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Zang Y, Guo B, Qiu Y, Liu H, Opyrchal M, Lu X. Adaptive phase I-II clinical trial designs identifying optimal biological doses for targeted agents and immunotherapies. Clin Trials 2024; 21:298-307. [PMID: 38205644 PMCID: PMC11132954 DOI: 10.1177/17407745231220661] [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: 01/12/2024]
Abstract
Targeted agents and immunotherapies have revolutionized cancer treatment, offering promising options for various cancer types. Unlike traditional therapies the principle of "more is better" is not always applicable to these new therapies due to their unique biomedical mechanisms. As a result, various phase I-II clinical trial designs have been proposed to identify the optimal biological dose that maximizes the therapeutic effect of targeted therapies and immunotherapies by jointly monitoring both efficacy and toxicity outcomes. This review article examines several innovative phase I-II clinical trial designs that utilize accumulated efficacy and toxicity outcomes to adaptively determine doses for subsequent patients and identify the optimal biological dose, maximizing the overall therapeutic effect. Specifically, we highlight three categories of phase I-II designs: efficacy-driven, utility-based, and designs incorporating multiple efficacy endpoints. For each design, we review the dose-outcome model, the definition of the optimal biological dose, the dose-finding algorithm, and the software for trial implementation. To illustrate the concepts, we also present two real phase I-II trial examples utilizing the EffTox and ISO designs. Finally, we provide a classification tree to summarize the designs discussed in this article.
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Affiliation(s)
- Yong Zang
- Department of Biostatistics and Health Data Sciences, School of Medicine, Indiana University
- Center for Computational Biology and Bioinformatics, School of Medicine, Indiana University
| | - Beibei Guo
- Department of Experimental Statistics, Louisiana State University
| | - Yingjie Qiu
- Department of Biostatistics and Health Data Sciences, School of Medicine, Indiana University
| | - Hao Liu
- Department of Biostatistics and Epidemiology, Cancer Institute of New Jersey, Rutgers University
| | | | - Xiongbin Lu
- Department of Medical and Molecular Genetics, School of Medicine, Indiana University
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2
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Yuan Y, Zhou H, Liu S. Statistical and practical considerations in planning and conduct of dose-optimization trials. Clin Trials 2024; 21:273-286. [PMID: 38243399 PMCID: PMC11134987 DOI: 10.1177/17407745231207085] [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] [Indexed: 01/21/2024]
Abstract
The U.S. Food and Drug Administration launched Project Optimus with the aim of shifting the paradigm of dose-finding and selection toward identifying the optimal biological dose that offers the best balance between benefit and risk, rather than the maximum tolerated dose. However, achieving dose optimization is a challenging task that involves a variety of factors and is considerably more complicated than identifying the maximum tolerated dose, both in terms of design and implementation. This article provides a comprehensive review of various design strategies for dose-optimization trials, including phase 1/2 and 2/3 designs, and highlights their respective advantages and disadvantages. In addition, practical considerations for selecting an appropriate design and planning and executing the trial are discussed. The article also presents freely available software tools that can be utilized for designing and implementing dose-optimization trials. The approaches and their implementation are illustrated through real-world examples.
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Affiliation(s)
- Ying Yuan
- Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, TX, USA
| | - Heng Zhou
- Biostatistics and Research Decision Sciences, Merck and Co., Inc, Rahway, NJ, USA
| | - Suyu Liu
- Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, TX, USA
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3
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Zang Y, Thall PF, Yuan Y. A generalized phase 1-2-3 design integrating dose optimization with confirmatory treatment comparison. Biometrics 2024; 80:ujad022. [PMID: 38364811 PMCID: PMC10873567 DOI: 10.1093/biomtc/ujad022] [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] [Received: 05/09/2023] [Revised: 10/10/2023] [Accepted: 12/06/2023] [Indexed: 02/18/2024]
Abstract
A generalized phase 1-2-3 design, Gen 1-2-3, that includes all phases of clinical treatment evaluation is proposed. The design extends and modifies the design of Chapple and Thall (2019), denoted by CT. Both designs begin with a phase 1-2 trial including dose acceptability and optimality criteria, and both select an optimal dose for phase 3. The Gen 1-2-3 design has the following key differences. In stage 1, it uses phase 1-2 criteria to identify a set of candidate doses rather than 1 dose. In stage 2, which is intermediate between phase 1-2 and phase 3, it randomizes additional patients fairly among the candidate doses and an active control treatment arm and uses survival time data from both stage 1 and stage 2 patients to select an optimal dose. It then makes a Go/No Go decision of whether or not to conduct phase 3 based on the predictive probability that the selected optimal dose will provide a specified substantive improvement in survival time over the control. A simulation study shows that the Gen 1-2-3 design has desirable operating characteristics compared to the CT design and 2 conventional designs.
