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Bergrún Magnúsdóttir
-- doctoral thesis --
Estimation and optimal designs for multi-response Emax models
Abstract
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 multiresponse
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.
Keywords: multi-response Emax models, Clinical Utility Index (CUI), optimal designs, system estimation, dose-response studies
ISBN 978-91-7447-909-6
Download Summarising chapter -->>
Download paper II
Optimal design problems for the bivariate Emax model -->>