Elemental Information Matrices in Optimal Design of Experiments

• Activity Number: 405
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Valerii Fedorov*+
• Companies: Quintiles, Inc.
• Keywords: adaptive design ; convex design theory ; elemental information matrix ; equivalence theorem

Abstract

The major step in the construction of optimal experimental designs for regression models is the derivation of the information matrix of a single observation. The latter relies on the knowledge of the elemental information matrices corresponding to the distribution of the response are known. I start with the tables of elemental information matrices for distributions that are often used in statistical modeling. They contain matrices for one- and two-parameter distributions (normal, gamma, Pareto, etc). Multivariate normal and multinomial cases are also included. The parameters of response distributions can themselves be parameterized to provide dependence on explanatory variables (covariates), thus leading to regression formulations for wide classes of models. These results together with the generalized equivalence theorem provide the unified approach to the numerous design problems. The approach is illustrated with a few examples including multivariate binary responses and gamma regression.