p-value calculation for multi-stage additive tests

Multi-stage additive tests are commonly used in applications. Appropriate definition of its test decisions, however, turns out to be challenging. There are a number of existing methods for this purpose, mainly by combining p-values of individual tests using a conditional error probability function. Although these methods are flexible enough to use in most applications, their results depend on the conditional error probability function and selection of this function is often subjective. Motivated by a research problem regarding comparison of two survival hazard rate functions, in this paper, we suggest using an alternative and simpler definition of the overall p-value of a multi-stage additive testing procedure. By this definition, no conditional error probability function needs to be chosen, the entire testing procedure is easy to interpret, and the overall p-value has an explicit formula for a general multi-stage additive testing procedure.