Exact calculations for the repeated many-one test

摘要

When group sequential methods are applied to compare several treatments with a control, multiplicity from the repeated significance testing as well as from the multiple comparison has to be accounted for properly to control the overall type I error. This often involves a multidimensional integration procedure to compute group sequential boundaries. Liu (1996, J. Appl. Statist. 23 (4)) proposed some group sequential procedures for comparing several treatments with a control. The group sequential boundaries needed to apply these procedures were estimated by simulation to two decimal places for specified α-levels. In this paper,we describe an algorithm that allows efficient calculation of these boundaries by combining a newly developed software in Genz and Keister (1996, J. Comput Appl. Math 71) and the dynamic programming technique described, for example, in Cormen et al. (1990, Introduction to Algorithms, MIT Press, Cambridge). The algorithm is then implemented to successfully solve the computation problem which is previously stated by Liu (1996) as "no simple exact calculation method is available".