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This paper is to extend Mehta and Pocock (2011) to provide a way in doing sample size increase in survival trials. Sample space is divided by observed test statistic at interim into three zones: un...

High placebo response has been a major source of bias and is difficult to deal with in many central nervous system (CNS) clinical trials. This bias has led to a high failure rate in mood disorder trials even with known effective drugs. For cancer trials, the traditional parallel group design biases the inference on the maintenance effect of the new drug with the traditional time-to-treatment failure analysis. To minimize bias, we propose a doubly randomized delayed-start design for clinical trials with enrichment. The design consists of two periods. In the first period, patients can be randomized to receive several doses of a new drug or a control. In the second period, control patients of the first period of an enriched population can be rerandomized to receive the same or fewer doses of the new drug or to continue on the control. Depending on the clinical needs, different randomization ratios can be applied to the two periods. The essential feature is that the design is naturally adaptive because of the randomization for the second period. As a result, other aspects of the second period, such as the sample size, can be modified adaptively when an interim analysis is set up for the first period. At the end of the trial, response data from both randomizations are combined in an integrated analysis. Because of the enrichment in the second period, the design increases the probability of trial success and, in addition, reduces the required sample size. Thus, for clinical development, the design offers greater efficiency.

Group sequential designs are rarely used for clinical trials with substantial over running due to fast enrollment or long duration of treatment and follow-up. Traditionally, such trials rely on fixed sample size designs. Recently, various two-stage adaptive designs have been introduced to allow sample size adjustment to increase statistical power or avoid unnecessarily large trials. However, these adaptive designs can be seriously inefficient. To address this infamous problem, we propose a likelihood-based two-stage adaptive design where sample size adjustment is derived from a pseudo group sequential design using cumulative conditional power. We show through numerical examples that this design cannot be improved by group sequential designs. In addition, the approach may uniformly improve any existing two-stage adaptive designs with sample size adjustment. For statistical inference, we provide methods for sequential p-values and confidence intervals, as well as median unbiased and minimum variance unbiased estimates. We show that the claim of inefficiency of adaptive designs by Tsiatis and Mehta ( 2003 ) is logically flawed, and thereby provide a strong defense of Cui et al. ( 1999 ).