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Bai X, Deng Q, Li W. Conditional bias adjusted estimator of treatment effect in 2-in-1 adaptive design. J Biopharm Stat 2024:1-20. [PMID: 38841980 DOI: 10.1080/10543406.2024.2359147] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 05/12/2024] [Indexed: 06/07/2024]
Abstract
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.
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Affiliation(s)
- Xiaofei Bai
- Biometrics, Servier Bio-Innovation LLC, Boston, Massachusetts, USA
| | - Qiqi Deng
- Biostatistics, Moderna Inc, Cambridge, Massachusetts, USA
| | - Wen Li
- Vaccine Clinical Research & Development, Pfizer, Inc, Collegeville, Pennsylvania, USA
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2
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Chen C, Sun L, Zhang X. A promising biomarker adaptive Phase 2/3 design - Explained and expanded. Contemp Clin Trials Commun 2023; 36:101229. [PMID: 38034840 PMCID: PMC10684793 DOI: 10.1016/j.conctc.2023.101229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Revised: 10/14/2023] [Accepted: 11/04/2023] [Indexed: 12/02/2023] Open
Abstract
This short communication concerns a biomarker adaptive Phase 2/3 design for new oncology drugs with an uncertain biomarker effect. Depending on the outcome of an interim analysis for adaptive decision, a Phase 2 study that starts in a biomarker enriched subpopulation may continue to the end without expansion to Phase 3, expand to Phase 3 in the same population or expand to Phase 3 in a broader population. Each path can enjoy full alpha for hypothesis testing without inflating the overall Type I error.
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Affiliation(s)
- Cong Chen
- Biostatistics and Research Decision Sciences, Merck & Co., Inc., Rahway, NJ 07065, USA
| | - Linda Sun
- Biostatistics and Research Decision Sciences, Merck & Co., Inc., Rahway, NJ 07065, USA
| | - Xuekui Zhang
- Department of Mathematics and Statistics, University of Victoria, Canada
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Duputel B, Stallard N, Montestruc F, Zohar S, Ursino M. Using dichotomized survival data to construct a prior distribution for a Bayesian seamless Phase II/III clinical trial. Stat Methods Med Res 2023; 32:963-977. [PMID: 36919403 PMCID: PMC10521165 DOI: 10.1177/09622802231160554] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/16/2023]
Abstract
Master protocol designs allow for simultaneous comparison of multiple treatments or disease subgroups. Master protocols can also be designed as seamless studies, in which two or more clinical phases are considered within the same trial. They can be divided into two categories: operationally seamless, in which the two phases are separated into two independent studies, and inferentially seamless, in which the interim analysis is considered an adaptation of the study. Bayesian designs are scarcely studied. Our aim is to propose and compare Bayesian operationally seamless Phase II/III designs using a binary endpoint for the first stage and a time-to-event endpoint for the second stage. At the end of Phase II, arm selection is based on posterior (futility) and predictive (selection) probabilities. The results of the first phase are then incorporated into prior distributions of a time-to-event model. Simulation studies showed that Bayesian operationally seamless designs can approach the inferentially seamless counterpart, allowing for an increasing simulated power with respect to the operationally frequentist design.
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Affiliation(s)
- Benjamin Duputel
- Universitè Paris Citè, Sorbonne Université, Inserm, Centre de Recherche des Cordeliers, Paris, France
- Inria, HeKA, Paris, France
- eXYSTAT, Malakoff, France
| | - Nigel Stallard
- Warwick Clinical Trials Unit, Warwick Medical School, University of Warwick, Coventry, UK
| | | | - Sarah Zohar
- Universitè Paris Citè, Sorbonne Université, Inserm, Centre de Recherche des Cordeliers, Paris, France
- Inria, HeKA, Paris, France
| | - Moreno Ursino
- Universitè Paris Citè, Sorbonne Université, Inserm, Centre de Recherche des Cordeliers, Paris, France
- Inria, HeKA, Paris, France
- Unit of Clinical Epidemiology, Assistance Publique-Hôpitaux de Paris, CHU Robert Debrè, Paris, France
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Zhang X, Jia H, Xing L, Chen C. Application of group sequential methods to the 2-in-1 design and its extensions for interim monitoring. Stat Biopharm Res 2023. [DOI: 10.1080/19466315.2023.2197402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/01/2023]
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5
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Bai X, Deng Q. Incorporating Intermediate Endpoint in Two-stage Design Decision Making. Stat Biopharm Res 2022. [DOI: 10.1080/19466315.2022.2108134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Li W, Zhou H, Jia C, Sun L. Family-wise type I error rate control for an extended 2-in-1 design with graphical approach in oncology drug development. Contemp Clin Trials 2022; 119:106846. [PMID: 35803494 DOI: 10.1016/j.cct.2022.106846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Revised: 05/27/2022] [Accepted: 07/02/2022] [Indexed: 11/03/2022]
Abstract
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.
