Commentary on “Applying CHW method to 2-in-1 design: gain or lose”

Conditional bias adjusted estimator of treatment effect in 2-in-1 adaptive design

For implementation of adaptive design, the adjustment of bias in treatment effect estimation becomes an increasingly important topic in recent years. While adaptive design literature traditionally focuses on the control of type I error rate and the adjustment of overall unconditional bias, the research on adjusting conditional bias has been limited. This paper proposes a conditional bias adjustment estimator of treatment effect under the context of 2-in-1 adaptive design and aims to provide a comprehensive investigation on their statistical properties including bias, mean squared error and coverage probability of confidence intervals. It demonstrated that conditional bias adjusted estimators greatly reduce the conditional bias and have similarly negligible unconditional bias compared with mean and median (unconditional) unbiased estimators. In addition, the test statistics is constructed based on the conditional bias adjustment estimators and compared with the naive unadjusted test.

Family-wise type I error rate control for an extended 2-in-1 design with graphical approach in oncology drug development

Nowadays, in oncology drug development, when an experimental treatment shows a promising anti-tumor effect in Phase I efficacy expansion, a Phase III pivotal trial may be launched directly. To mitigate the risk of skipping the traditional randomized Phase II proof of concept (POC) study, the 2-in-1 design was proposed by Chen et al. (2018). This design has gained great research and application interest since its publication and been extended in many ways. The original 2-in-1 design controls family-wise type I error rate (FWER) for one hypothesis in Phase II part and one hypothesis in Phase III part. However, in practice, for a stand-alone Phase III study usually there are multiple hypotheses with group sequential interim analyses and the multiplicity is controlled by the graphical approach. It is desirable that these features of the Phase III design are retained when 2-in-1 design is considered. The multiplicity control for a 2-in-1 design with multiple hypotheses in Phase III has been addressed mainly by the Bonferroni approach in the literature. For the more powerful graphical approach, while Jin and Zhang (2021) discussed the FWER control for a special 2-in-1 design, in which Phase II and Phase III have exactly the same hypotheses, the FWER control for a more common 2-in-1 design (i.e., one hypothesis in Phase II and multiple hypotheses in Phase III) is yet investigated. This paper provides the analytical conditions under which FWER is controlled with the graphical approach in such a 2-in-1 design. It also provides the numeric explorations of FWER control for such design with group sequential interim analyses in Phase III, as a direct Phase III design normally would have. As a result, our work helps lower the hurdle of the application of the 2-in-1 design and pave the way for its wider application.

Estimation of treatment effect in 2-in-1 adaptive design and some of its extensions

The 2-in-1 adaptive design allows seamless expansion of an ongoing Phase II trial into a Phase III trial to expedite a drug development program. Since its publication, it has generated a lot of interest. So far, most of the related research focused on type I error control. Similar to most adaptive designs, 2-in-1 design could also pose a great challenge on estimation of treatment effect due to the data-driven adaptation. In addition, the use of intermediate endpoint for interim adaptive decision-making is a less well-studied field. In this paper, we investigate the bias and variances in estimation for 2-in-1 design and some of its extensions, and propose some bias-adjusted estimators for 2-in-1 design. The properties of the proposed estimators are further studied theoretically and/or numerically, so as to provide guidance on how to interpret the estimated treatment effect of 2-in-1 design.

Sample size re-estimation for pivotal clinical trials

It is well known that if the hypothesis test is left unchanged, the Type I error rate may be inflated for sample size re-estimation (SSR) designs. To address this issue, three main approaches have been proposed in the literature: combination test, conditional error and conventional test with sample size increase in the allowable region (AR) only. These three seemingly different approaches are in fact connected. For each combination test, there is a corresponding conditional error function and AR. Designing adaptation rules in this AR with conventional test guarantees the Type I error rate control but at the same time always leads to smaller power comparing to the corresponding combination test (or conditional error) approach. In cases where conventional test is still preferable, step-wise type adaptation rules that do not fully reside in the AR can be alternatively considered. We believe controversies in the statistical community on the efficiency comparisons between group sequential (GS) and SSR design stem partially from the misalignment of performance metrics and conditional versus unconditional evaluations. We advocate summary metrics, such as median, variance or tail probabilities of the sample size in addition to expectation and personalizing efficiency definition for each trial sponsor. Conditional metrics by favorable, promising and unfavorable zones of the interim results provide additional insights and should always be incorporated into the decision-making process.

The extension of 2-in-1 adaptive phase 2/3 designs and its application in oncology clinical trials

A 2-in-1 adaptive Phase 2/3 design was proposed by Chen et al. The 2-in-1 design improves the overall clinical trial development efficiency by 1) building in an early and informative decision-making; 2) allowing the flexible endpoint-usage at the decision and the final analysis; 3) potential registration path forward in either Phase 2 or Phase 3. The original paper illustrates a general idea. In this paper, we extend this design to fit more common scenarios. The type I error control in the extended 2-in-1 adaptive Phase 2/3 designs is investigated in both simulation and theoretical ways.