence the following papers were unpublished and had a status as follows: Paper 1: Manuscript; Paper 2: Manuscript; Paper 3: Manuscript; Paper 4: Manuscript.

Available from: 2014-05-08 Created: 2014-04-24 Last updated: 2014-05-05Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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