Speaker
Description
Comparing the means of several experimental groups is an old and well known
problem in the statistical literature which arises in many application areas. In the
past decades, a large body of literature about the design of experiments for treatment
comparisons has flourished. However, the attention has been almost exclusively devoted
to estimation precision, and not to optimal testing. This paper develops a unified
approach for deriving optimal designs for testing the efficacy of several heterogeneous
treatments. Adopting the general framework of heteroscedastic treatment
groups, which also encompasses the general ANOVA set-up with heteroscedastic
errors, the design maximizing the power of the multivariateWald test of homogeneity
is derived. Specifically, this optimal design is a generalized Neyman allocation
involving only two experimental groups. Moreover, in order to account for the ordering
among the treatments, which can be of particular interest in many applications,
we obtained the constrained optimal design where the allocation proportions
reflects the effectiveness of the treatments. Although, in general, the treatments ordering
is a-priori unknown, the proposed allocations are locally optimal designs
that can be implemented via response-adaptive randomization procedures after suitable
smoothing techniques. The advantages of the proposed designs are illustrated
both theoretically and through several numerical examples including normal, binary,
Poisson and exponential data (with and without censoring). The comparisons with
other allocations suggested in the literature confirm that our proposals provide good
performance in terms of both statistical power and ethical demands.