Two-Stage Adaptive-Optimal Design with Fixed First-Stage Sample Size

• Activity Number: 605
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Nancy Flournoy*+ and Adam Lane
• Companies: University of Missouri and Cincinnati Children's Hospital Medical Center
• Keywords: Dose-finding ; Pilot studies ; Informative designs ; Mixture distribution ; Maximum Likelihood Estimation ; Minimum variance dose selection

Abstract

Adaptive optimal designs form a special case of response-adaptive allocation procedures. In adaptive optimal procedures, the design at each stage is an estimate of the optimal design based on all previous data. These designs are ancillary to, but not independent of, the experimental outcomes. This talk discusses important consequences of this dependency. For this exposition, we assume a one parameter nonlinear regression model with normal errors. The second stage design point is chosen to minimize the estimated variance of the parameter estimate, and hence it is a function of the sufficient statistics from the first stage. The density of experimental outcomes from the second stage has the form of a normal density, but in fact it is not a member of the exponential family. In spite of the dependency between stages, if the sample size at each stage goes to infinity with the overall sample size, standard results for the asymptotic normality of maximum likelihood estimates follow. However, it is not uncommon for a small pilot study of fixed size to be followed by a much larger experiment. We study the large sample behavior of such studies. That is, we take the sample size of th