Stepwise confidence intervals without multiplicity adjustment for dose-response and toxicity studies

Nor all simultaneous inferences need multiplicity adjustment. If the sequen ce of individual inferences is predefined, and failure to achieve the desir ed inference at any step renders subsequent inferences unnecessary, then mu ltiplicity adjustment is not needed. This can be justified using the closed testing principle to test appropriate hypotheses that are nested in sequen ce, starting with the most restrictive one. But what hypotheses are appropr iate may not be obvious in some problems. We give a fundamentally different , confidence set-based justification by partitioning the parameter space na turally and using the principle that exactly one member of the partition co ntains the true parameter. In dose-response studies designed to show superi ority of treatments over a placebo (negative control) or a drug known to be efficacious (active control), the confidence set approach generates method s with meaningful guarantee against incorrect decision, whereas previous ap plications of the closed testing approach have not always done so. Applicat ion of the confidence set approach to toxicity studies designed to show equ ivalence of treated groups with a placebo is also given.