Three p-value consistent procedures for multiple comparisons with a control in direction-mixed families

In clinical studies, it is common to compare several treatments with a control. In such cases, the most popular statistical technique is the Dunnett procedure. However, the Dunnett procedure is designed to deal with particular families of inferences in which all hypotheses are either one sided or two sided. Recently, based on the minimization of average simultaneous confidence interval width, a single-step procedure was derived to handle more general inferential families that contained a mixture of one- and two-sided inferences. But that single-step procedure is unable to guarantee the condition of p-value consistency which means that when a hypothesis with a certain p-value is rejected, all other hypotheses with smaller p-values are also rejected. In this paper, we present a single-step procedure and two stepwise procedures which are p-value consistent. The two proposed stepwise procedures provide more powerful testing methods when compared with single-step procedures. The extent of their superiority is demonstrated with a simulation study of average power. Selected critical values are tabulated for the implementation of the three proposed procedures. Additional simulation studies provide evidence that the new stepwise procedures are robust to moderate changes in the underlying probability distributions, and the proposed step-up procedure is uniformly more powerful than the resampling-based Hochberg step-up approach in all considered distribution models. Finally, we provide a practical example with sample data extracted from a medical experiment.