On the efficiency of adaptive designs

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.