Multiple comparisons with a control in families with both one-sided and two-sided hypotheses

Comparing several treatments with a control is a common objective of clinical studies. However, existing procedures mainly deal with particular families of inferences in which all hypotheses are either one- or two-sided. In this article, we seek to develop a procedure which copes with a more general testing environment in which the family of inferences is composed of a mixture of one- and two-sided hypotheses. The proposed procedure provides a more flexible and powerful tool than the existing method. The superiority of this method is also substantiated by a simulation study of average power. Selected critical values are tabulated for the implementation of the proposed procedure. Finally, we provide an illustrative example with sample data extracted from a medical experiment.