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Affiliation(s)
- Yong Zang
- Department of Biostatistics and Health Data Science; Center for Computational Biology and Bioinformatics, School of Medicine, Indiana University, Indianapolis, IN 46202, United States
| | - Peter F Thall
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, United States
| | - Ying Yuan
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, United States
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4
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Guo B, Yuan Y. DROID: dose-ranging approach to optimizing dose in oncology drug development. Biometrics 2023; 79:2907-2919. [PMID: 36807110 DOI: 10.1111/biom.13840] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 01/26/2023] [Indexed: 02/22/2023]
Abstract
In the era of targeted therapy, there has been increasing concern about the development of oncology drugs based on the "more is better" paradigm, developed decades ago for chemotherapy. Recently, the US Food and Drug Administration (FDA) initiated Project Optimus to reform the dose optimization and dose selection paradigm in oncology drug development. To accommodate this paradigm shifting, we propose a dose-ranging approach to optimizing dose (DROID) for oncology trials with targeted drugs. DROID leverages the well-established dose-ranging study framework, which has been routinely used to develop non-oncology drugs for decades, and bridges it with established oncology dose-finding designs to optimize the dose of oncology drugs. DROID consists of two seamlessly connected stages. In the first stage, patients are sequentially enrolled and adaptively assigned to investigational doses to establish the therapeutic dose range (TDR), defined as the range of doses with acceptable toxicity and efficacy profiles, and the recommended phase 2 dose set (RP2S). In the second stage, patients are randomized to the doses in RP2S to assess the dose-response relationship and identify the optimal dose. The simulation study shows that DROID substantially outperforms the conventional approach, providing a new paradigm to efficiently optimize the dose of targeted oncology drugs. DROID aligns with the approach of a randomized, parallel dose-response trial design recommended by the FDA in the Guidance on Optimizing the Dosage of Human Prescription Drugs and Biological Products for the Treatment of Oncologic Diseases.
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Affiliation(s)
- Beibei Guo
- Department of Experimental Statistics, Louisiana State University, Baton Rouge, Louisiana, USA
| | - Ying Yuan
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA
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5
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Thall PF, Zang Y, Chapple AG, Yuan Y, Lin R, Marin D, Msaouel P. Novel Clinical Trial Designs with Dose Optimization to Improve Long-term Outcomes. Clin Cancer Res 2023; 29:4549-4554. [PMID: 37725573 PMCID: PMC10841062 DOI: 10.1158/1078-0432.ccr-23-2222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Revised: 08/25/2023] [Accepted: 09/14/2023] [Indexed: 09/21/2023]
Abstract
Conventional designs for choosing a dose for a new therapy may select doses that are unsafe or ineffective and fail to optimize progression-free survival time, overall survival time, or response/remission duration. We explain and illustrate limitations of conventional dose-finding designs and make four recommendations to address these problems. When feasible, a dose-finding design should account for long-term outcomes, include screening rules that drop unsafe or ineffective doses, enroll an adequate sample size, and randomize patients among doses. As illustrations, we review three designs that include one or more of these features. The first illustration is a trial that randomized patients among two cell therapy doses and standard of care in a setting where it was assumed on biological grounds that dose toxicity and dose-response curves did not necessarily increase with cell dose. The second design generalizes phase I-II by first identifying a set of candidate doses, rather than one dose, randomizing additional patients among the candidates, and selecting an optimal dose to maximize progression-free survival over a longer follow-up period. The third design combines a phase I-II trial and a group sequential randomized phase III trial by using survival time data available after the first stage of phase III to reoptimize the dose selected in phase I-II. By incorporating one or more of the recommended features, these designs improve the likelihood that a selected dose or schedule will be optimal, and thus will benefit future patients and obtain regulatory approval.
