Continuous and group sequential conditional probability ratio tests for phase II clinical trials.

We present continuous and group sequential designs for phase II clinical trials based on the sequential conditional probability ratio test (SCPRT). The SCPRT is derived from a conditional likelihood ratio, where the conditioning is on what the corresponding (reference) fixed sample size test (RFSST) would achieve. In other words, we obtain the sequential design by controlling the maximum probability that the SCPRT does not agree with the RFSST. We shall discuss the difference between SCPRT and stochastic curtailment which also uses the concept of conditional distribution. We show that the power function of the SCPRT is virtually the same as that of the RFSST and its average sample numbers (ASNs) are close to those of Wald's sequential probability ratio test (SPRT), whereas its maximum sample size is no greater than that of the RFSST. Thus the SCPRT has all the desirable properties, such as allowing the use of the RFSST at the last analysis, of the Fleming procedure for phase II trials. The SCPRT, however, preserves the power function of the RFSST better and gives us the option for continuous monitoring. Our recommendation, therefore, is to use a group SCPRT boundary (for interim analyses performed as scheduled) embedded in a continuous SCPRT boundary (for unplanned interim analyses and analyses at times based on data trends). We provide as well a bias-adjusted estimator of the success rate after sequential stopping. We illustrate the method with several examples. The method applies to any single-arm clinical trial with binary endpoints, such as the classic paired design.