Marcus-Talpaz simultaneous lower confidence bounds for contrasts between treatment and control means

We consider comparisons of several treatments with a common control when it is believed that the treatments are at least as effective as the control. In this setting, which is called the tree order, the classical work by Dunnett (1955) is well known. Dunnett proposed a multiple-comparison procedure for treatment means vs. the control mean, which could be inverted to obtain simultaneous lower confidence bounds (SLCBs). Under the same setting, Marcus and Talpaz (1992) proposed a test of homogeneity and SLCBs for contrasts of means. These SLCBs, however, assumed that the contrast coefficients were tree ordered but that the means were unordered. Using the Marcus-Talpaz test of homogeneity, we develop another set of SLCBs, which does utilize the fact that the means are tree ordered and has the desired coverage probability. Using Monte Carlo simulations, we compare Dunnett's SLCBs and the newly developed SLCBs for equal sample sizes. We examine the two sets of SLCBs in terms of their abilities to detect true mean differences and their relative efficiencies. The results reveal that Dunnett's SLCBs perform better in the interior of the tree-order cone. When the entire cone, including the boundary, is considered, the new SLCBs perform more favorably. A numerical example is given.