Statistics and Data Science Seminar
Prof. John Morgan
Virginia Tech
Optimal Design for Experiments with a Control
Abstract: Standard optimality arguments for designed experiments rest on the
assumption that all treatments are of equal interest. A notable
exception is found in the ``test treatment versus control" (TvC)
literature, where the control is allocated special status.
Optimality work there has focused on all pairwise comparisons with
the control, making no explicit account of how well test treatments
are compared to one another. If the latter are also of consequence,
it would be preferable to choose a design reflecting the relative
importance placed on contrasts involving the control to that placed
on contrasts of test treatments only. This talk develops the
\emph{weighted} optimality approach for situations such as this, so
that design selection may better reflect experimenter goals.
When evaluating designs for comparing $v$ treatments, the basic idea
is to assign weights $w_1,\ldots,w_v$ ($\sum_iw_i=1$) to account for
differential treatment interest. In experiments with a control, and
equal interest in the test treatments, this means weight $w_1$ is
assigned to the control, and weight $w_2=(1-w_1)/(v-1)$ to each test
treatment. These weights enter the evaluation through optimality
measures, leading to, for example, weighted versions of the popular
A, E, and MV measures of design efficacy. Families of
weighted-optimal designs are identified under these criteria.
Compared to their unweighted versions, it is shown that they less
frequently agree on the best design. The classical approach in TvC
design is shown to be a limiting case of the theory developed here.
Friday April 23, 2010 at 4:15 PM in SEO 636