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Affiliation(s)
- Peter F. Thall
- Department of Biostatistics, M.D. Anderson Cancer Center, Houston, Texas, USA
| | - Yong Zang
- Department of Biostatistics and Health Data Science, Center for Computational Biology and Bioinformatics, School of Medicine, Indiana University, Indianapolis, Indiana, USA
| | - Andrew G. Chapple
- Department of Interdisciplinary Oncology, School of Medicine, LSU Health Sciences Center, New Orleans, USA
| | - Ying Yuan
- Department of Biostatistics, M.D. Anderson Cancer Center, Houston, Texas, USA
| | - Ruitao Lin
- Department of Biostatistics, M.D. Anderson Cancer Center, Houston, Texas, USA
| | - David Marin
- Department of Stem Cell Transplantation and Cellular Therapy, M.D. Anderson Cancer Center, Houston, Texas, USA
| | - Pavlos Msaouel
- Department of Genitourinary Medical Oncology, M.D. Anderson Cancer Center, Houston, Texas, USA
- Department of Translational Molecular Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA
- David H. Koch Center for Applied Research of Genitourinary Cancers, The University of Texas, MD Anderson Cancer Center, Houston, USA
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6
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Lin LH, Han Y, Zhang R, Guo B. Biomarker-based precision dose finding for immunotherapy combined with radiotherapy. Biom J 2023; 65:e2200246. [PMID: 37212398 DOI: 10.1002/bimj.202200246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2022] [Revised: 02/02/2023] [Accepted: 04/02/2023] [Indexed: 05/23/2023]
Abstract
Recent success of sequential administration of immunotherapy following radiotherapy (RT), often referred to as immunoRT, has sparked the urgent need for novel clinical trial designs to accommodate the unique features of immunoRT. For this purpose, we propose a Bayesian phase I/II design for immunotherapy administered after standard-dose RT to identify the optimal dose that is personalized for each patient according to his/her measurements of PD-L1 expression at baseline and post-RT. We model the immune response, toxicity, and efficacy as functions of dose and patient's baseline and post-RT PD-L1 expression profile. We quantify the desirability of the dose using a utility function and propose a two-stage dose-finding algorithm to find the personalized optimal dose. Simulation studies show that our proposed design has good operating characteristics, with a high probability of identifying the personalized optimal dose.
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Affiliation(s)
- Li-Hsiang Lin
- Department of Experimental Statistics, Louisiana State University, Baton Rouge, Louisiana, USA
| | - Yan Han
- Department of Biostatistics and Health Data Science, School of Medicine, Indiana University, Indianapolis, Indiana, USA
| | - Rui Zhang
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana, USA
- Department of Radiation Oncology, Mary Bird Perkins Cancer Center, Baton Rouge, Louisiana, USA
| | - Beibei Guo
- Department of Experimental Statistics, Louisiana State University, Baton Rouge, Louisiana, USA
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7
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Thall PF, Zang Y, Yuan Y. Generalized phase I-II designs to increase long term therapeutic success rate. Pharm Stat 2023; 22:692-706. [PMID: 37038957 PMCID: PMC10524372 DOI: 10.1002/pst.2301] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Revised: 03/11/2023] [Accepted: 03/24/2023] [Indexed: 04/12/2023]
Abstract
Designs for early phase dose finding clinical trials typically are either phase I based on toxicity, or phase I-II based on toxicity and efficacy. These designs rely on the implicit assumption that the dose of an experimental agent chosen using these short-term outcomes will maximize the agent's long-term therapeutic success rate. In many clinical settings, this assumption is not true. A dose selected in an early phase oncology trial may give suboptimal progression-free survival or overall survival time, often due to a high rate of relapse following response. To address this problem, a new family of Bayesian generalized phase I-II designs is proposed. First, a conventional phase I-II design based on short-term outcomes is used to identify a set of candidate doses, rather than selecting one dose. Additional patients then are randomized among the candidates, patients are followed for a predefined longer time period, and a final dose is selected to maximize the long-term therapeutic success rate, defined in terms of duration of response. Dose-specific sample sizes in the randomization are determined adaptively to obtain a desired level of selection reliability. The design was motivated by a phase I-II trial to find an optimal dose of natural killer cells as targeted immunotherapy for recurrent or treatment-resistant B-cell hematologic malignancies. A simulation study shows that, under a range of scenarios in the context of this trial, the proposed design has much better performance than two conventional phase I-II designs.
