FRIDAY, October 13, 2006
Time: 1:30 PM
Constant Hall 1043

Title: Confounded Cross-Over Designs for Factorial Experiments Tumor

Sudhir Gupta
Division of Statistics
Northern Illinois University

Cross-over designs are popular especially in the pharmaceutical industry, though they are also useful in psychological experiments, veterinary research, and industrial experiments, among others. In a cross-over trial, a subject receives a sequence of treatments over time, called periods. The most popular is the two-treatment, two-period design, called the AB/BA design. Cross-over designs with several treatments and several periods, including factorial treatments, are also used. In this paper we are concerned with cross-over designs with factorial treatments. With factorial treatments, a subject usually receives only a subset of the treatments to keep the number of periods to within reasonable limits. If each subject is viewed as a block, then in the terminology of block designs this means that subjects form incomplete blocks in a factorial cross-over design. Block contents for each subject are, then, to be chosen so that the cross-over design has high efficiency for factorial contrasts of interest. Fletcher and John (1985) defined factorial structure in cross-over designs along the lines of the usual block designs. They showed that the generalized cyclic designs of John (1973) provide a useful class of cross-over designs having factorial structure. Often some higher order interactions can be safely assumed to be negligible or absent on the basis of prior information. Thus, as is the case in block designs, efficiency of estimation of the contrasts of interest can be improved by completely confounding such higher order interactions in a cross-over design. A method based on the classical method of confounding is discussed in this paper. This method was also previously discussed by Shing and Hinkelmann (1992). However, our approach is simple, and can also be extended to extra-period designs. The question of reducing the number of subjects is also discussed.