Abstract: In clinical trials, asymmetric designs are often used to reflect prior preference of treatments based on factors other than efficacy, such as toxicity and cost. We consider the case where treatments have a linear order of prior preference, and derive likelihood-based invariant procedures which select the most preferred treatment among the equally most effective ones with a preassigned error probability for normal errors, when the prior preference is solely reflected through a set of hypotheses. Extensions are given for the case where different levels of error probabilities are preassigned to the hypotheses. Application to binomial or exponential data with random censoring is through large sample approximation.
Key words and phrases: Invariance, likelihood, selection.