Abstract
Group sequential hypothesis testing is now widely used to analyze prospective data. If Monte Carlo simulation is used to construct the signaling threshold, the challenge is how to manage the type I error probability for each one of the multiple tests without losing control on the overall significance level. This paper introduces a valid method for a true management of the alpha spending at each one of a sequence of Monte Carlo tests. The method also enables the use of a sequential simulation strategy for each Monte Carlo test, which is useful for saving computational execution time. Thus, the proposed procedure allows for sequential Monte Carlo test in sequential analysis, and this is the reason that it is called 'composite sequential' test. An upper bound for the potential power losses from the proposed method is deduced. The composite sequential design is illustrated through an application for post-market vaccine safety surveillance data.