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LTCC Topics in the Design of Experiments - Advanced Course |
COURSE DESCRIPTION This course
covers some of the topics which are essential background for much of the
current research in the design of experiments. It is in two parts: 1. Optimal design theory: A very natural
way to design an experiment is to specify an optimality criterion which
captures the objectives of the experiment and then to find a design which
optimizes this criterion. The theory of optimal design has been developed
mainly in the context of generally useful criteria, such as D-optimality, and
this is now starting to have a major impact on practice in areas as diverse
as mixtures experiments in agrochemical formulation studies and
pharmacokinetic and pharmacodynamic studies using
nonlinear models. The general theory will be described, with an emphasis on
equivalence theorems for finding optimal designs, and applications to linear
and nonlinear models will be discussed. 2. Sequential design: In clinical
medicine, there are both economic and ethical advantages to designing trials
sequentially, due to the reduced number of subjects required and the
possibility of early stopping. In this course, the ideas of stopping rules
and the impact they have on inference after the experiment, will be
introduced. The possibility of adaptive design, in which the allocation of
treatments is decided sequentially, will also be discussed. Recommended reading: Atkinson, A.C., Donev, A.N. and Tobias, R. (2007) Optimum Experimental
Designs, with SAS. Whitehead, J. R.
(1997) Design and Analysis of Sequential Clinical Trials, 2nd edition. Wiley. Prerequisites: Fundamental Theory of Statistical Inference; Statistical Modelling and Estimation or an undergraduate level course
in linear models. |