Impact of a mis-specification of the response rate under standard treatment in sequential clinical trials

Phase III trials are aimed at assessing whether new treatments have superior efficacy than standards. Sequential methods, such as the single triangular test (STT) and the double triangular test (DTT), allow for early stopping of such trials. They use stopping boundaries which depend, for a binary endpoint, on pi(0) and pi(1) (response rates under standard and new treatment, respectively) and alpha and beta (type I and II errors, respectively). Thus, a wrong estimation of pi(0) at planning phase might have an influence on their statistical properties. We assessed the extent of this influence by simulations regarding alpha, 1--beta, and average sample number (ASN) and compared the two methods with the one-sided and two-sided single-stage designs (SSD). There was no influence on alpha for any test and the power achieved by the one-sided or two-sided SSD was moderately affected by a wrong estimation of pi(0). However, important drifts (whose magnitude depended on chosen design) were observed for sequential methods concerning power and ASN in case of moderate under- or overestimation of pi(0) (+/-20% compared with its 'true' value). For example, when 'true' values of pi(0) and pi(1) are 0.30 and 0.40, respectively, using design values of 0.10 and 0.20, the power is 0.57 and 0.50 for the STT and DTT, respectively, instead of 0.95. When 'true' values of pi(0) and pi(1) are 0.10 and 0.20, respectively, using design values of 0.30 and 0.40, the ASN under H(0) is 1,309 and 2,019 for the STT and DTT, respectively, instead of 392 and 601, respectively, using the right design. Using sequential methods in comparative clinical trials with binary responses requires a precise knowledge of the response rate under standard treatment to avoid losses in power or inappropriate increases in sample size.