Comparison of four sequential methods allowing for early stopping of comparative clinical trials

Abstract

Phase III trials aim to assess whether a new treatment has superior efficacy than a standard treatment. Sequential methods, such as the sequential probability ratio test (SPRT), the triangular test (TT) and so-called one-parameter boundaries (OPB), now allow early stopping of such trials, both in the case of efficacy (alternative hypothesis; H(1)) and in the case of lack of efficacy (null hypothesis; H(0)). We compared the statistical properties of the SPRT and the TT, and of OPB with Pocock (OPB(Delta=0.5)) and O'Brien and Fleming (OPB(Delta=0)) type boundaries, in the setting of one-sided comparative trials with normal response. We studied the type I error (alpha), power (1-beta), average sample number (ASN) and 90th percentile (P90) of the number of patients required to reach a conclusion using simulations. The four tests were also compared with the corresponding single-stage design (SSD). All sequential tests display alpha and 1-beta close to nominal values and, as compared with SSD, allow important decreases in ASN: for example, -48%, -42%, -40% and -31% under H(0) and H(1) for SPRT, TT, OPB(Delta=0.5) and OPB(Delta=0) respectively. For situations between H(0) and H(1), ASNs of all sequential tests were still smaller than the sample size required by SSD, with the TT displaying the largest decrease (-25%). The P90s of the TT and OPB(Delta=0) under H(0) and H(1) were smaller than the P90s of the SPRT and OPB(Delta=0.5), which were similar to the sample size required by SSD. If all sequential tests display approximately similar features, the TT is the most appealing regarding decreases in sample size, especially for situations between H(0) and H(1).