Abstract: Two-stage tests may be defined in terms of a combination function for the p-values of the separate stages, or alternatively by specifying a conditional error function, i.e., the conditional probability for an erroneous rejection given the first stage. Examples have been published suggesting that these two approaches are essentially equivalent. We provide a formal link between them that yields a general framework for two-stage tests. Our viewpoint leads to an overall p-value notion that covers different previously proposed concepts, and it allows an easy construction of new two-stage tests. One particular test is further characterized.
Key words and phrases: Adaptive design, combination test, conditional error function, interim analysis, overall p-value, two-stage test.