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Affiliation(s)
- Peter F. Thall
- Department of Biostatistics, M.D. Anderson Cancer Center
| | - Yong Zang
- Department of Biostatistics and Health Data Science; Center for Computational Biology and Bioinformatics, Indiana University
| | - Ying Yuan
- Department of Biostatistics, M.D. Anderson Cancer Center
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Qiu Y, Zhao Y, Liu H, Cao S, Zhang C, Zang Y. Modified isotonic regression based phase I/II clinical trial design identifying optimal biological dose. Contemp Clin Trials 2023; 127:107139. [PMID: 36870476 PMCID: PMC10065963 DOI: 10.1016/j.cct.2023.107139] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Revised: 01/24/2023] [Accepted: 02/25/2023] [Indexed: 03/06/2023]
Abstract
Conventional phase I/II clinical trial designs often use complicated parametric models to characterize the dose-response relationships and conduct the trials. However, the parametric models are hard to justify in practice, and the misspecification of parametric models can lead to substantially undesirable performances in phase I/II trials. Moreover, it is difficult for the physicians conducting phase I/II trials to clinically interpret the parameters of these complicated models, and such significant learning costs impede the translation of novel statistical designs into practical trial implementation. To solve these issues, we propose a transparent and efficient phase I/II clinical trial design, referred to as the modified isotonic regression-based design (mISO), to identify the optimal biological doses for molecularly targeted agents and immunotherapy. The mISO design makes no parametric model assumptions on the dose-response relationship and yields desirable performances under any clinically meaningful dose-response curves. The concise, clinically interpretable dose-response models and dose-finding algorithm make the proposed designs highly translational from the statistical community to the clinical community. We further extend the mISO design and develop the mISO-B design to handle the delayed outcomes. Our comprehensive simulation studies show that the mISO and mISO-B designs are highly efficient in optimal biological dose selection and patients allocation and outperform many existing phase I/II clinical trial designs. We also provide a trial example to illustrate the practical implementation of the proposed designs. The software for simulation and trial implementation are available for free download.
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Affiliation(s)
- Yingjie Qiu
- Department of Biostatistics and Health Data Science, Indiana University, USA
| | - Yi Zhao
- Department of Biostatistics and Health Data Science, Indiana University, USA
| | - Hao Liu
- Department of Biostatistics and Epidemiology, Cancer Institute of New Jersey, Rutgers University, USA
| | - Sha Cao
- Department of Biostatistics and Health Data Science, Indiana University, USA; Center of Computational Biology and Bioinformatics, Indiana University, USA
| | - Chi Zhang
- Center of Computational Biology and Bioinformatics, Indiana University, USA; Department of Medical and Molecular Genetics, Indiana University, USA
| | - Yong Zang
- Department of Biostatistics and Health Data Science, Indiana University, USA; Center of Computational Biology and Bioinformatics, Indiana University, USA.
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9
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Zhang R, Clark SD, Guo B, Zhang T, Jeansonne D, Jeyaseelan SJ, Francis J, Huang W. Challenges in the combination of radiotherapy and immunotherapy for breast cancer. Expert Rev Anticancer Ther 2023; 23:375-383. [PMID: 37039098 PMCID: PMC10929662 DOI: 10.1080/14737140.2023.2188196] [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] [Received: 05/03/2022] [Accepted: 03/03/2023] [Indexed: 04/12/2023]
Abstract
INTRODUCTION Immunotherapy (IT) is showing promise in the treatment of breast cancer, but IT alone only benefits a minority of patients. Radiotherapy (RT) is usually included in the standard of care for breast cancer patients and is traditionally considered as a local form of treatment. The emerging knowledge of RT-induced systemic immune response, and the observation that the rare abscopal effect of RT on distant cancer metastases can be augmented by IT, have increased the enthusiasm for combinatorial immunoradiotherapy (IRT) for breast cancer patients. However, IRT largely follows the traditional sole RT and IT protocols and does not consider patient specificity, although patients' responses to treatment remain heterogeneous. AREAS COVERED This review discusses the rationale of IRT for breast cancer, the current knowledge, challenges, and future directions. EXPERT OPINION The synergy between RT and the immune system has been observed but not well understood at the basic level. The optimal dosages, timing, target, and impact of biomarkers are largely unknown. There is an urgent need to design efficacious pre-clinical and clinical trials to optimize IRT for cancer patients, maximize the synergy of radiation and immune response, and explore the abscopal effect in depth, taking into account patients' personal features.
