P-VALUES AFTER REPEATED SIGNIFICANCE TESTING - A SIMPLE APPROXIMATIONMETHOD

The P-value after a repeated significance test is a useful measure of the strength of evidence against the null hypothesis. Its computation, however, requires a computer-intensive numerical integration method. The P-value is not conceptually straightforward, because it depends on how the sample space is ordered, which can be arbitrary. We look at t wo orderings of the sample space, one proposed by Tsiatis et al. and t he other by Rosner and Tsiatis, and Chang. Although studies have shown that the latter ordering gives more reasonable confidence intervals t han the former, the former gives a conservative and therefore more rea sonable P-value. Both, however, should yield an identical P-value in m ost applications. In this paper we present a simple method of approxim ating P-values. We provide tables to implement the method for two to t en stages with alpha = 0.1, 0.05 and 0.01 for the Pocock and O'Brien-F leming procedures. The proposed method can be applied to both ordering s.