For clinical comparison of treatment effects, the statistical method of Multiple Comparisons with the Best (MCB), developed by Hsu (1981, 1984a,b) and coworkers, provides the sharpest separation of the good treatments from the bad treatments among all existing methods. We propose to study nonparametric and discrete distributions extensions of MCB, and to add these extensions to the RS-MCB computer package. They will yield immediate benefits over X2 and X2 type rank methods in analyses of tumor response rates and cell bioassay data, for example, as demonstrated in Section D of the proposal. A new frontier in statistical treatment comparisons was recently created with the concept of Comparison with the Sample Best Treatment (CSB) in Kim, Hsu, and Stefansson (1985), in which it is shown that, for the usual balanced ANOVA model, if the sample best treatment is inferred to be the true best treatment each time the two-sample size-Alpha t-test between the sample best and sample second best treatments rejects, then the error rate is controlled at Alpha. The simplicity and the strength of this result sould make it most useful in practice. We propose to extend CSB to unbalanced designs. An important aspect of designing a clinical trial is the choice of sample size. We have developed a numerical algorithm for computing power charts of CSB statistical inference, given any plausible separation of treatment effects by the user. We propose to implement this algorithm on the computer, including an interface with SAS/GRAPH which will allow the user instantaneous interactive access to the power charts on all the standard graphical devices.
