Sequential Conditional Probability Ratio Tests for Normalized Test Statistic on Information Time

Sequential conditional probability ratio tests (SCPRTs) provide monitoring procedures with a unique property that a decision reached at early stopping is unlikely to be reversed should the trial continue to the planned end ( Xiong, X., 1995, Journal of the American Statistical Association90, 1463–1473; Tan, M., Xiong, X., and Kutner, M. H., 1998, Biometrics54, 682–695). It actually provides a probability statement of a conclusion reversal, should the proposed interim analysis plan be used. To broaden its scope of applications, in this article we develop the SCPRT in terms of Brownian motion, which is applicable to most clinical trials with various endpoints. In addition, we utilize the unique structure of the SCPRT to derive a class of adaptive sequential tests that retain the significance level and power in the presence of a nuisance parameter. We illustrate the proposed methods with examples in clinical trials.