LTCC Topics in the Design of Experiments - Advanced Course
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.
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.