On the efficiency of adaptive designs
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Date
2010-10-12
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Abstract
In this paper we develop a method to investigate the efficiency of two-stage adaptive designs from
a theoretical point of view. Our approach is based on an explicit expansion of the information matrix
for an adaptive design. The results enables one to compare the performance of adaptive designs
with non-adaptive designs, without having to rely on extensive simulation studies. We demonstrate
that their relative efficiency depends sensitively on the statistical problem under investigation and
derive some general conclusions when to prefer an adaptive or a non-adaptive design. In particular,
we show that in nonlinear regression models with moderate or large variances the first stage sample
size of an adaptive design should be chosen sufficiently large in order to address variability in the
interim parameter estimates. We illustrate the methodology with several examples.
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Keywords
maximum likelihood estimation, mean squared error, nonlinear regression, optimal design