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Affiliation(s)
- Rui Zhang
- Medical Physics Program, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, USA
- Department of Radiation Oncology, Mary Bird Perkins Cancer Center, Baton Rouge, LA, USA
| | - Samantha D Clark
- Department of Pathobiological Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, USA
| | - Beibei Guo
- Department of Experimental Statistics, Louisiana State University, Baton Rouge, LA, USA
| | - Tianyi Zhang
- Department of Pathobiological Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, USA
| | - Duane Jeansonne
- Department of Pathobiological Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, USA
| | - Samithamby J Jeyaseelan
- Department of Pathobiological Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, USA
| | - Joseph Francis
- Department of Comparative Biomedical Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, USA
| | - Weishan Huang
- Department of Pathobiological Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, USA
- Department of Microbiology and Immunology, College of Veterinary Medicine, Cornell University, Ithaca, NY, USA
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10
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Li Z, Chen J, Laber E, Liu F, Baumgartner R. Optimal Treatment Regimes: A Review and Empirical Comparison. Int Stat Rev 2023. [DOI: 10.1111/insr.12536] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
Affiliation(s)
- Zhen Li
- Department of Statistics North Carolina State University Raleigh 27607 NC USA
| | - Jie Chen
- Department of Biometrics Overland Pharmaceuticals Dover 19901 DE USA
| | - Eric Laber
- Department of Statistical Science, Department of Biostatistics and Bioinformatics Duke University Durham 27708 NC USA
| | - Fang Liu
- Biostatistics and Research Decision Sciences Merck & Co., Inc. Kenilworth NJ 07033 USA
| | - Richard Baumgartner
- Biostatistics and Research Decision Sciences Merck & Co., Inc. Kenilworth NJ 07033 USA
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11
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Alam MI, Shanto SI. Patient-specific dose finding in seamless phase I/II clinical trials. Seq Anal 2022. [DOI: 10.1080/07474946.2022.2105361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- M. Iftakhar Alam
- Institute of Statistical Research and Training, University of Dhaka, Dhaka, Bangladesh
| | - Shantonu Islam Shanto
- Institute of Statistical Research and Training, University of Dhaka, Dhaka, Bangladesh
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12
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Guo B, Zang Y. A Bayesian phase I/II biomarker-based design for identifying subgroup-specific optimal dose for immunotherapy. Stat Methods Med Res 2022; 31:1104-1119. [PMID: 35191780 DOI: 10.1177/09622802221080753] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Immunotherapy is an innovative treatment that enlists the patient's immune system to battle tumors. The optimal dose for treating patients with an immunotherapeutic agent may differ according to their biomarker status. In this article, we propose a biomarker-based phase I/II dose-finding design for identifying subgroup-specific optimal dose for immunotherapy (BSOI) that jointly models the immune response, toxicity, and efficacy outcomes. We propose parsimonious yet flexible models to borrow information across different types of outcomes and subgroups. We quantify the desirability of the dose using a utility function and adopt a two-stage dose-finding algorithm to find the optimal dose for each subgroup. Simulation studies show that the BSOI design has desirable operating characteristics in selecting the subgroup-specific optimal doses and allocating patients to those optimal doses, and outperforms conventional designs.
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Affiliation(s)
- Beibei Guo
- Department of Experimental Statistics, 5779Louisiana State University, Baton Rouge, USA
| | - Yong Zang
- Department of Biostatistics and Health Data Science, Indiana University, Indianapolis, USA.,Center for Computational Biology and Bioinformatics, Indiana University, Indianapolis, USA
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13
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TITE‐BOIN12: A Bayesian phase I/II trial design to find the optimal biological dose with late‐onset toxicity and efficacy. Stat Med 2022; 41:1918-1931. [DOI: 10.1002/sim.9337] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2021] [Revised: 12/19/2021] [Accepted: 01/09/2022] [Indexed: 12/17/2022]
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14
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Mozgunov P, Cro S, Lingford-Hughes A, Paterson LM, Jaki T. A dose-finding design for dual-agent trials with patient-specific doses for one agent with application to an opiate detoxification trial. Pharm Stat 2021; 21:476-495. [PMID: 34891221 PMCID: PMC7612599 DOI: 10.1002/pst.2181] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Revised: 08/31/2021] [Accepted: 11/21/2021] [Indexed: 11/08/2022]
Abstract
There is a growing interest in early phase dose-finding clinical trials studying combinations of several treatments. While the majority of dose finding designs for such setting were proposed for oncology trials, the corresponding designs are also essential in other therapeutic areas. Furthermore, there is increased recognition of recommending the patient-specific doses/combinations, rather than a single target one that would be recommended to all patients in later phases regardless of their characteristics. In this paper, we propose a dose-finding design for a dual-agent combination trial motivated by an opiate detoxification trial. The distinguishing feature of the trial is that the (continuous) dose of one compound is defined externally by the clinicians and is individual for every patient. The objective of the trial is to define the dosing function that for each patient would recommend the optimal dosage of the second compound. Via a simulation study, we have found that the proposed design results in high accuracy of individual dose recommendation and is robust to the model misspecification and assumptions on the distribution of externally defined doses.
