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In phase II clinical trials, patients are recruited sequentially and consequently the time required to complete the clinical trial will become long if the accrual rate is low. To speed up the drug development process and account for ethical issues, stochastically and non-stochastically curtailed two-stage designs have been proposed in single-arm phase II clinical trials. More recently, randomized phase II clinical trials are being increasingly recommended to avoid biased evaluation of the treatment effect when compared with a historical control. The current patient population and the historical one may be quite heterogeneous. Moreover, it is impossible to randomly assign patients for treatments. Consequently, various two-stage designs have been presented for comparing two arms. Since the sample size required in a randomized phase II trial is usually larger than that required in a single-arm phase II trial, we introduce the concept of curtailed sampling procedure to develop curtailed two-stage design for two-armed, randomized phase II clinical trials. The proposed design does not require pairwise patient response comparison, yet it allows a trial to be stopped early as soon as the difference in therapeutic effect of the experimental therapy and the standard at the end of a trial is foreknown., (Copyright © 2017 Taylor & Francis Group, LLC.)

When phase I clinical trials were found to be unable to precisely estimate the frequency of toxicity, Brayan and Day proposed incorporating toxicity considerations into two-stage designs in phase II clinical trials. Conaway and Petroni further pointed out that it is important to evaluate the clinical activity and safety simultaneously in studying cancer treatments with more toxic chemotherapies in a phase II clinical trial. Therefore, they developed multi-stage designs with two dependent binary endpoints. However, the usual sample sizes in phase II trials make these designs difficult to control the type I error rate at a desired level over the entire null region and still have sufficient power against reasonable alternatives. Therefore, the curtailed sampling procedure summarized by Phatak and Bhatt will be applied to the two-stage designs with two dependent binary endpoints in this paper to reduce sample sizes and speed up the development process for drugs., (Copyright © 2011 John Wiley & Sons, Ltd.)

When the accrual rate is low and the treatment period is long, a long observational period is required before information concerning the primary end point, such as binary response, becomes available in the study. Simon's two-stage designs are often employed in Phase II clinical trials to avoid giving patient an ineffective drug. Thus, if the new drug is ineffective then this design would certainly accelerate the process of drug discovery and development. However, for a promising new drug this design may still require a long observational period. Therefore, when drug safety is not a primary concern, this paper proposes curtailed two-stage designs to shorten the drug development process as soon as the treatment either shows lack of efficacy or is very effective. The proposed design is superior to Simon's two-stage designs in terms of savings in expected sample size and is much easier to implement in practice than stochastically curtailed Simon's designs.

Generally, a two-stage design is employed in Phase II clinical trials to avoid giving patients an ineffective drug. If the number of patients with significant improvement, which is a binomial response, is greater than a pre-specified value at the first stage, then another binomial response at the second stage is also observed. This paper considers interval estimation of the response probability when the second stage is allowed to continue. Two asymptotic interval estimators, Wald and score, as well as two exact interval estimators, Clopper-Pearson and Sterne, are constructed according to the two binomial responses from this two-stage design, where the binomial response at the first stage follows a truncated binomial distribution. The mean actual coverage probability and expected interval width are employed to evaluate the performance of these interval estimators. According to the comparison results, the score interval is recommended for both Simon's optimal and minimax designs., (Copyright (c) 2007 John Wiley & Sons, Ltd.)