Stepwise Confidence Intervals without Multiplicity Adjustment for Dose—Response and Toxicity Studies

Not all simultaneous inferences need multiplicity adjustment. If the sequence of individual inferences is predefined, and failure to achieve the desired inference at any step renders subsequent inferences unnecessary, then multiplicity adjustment is not needed. This can be justified using the closed testing principle to test appropriate hypotheses that are nested in sequence, starting with the most restrictive one. But what hypotheses are appropriate may not be obvious in some problems. We give a fundamentally different, confidence set–based justification by partitioning the parameter space naturally and using the principle that exactly one member of the partition contains the true parameter. In dose–response studies designed to show superiority of treatments over a placebo (negative control) or a drug known to be efficacious (active control), the confidence set approach generates methods with meaningful guarantee against incorrect decision, whereas previous applications of the closed testing approach have not always done so. Application of the confidence set approach to toxicity studies designed to show equivalence of treated groups with a placebo is also given.