In this article, universally optimal multivariate crossover designs are
studied. The multiple response crossover design is motivated by a 3×3
crossover setup, where the effect of 3 doses of an oral drug are studied on
gene expressions related to mucosal inflammation. Subjects are assigned to
three treatment sequences and response measurements on 5 different gene
expressions are taken from each subject in each of the 3 time periods. To
model multiple or g responses, where g>1, in a crossover setup, a
multivariate fixed effect model with both direct and carryover treatment
effects is considered. It is assumed that there are non zero within response
correlations, while between response correlations are taken to be zero. The
information matrix corresponding to the direct effects is obtained and some
results are studied. The information matrix in the multivariate case is shown
to differ from the univariate case, particularly in the completely symmetric
property. For the g>1 case, with t treatments and p periods, for p=t≥3, the design represented by a Type I orthogonal array of strength 2
is proved to be universally optimal over the class of binary designs, for the
direct treatment effects.Comment: 17 Pages, 2 Figure