Extension of one-sided test to multiple treatment trials

In a two-treatment clinical trial, a one-sided test is sometimes used in reaching a decision. Usually we are interested in doing a one-sided test because of the existence of an unequal preference between the two treatments. When a standard control is just as good or better than the new experimental treatment (which has more toxicity or cost), we will stay with the standard control. In this paper, we extend the concept of a one-sided test to the multiple treatment trial where three or more treatments are involved. We assume that there is an order of strictly decreasing preference among the treatments. We propose two multiple-step decision procedures that are similar to the bubble sorting algorithm and will guarantee a high probability of finally selecting the correct treatment. We also provide methods to calculate the sample size required to detect a specific difference. The derivation is based on normal data, and the extension to binomial or exponential data with random censoring is through large sample approximation.