A Calculus for Design of Two-Stage Adaptive Procedures

On efficient two-stage adaptive designs for clinical trials with sample size adjustment

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 ).

Understanding the FDA guidance on adaptive designs: historical, legal, and statistical perspectives

The recent Food and Drug Administration (FDA) guidance for industry on adaptive designs is perhaps one of the important undertakings by CDER/CBER Office of Biostatistics. Undoubtedly, adaptive designs may affect almost all phases of clinical development and impact nearly all aspects of clinical trial planning, execution and statistical inference. Thus, it is a significant accomplishment for the Office of Biostatistics to develop this well-thought-out and all-encompassing guidance document. In this paper, we discuss some critical topical issues of adaptive designs with supporting methodological work from either existing literature, additional technical notes, or accompanying papers. In particular, we provide numerous sources of design, conduct, analysis, and interpretation bias that arise from statistical procedures. We illustrate, as a result, and caution that substantial research is necessary for many adaptive designs to meet required scientific standards prior to their applications in clinical trials.

Flexible design of two-stage adaptive procedures for phase III clinical trials

The recent popularity of two-stage adaptive designs has fueled a number of proposals for their use in phase III clinical trials. Many of these designs assign certain restrictive functional forms to the design elements of stage 2, such as sample size, critical value and conditional power functions. We propose a more flexible method of design without imposing any particular functional forms on these design elements. Our methodology permits specification of a design based on either conditional or unconditional characteristics, and allows accommodation of sample size limit. Furthermore, we show how to compute the P value, confidence interval and a reasonable point estimate for any design that can be placed under the proposed framework.

Decision-Theoretic Views on Simultaneous Testing of Superiority and Noninferiority

In a simultaneous testing of noninferiority and superiority in clinical trials, there is no multiplicity penalty. Ng (2003), however, argues that even though there is no inflation of the Type I error rate, this type of simultaneous testing is problematic because it may lead to loss of power in the subsequent confirmatory trial. And he recommends to conduct only one test chosen on the basis of the sponsor's preliminary assessment. We view the question of whether one should simultaneously test for noninferiority and superiority from a decision-theoretic view point. We develop the loss function approach implicit in Ng's research and compare his recommendation to simultaneous testing procedures indexed by a variety of design parameters. We find that the simultaneous testing procedure generally provides smaller loss than Ng's method, except when the prior distribution allocates a large probability to equivalence of the two treatments.

How practical are adaptive designs likely to be for confirmatory trials?

This is a discussion of the following papers appearing in this special issue on adaptive designs: 'Confirmatory Seamless Phase II/III Clinical trials with Hypotheses Selection at Interim: General Concepts' by Frank Bretz, Heinz Schmidli, Franz König, Amy Racine and Willi Maurer; and 'Confirmatory Seamless Phase II/III Clinical Trials with Hypotheses Selection at Interim: Applications and Practical Considerations' by Heinz Schmidli, Frank Bretz, Amy Racine and Willi Maurer.

An Adaptive Two-stage Design with Treatment Selection Using the Conditional Error Function Approach

As an approach to combining the phase II dose finding trial and phase III pivotal trials, we propose a two-stage adaptive design that selects the best among several treatments in the first stage and tests significance of the selected treatment in the second stage. The approach controls the type I error defined as the probability of selecting a treatment and claiming its significance when the selected treatment is indifferent from placebo, as considered in Bischoff and Miller (2005). Our approach uses the conditional error function and allows determining the conditional type I error function for the second stage based on information observed at the first stage in a similar way to that for an ordinary adaptive design without treatment selection. We examine properties such as expected sample size and stage-2 power of this design with a given type I error and a maximum stage-2 sample size under different hypothesis configurations. We also propose a method to find the optimal conditional error function of a simple parametric form to improve the performance of the design and have derived optimal designs under some hypothesis configurations. Application of this approach is illustrated by a hypothetical example.

A framework for two-stage adaptive procedures to simultaneously test non-inferiority and superiority

In clinical trials it is often desirable to test for non-inferiority and for superiority simultaneously. For such a situation a two-stage adaptive procedure may be advantageous to a conventional single-stage procedure because a two-stage adaptive procedure allows the design of stage II, including the main study objective and sample size, to depend on the outcome of stage I. We propose a framework for designing two-stage adaptive procedures with a possible switch of the primary study objectives at the end of stage I between non-inferiority and superiority. The framework permits control of the type I error rate and specification of the unconditional powers and maximum sample size for each of non-inferiority and superiority objectives. The actions at the end of stage I are predetermined as functions of the stage I observations, thus making specification of the unconditional powers possible. Based on the results at the end of stage I, the primary objective for stage II is chosen, and sample sizes and critical values for stage II are determined.