Estimation and optimal designs for multi-response Emax models

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when the study has not been designed in an efficient way.At the time of the doctoral defence the following papers were unpublished and had a status as follows: Paper 1: Manuscript; Paper 2: Manuscript; Paper 3: Manuscript; Paper 4: Manuscript.