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Estimation and optimal designs for multi-response Emax models
Stockholm University, Faculty of Social Sciences, Department of Statistics.
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 [en]
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: urn:nbn:se:su:diva-102888ISBN: 978-91-7447-909-6 (print)OAI: oai:DiVA.org:su-102888DiVA: diva2:713888
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
List of papers
1. Optimal designs for finding the dose that maximizes a Clinical Utility Index
Open this publication in new window or tab >>Optimal designs for finding the dose that maximizes a Clinical Utility Index
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The importance of dose finding studies in the clinical development process cannot be overstated. Phase I dose finding studies usually focus on finding a safe dose while in later phases the focus is on finding an effective dose. The primary objectives in these different phases are often to estimate the maximum tolerable dose and the minimum effective dose respectively. The ultimate goal of any dose finding study is however to estimate the best dose for each patient. For the obvious reason this is not possible but in this paper we build a framework for designing dose finding studies aimed at estimating the single best dose for a population of patients. A dose that is both safe and effective. We use a utility function to model the patient net benefit from different doses of the drug taking both effects and side-effects into account. We then derive some locally c-optimal designs that minimize the asymptotic variance of the estimated target dose, the dose that maximizes the utility function. We use simulation studies to verify that the designs are appropriate and good even for small sample sizes. Efficacy calculations are carried out to study the impact of misspecification of the model parameters. We concluded that the proposed designs are good when the true parameters are equal to or larger than expected.

Keyword
Emax model, Clinical Utility Index (CUI), c-optimal design, dose-response studies
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-102868 (URN)
Available from: 2014-04-24 Created: 2014-04-23 Last updated: 2014-04-24
2. Optimal design problems for the bivariate Emax model
Open this publication in new window or tab >>Optimal design problems for the bivariate Emax model
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Finding a suitable dose is among the most difficult tasks during clinical development of a new drug. In early phases dose finding studies usually focus on finding a safe dose. Safety variables are thus of main interest. In later phases the focus is shifted towards efficacy. Typically a primary efficacy variable is defined and modeled. Various dose-response models have been suggested. For continuous responses among the most successful ones is the Emax model. Here both efficacy and safety are considered simultaneously and the Emax model is extended to a model with a bivariate response, one response being a primary efficacy variable and one being a primary safety variable. This model is referred to as the bivariate Emax model. The focus is on locally c-optimal designs for the bivariate Emax model and a simplified version of it. More specifically the locallyc-optimal designs minimize the asymptotic variance for the estimate of the dose that maximizes the patient's utility. The utility is a function of the efficacy and safety variables and referred to as the Clinical Utility Index (CUI).

Keyword
bivariate Emax model, Clinical Utility Index (CUI), c-optimal design, dose-response studies
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-102867 (URN)
Available from: 2014-04-24 Created: 2014-04-23 Last updated: 2014-04-24
3. Simultaneous estimation of parameters in the bivariate Emax model
Open this publication in new window or tab >>Simultaneous estimation of parameters in the bivariate Emax model
(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
multi-response nonlinear models; system estimation; clinical trials; Emax model
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-102866 (URN)
Available from: 2014-04-24 Created: 2014-04-23 Last updated: 2014-04-24
4. Optimal designs for a multi-response Emax model and efficient parameter estimation
Open this publication in new window or tab >>Optimal designs for a multi-response Emax model and efficient parameter estimation
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The aim of dose finding studies is sometimes to estimate parameters in a fitted model. The precision of the parameter estimates should be as high as possible. This can be obtained by increasing the number of subjects in the study, N, choosing a good and efficient estimation approach and by designing the dose finding study in an optimal way. Increasing the number of subjects is not always feasible because of increasing cost, time limitations etc. In this paper we assume fixed N and consider estimation approaches and study designs for multi-response dose finding studies. We work with diabetes dose response data and compare a system estimation approach that fits a multi-response Emax model to the data to equation-by-equation estimation that fits uni-response Emax models to the data. We then derive some optimal designs for estimating the parameters in the multi- and uni-response Emax model and study the efficiency of these designs.

Keyword
multi-response Emax model, optimal design, system estimation, dose-response studies
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-102865 (URN)
Available from: 2014-04-23 Created: 2014-04-23 Last updated: 2014-04-24

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