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Affiliation(s)
- Wen Li
- Vaccine Clinical Research & Development, Pfizer, Inc., Collegeville, PA 19426, USA
| | - Heng Zhou
- Biostatistics and Research Decision Sciences, Merck & Co., Inc., Rahway, NJ 07065, USA.
| | - Calvin Jia
- Biostatistics and Research Decision Sciences, Merck & Co., Inc., Rahway, NJ 07065, USA
| | - Linda Sun
- Biostatistics and Research Decision Sciences, Merck & Co., Inc., Rahway, NJ 07065, USA
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Li Q, Lin J, Liu M, Wu L, Liu Y. Using Surrogate Endpoints in Adaptive Designs with Delayed Treatment Effect. Stat Biopharm Res 2021. [DOI: 10.1080/19466315.2021.1938203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Qing Li
- Takeda Pharmaceuticals, Cambridge, MA
| | | | | | - Liwen Wu
- Department of Biostatistics, University of Pittsburgh, Pittsburgh, PA
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Li W, Bai X, Deng Q, Liu F, Chen C. Estimation of treatment effect in 2-in-1 adaptive design and some of its extensions. Stat Med 2021; 40:2556-2577. [PMID: 33723865 DOI: 10.1002/sim.8917] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Revised: 01/26/2021] [Accepted: 02/03/2021] [Indexed: 11/06/2022]
Abstract
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.
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Affiliation(s)
- Wen Li
- Biostatistics and Research Decision Sciences, MRL, Merck & Co., Inc, Kenilworth, New Jersey, USA
| | - Xiaofei Bai
- Biostatistics and Data Science, Boehringer Ingelheim Pharmaceuticals Inc, Ridgefield, Connecticut, USA
| | - Qiqi Deng
- Biostatistics and Data Science, Boehringer Ingelheim Pharmaceuticals Inc, Ridgefield, Connecticut, USA
| | - Fang Liu
- Biostatistics and Research Decision Sciences, MRL, Merck & Co., Inc, Kenilworth, New Jersey, USA
| | - Cong Chen
- Biostatistics and Research Decision Sciences, MRL, Merck & Co., Inc, Kenilworth, New Jersey, USA
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Li Q, Lin J, Lin Y. Adaptive design implementation in confirmatory trials: methods, practical considerations and case studies. Contemp Clin Trials 2020; 98:106096. [PMID: 32739496 DOI: 10.1016/j.cct.2020.106096] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Revised: 07/13/2020] [Accepted: 07/27/2020] [Indexed: 10/23/2022]
Abstract
The rapidly changing drug development landscapes have brought unique challenges to sponsors in designing clinical trials in a faster and more efficient way. With the ability to accelerate development timeline, reduce redundant sample size, and select the right dose and patient population during the clinical trial, adaptive designs help to increase the probability of success of clinical trials and eventually contribute to bringing the promising drugs to patients earlier and fulfilling their unmet medical needs. Although extensive adaptive design methods have been proposed in recent years, a comprehensive review of how to implement adaptive design in the practical confirmatory trials is still lacking. In this paper, we will review the evolving history of adaptive designs, updates of newly released regulatory guidance and emerging practical adaptive designs, including but not limited to sample size re-estimation, seamless design and surrogate endpoint used in the interim analysis. Furthermore, we will discuss the current practice of adaptive design implementation by demonstrating a complex oncology seamless phase 2/3 adaptive design case study. Through this example, we will introduce the critical roles of each cross disciplinary function, communication process and important documents when adaptive designs are implemented in real-world setting.
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Affiliation(s)
- Qing Li
- Takeda Pharmaceuticals, 300 Massachusetts Ave, Cambridge, MA 02139, United States of America.
| | - Jianchang Lin
- Takeda Pharmaceuticals, 300 Massachusetts Ave, Cambridge, MA 02139, United States of America
| | - Yunzhi Lin
- Sanofi, 50 Binney Street, Cambridge, MA 02142, United States of America
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