Simulation based optimal design and some applications in clinical 
                              trials 

                     Peter Muller
             Institute of Statistics and Decision Sciences
                    Duke University



I review simulation based methods for exploration and maximization of
expected utility surfaces.  Expected utility maximization, i.e.,
optimal design, is concerned with maximizing with respect to some
design parameter an integral expression representing the expected
utility. Except in special cases neither the maximization nor the
integration can be solved analytically and approximations and/or
simulation based methods are needed. I will discuss several related
strategies: large scale Monte Carlo simulation; smoothing of Monte
Carlo simulations; Markov chain Monte Carlo (MCMC) simulation in an
augmented probability model; a simulated annealing type approach; and
the use of forward simulation to evaluate expected utility integrals
required in backward induction. The latter method addresses optimal
design in a sequential decision problem.

I will discuss two applications related to optimal planning of 
clinical trials. The first example is about optimal choice of sampling
times in a limited sampling problem. The second example addresses
optimal design for a termination decision in a clinical trial and involves
a sequential decision problem.