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Affiliation(s)
- Pavel Mozgunov
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - Suzie Cro
- Imperial Clinical Trials Unit, School of Public Health, Imperial College, London, UK
| | - Anne Lingford-Hughes
- Division of Psychiatry, Department of Brain Sciences, Imperial College, London, UK
| | - Louise M Paterson
- Division of Psychiatry, Department of Brain Sciences, Imperial College, London, UK
| | - Thomas Jaki
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK.,Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
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15
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Guo B, Zang Y. BIPSE: A biomarker-based phase I/II design for immunotherapy trials with progression-free survival endpoint. Stat Med 2021; 41:1205-1224. [PMID: 34821409 PMCID: PMC9335906 DOI: 10.1002/sim.9265] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Revised: 09/30/2021] [Accepted: 11/03/2021] [Indexed: 12/19/2022]
Abstract
A Bayesian biomarker-based phase I/II design (BIPSE) is presented for immunotherapy trials with a progression-free survival (PFS) endpoint. The objective is to identify the subgroup-specific optimal dose, defined as the dose with the best risk-benefit tradeoff in each biomarker subgroup. We jointly model the immune response, toxicity outcome, and PFS with information borrowing across subgroups. A plateau model is used to describe the marginal distribution of the immune response. Conditional on the immune response, we model toxicity using probit regression and model PFS using the mixture cure rate model. During the trial, based on the accumulating data, we continuously update model estimates and adaptively randomize patients to doses with high desirability within each subgroup. Simulation studies show that the BIPSE design has desirable operating characteristics in selecting the subgroup-specific optimal doses and allocating patients to those optimal doses, and outperforms conventional designs.
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Affiliation(s)
- Beibei Guo
- Department of Experimental Statistics, Louisiana State University, Baton Rouge, Louisiana, USA
| | - Yong Zang
- Department of Biostatistics and Health Data Science, Indiana University, Indianapolis, Indiana, USA.,Center for Computational Biology and Bioinformatics, Indiana University, Indianapolis, Indiana, USA
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16
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Mu R, Xu J, Tang RS, Kopetz S, Yuan Y. A Bayesian phase I/II platform design for co-developing drug combination therapies for multiple indications. Stat Med 2021; 41:374-389. [PMID: 34730248 DOI: 10.1002/sim.9242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 10/10/2021] [Accepted: 10/12/2021] [Indexed: 12/26/2022]
Abstract
There is a growing trend to combine a new targeted or immunotherapy agent with the cancer-specific standard of care to treat different types of cancers. We propose a master-protocol-based, Bayesian phase I/II platform design to co-develop combination (BPCC) therapies in multiple indications. Under the BPCC design, only a single master protocol is needed, and the combined drug is evaluated in different indications in a concurrent or staggered fashion. For each indication, we jointly model dose-toxicity and -efficacy relationships and employ Bayesian hierarchical models to borrow information across them for more efficient indication-specific decision-making. To account for the characteristic of targeted or immunotherapy agents that their efficacy may not monotonically increase with the dose, and often plateau at high doses, we use the utility to quantify the risk-benefit tradeoff of the treatment. At each interim, we update the toxicity and efficacy model, as well as the estimate of the utility, based on the observed data across indications to inform the indication-specific decision of dose escalation and de-escalation and identify the optimal biological dose for each indication. Simulation study shows that the BPCC design has desirable operating characteristics, and that it provides an efficient approach to accelerate the development of combination therapies.
