On the Equivalence of Optimality Design Criteria for the Placebo-Treatment Problem

Abstract

We consider a class of optimality criteria and show that each crite- rion has its unique and equivalent dual within the class. This property can be used to find a variety of optimal designs, including a class of compound optimal designs and their relationships. As an example, we show that one type of D-optimal design provides analytical formula for a class of compound optimal designs, while its dual, the more traditional criterion, cannot. --Compound optimality,D-optimality,design efficiency,minimax optimality