On the Efficiency of Two-Stage Response-Adaptive Designs

• Activity Number: 556
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Frank Bretz*+ and Holger Dette and Björn Bornkamp
• Companies: Novartis and Ruhr-Universität Bochum and Novartis
• Keywords: dose estimation ; dose finding ; mean squared error ; optimal design ; maximum likelihood estimation ; nonlinear regression

Abstract

We investigate the efficiency of two-stage response-adaptive designs, where after the first stage the accrued data is used to determine a locally optimum design for the second stage. Based on an explicit expansion of the information matrix, we compare the variance of the maximum likelihood estimates obtained from a two-stage adaptive design and a fixed design without adaptation. For several one-parameter models, we provide explicit expressions for the relative efficiency of these two designs, which is seen to depend sensitively on the statistical problem under investigation. 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. These findings support the results of recent simulation studies conducted to compare adaptive designs in more complex situations. We finally present an application to a real clinical dose finding trial aiming at the estimation of the smallest dose achieving a certain percentage of the maximum treatment effect using a three-parameter Emax model.