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Affiliation(s)
- Rongji Mu
- Clinical Research Center, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Jin Xu
- KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, China
| | - Rui Sammi Tang
- Department of Biometrics, Servier Pharmaceuticals, Boston, Massachusetts, USA
| | - Scott Kopetz
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA
| | - Ying Yuan
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA
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17
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Lin R, Yin G, Shi H. Bayesian adaptive model selection design for optimal biological dose finding in phase I/II clinical trials. Biostatistics 2021; 24:277-294. [PMID: 34296266 PMCID: PMC10102885 DOI: 10.1093/biostatistics/kxab028] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Revised: 05/26/2021] [Accepted: 06/06/2021] [Indexed: 11/13/2022] Open
Abstract
Identification of the optimal dose presents a major challenge in drug development with molecularly targeted agents, immunotherapy, as well as chimeric antigen receptor T-cell treatments. By casting dose finding as a Bayesian model selection problem, we propose an adaptive design by simultaneously incorporating the toxicity and efficacy outcomes to select the optimal biological dose (OBD) in phase I/II clinical trials. Without imposing any parametric assumption or shape constraint on the underlying dose-response curves, we specify curve-free models for both the toxicity and efficacy endpoints to determine the OBD. By integrating the observed data across all dose levels, the proposed design is coherent in dose assignment and thus greatly enhances efficiency and accuracy in pinning down the right dose. Not only does our design possess a completely new yet flexible dose-finding framework, but it also has satisfactory and robust performance as demonstrated by extensive simulation studies. In addition, we show that our design enjoys desirable coherence properties, while most of existing phase I/II designs do not. We further extend the design to accommodate late-onset outcomes which are common in immunotherapy. The proposed design is exemplified with a phase I/II clinical trial in chronic lymphocytic leukemia.
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Affiliation(s)
- Ruitao Lin
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX 77030, USA
| | - Guosheng Yin
- Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Haolun Shi
- Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Dr, Burnaby, BC V5A 1S6, Canada
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18
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Mu R, Xu G, Liu G, Pan H. A two-stage Bayesian adaptive design for minimum effective dose (MinED)-based dosing-finding trials. Contemp Clin Trials 2021; 108:106504. [PMID: 34303862 DOI: 10.1016/j.cct.2021.106504] [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: 03/11/2021] [Revised: 06/02/2021] [Accepted: 07/08/2021] [Indexed: 12/01/2022]
Abstract
Conventional phase I designs for finding a phase II recommended dose (P2RD) based on toxicity alone is problematic because the maximum tolerated dose (MTD) is not necessarily the optimal dose. Instead, recently attention has been given to find the minimum effective dose (MinED) - defined as the lowest effective dose. Traditional paradigms for the MinED studies are conducted as dose-ranging or dose-response trials which involve several doses and randomize patients among doses to find the MinED. An alternative approach for the MinED study is the so-called MinED-based dose-finding study, in which instead of conducting hypothesis testings and without power analysis, this kind of trial conduct dose escalation/de-escalation to target a pre-set MinED target. In this study, we propose a new Bayesian two-stage adaptive design schema based on framework of the interval-based phase I method. The proposed method is model-free without curve pre-specifications, which is suitable for various dose-efficacy relationships. The proposed method shows desirable theoretical finite property of semi-coherence and large sample property of consistency. A random scenario generative algorithm for the MinED has also been proposed for extensive simulation studies, which demonstrated desirable performances of the proposed method. An R package "MinEDfind" and a Shiny app have been developed for implementing the method.
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Affiliation(s)
- Rongji Mu
- Clinical Research Center, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China
| | - Guoying Xu
- Jiangsu Hengrui Medicine Co., Ltd, Shanghai 201203, China
| | - Guanfu Liu
- School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China
| | - Haitao Pan
- Department of Biostatistics, St. Jude Children's Research Hospital, Memphis, TN 38105, USA.
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19
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Guo B, Garrett‐Mayer E, Liu S. A Bayesian phase I/II design for cancer clinical trials combining an immunotherapeutic agent with a chemotherapeutic agent. J R Stat Soc Ser C Appl Stat 2021. [DOI: 10.1111/rssc.12508] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Beibei Guo
- Department of Experimental Statistics Louisiana State University Baton Rouge LA70803USA
| | - Elizabeth Garrett‐Mayer
- Center for Research and Analytics (CENTRA) American Society of Clinical Oncology Alexandria VA22314USA
| | - Suyu Liu
- Department of Biostatistics The University of Texas MD Anderson Cancer Center Houston Texas77030USA
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20
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Yada S. Bayesian adaptive design of early-phase clinical trials for precision medicine based on cancer biomarkers. Int J Biostat 2021; 18:109-125. [PMID: 34114385 DOI: 10.1515/ijb-2021-0009] [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: 11/16/2020] [Accepted: 05/25/2021] [Indexed: 11/15/2022]
Abstract
Cancer tissue samples obtained via biopsy or surgery were examined for specific gene mutations by genetic testing to inform treatment. Precision medicine, which considers not only the cancer type and location, but also the genetic information, environment, and lifestyle of each patient, can be applied for disease prevention and treatment in individual patients. The number of patient-specific characteristics, including biomarkers, has been increasing with time; these characteristics are highly correlated with outcomes. The number of patients at the beginning of early-phase clinical trials is often limited. Moreover, it is challenging to estimate parameters of models that include baseline characteristics as covariates such as biomarkers. To overcome these issues and promote personalized medicine, we propose a dose-finding method that considers patient background characteristics, including biomarkers, using a model for phase I/II oncology trials. We built a Bayesian neural network with input variables of dose, biomarkers, and interactions between dose and biomarkers and output variables of efficacy outcomes for each patient. We trained the neural network to select the optimal dose based on all background characteristics of a patient. Simulation analysis showed that the probability of selecting the desirable dose was higher using the proposed method than that using the naïve method.
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Affiliation(s)
- Shinjo Yada
- Department of Clinical Biostatistics, Graduate School of Medicine, Kyoto University, Yoshida Konoe-cho, Sakyo-ku, Kyoto606-8501, Japan
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21
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Zhang Y, Zang Y. CWL: A conditional weighted likelihood method to account for the delayed joint toxicity-efficacy outcomes for phase I/II clinical trials. Stat Methods Med Res 2020; 30:892-903. [PMID: 33349166 DOI: 10.1177/0962280220979328] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The delayed outcome issue is common in early phase dose-finding clinical trials. This problem becomes more intractable in phase I/II clinical trials because both toxicity and efficacy responses are subject to the delayed outcome issue. The existing methods applying for the phase I trials cannot be used directly for the phase I/II trial due to a lack of capability to model the joint toxicity-efficacy distribution. In this paper, we propose a conditional weighted likelihood (CWL) method to circumvent this issue. The key idea of the CWL method is to decompose the joint probability into the product of marginal and conditional probabilities and then weight each probability based on each patient's actual follow-up time. The CWL method makes no parametric model assumption on either the dose-response curve or the toxicity-efficacy correlation and therefore can be applied to any existing phase I/II trial design. Numerical trial applications show that the proposed CWL method yields desirable operating characteristics.
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Affiliation(s)
- Yifei Zhang
- Department of Biostatistics, Indiana University, Indianapolis, IN, USA
| | - Yong Zang
- Department of Biostatistics, Indiana University, Indianapolis, IN, USA.,Center for Computational Biology and Bioinformatics, Indiana University, Indianapolis, IN, USA
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22
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Mu R, Pan H, Xu G. A Bayesian adaptive phase I/II platform trial design for pediatric immunotherapy trials. Stat Med 2020; 40:382-402. [PMID: 33094528 DOI: 10.1002/sim.8780] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2020] [Revised: 08/23/2020] [Accepted: 10/01/2020] [Indexed: 11/11/2022]
Abstract
Immunotherapy is the most promising new cancer treatment for various pediatric tumors and has resulted in an unprecedented surge in the number of novel immunotherapeutic treatments that need to be evaluated in clinical trials. Most phase I/II trial designs have been developed for evaluating only one candidate treatment at a time, and are thus not optimal for this task. To address these issues, we propose a Bayesian phase I/II platform trial design, which accounts for the unique features of immunotherapy, thereby allowing investigators to continuously screen a large number of immunotherapeutic treatments in an efficient and seamless manner. The elicited numerical utility is adopted to account for the risk-benefit trade-off and to quantify the desirability of the dose. During the trial, inefficacious or overly toxic treatments are adaptively dropped from the trial and the promising treatments are graduated from the trial to the next stage of development. Once an experimental treatment is dropped or graduated, the next available new treatment can be immediately added and tested. Extensive simulation studies have demonstrated the desirable operating characteristics of the proposed design.
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Affiliation(s)
- Rongji Mu
- KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, China
| | - Haitao Pan
- Department of Biostatistics, St. Jude Children's Research Hospital, Memphis, Tennessee, USA
| | - Guoying Xu
- Clinical Research Center, Shanghai Jiao Tong University School of Medicine, Shanghai, China
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23
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Han Y, Liu H, Cao S, Zhang C, Zang Y. TSNP: A two-stage nonparametric phase I/II clinical trial design for immunotherapy. Pharm Stat 2020; 20:282-296. [PMID: 33025762 DOI: 10.1002/pst.2075] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Revised: 08/27/2020] [Accepted: 09/15/2020] [Indexed: 12/17/2022]
Abstract
We develop a transparent and efficient two-stage nonparametric (TSNP) phase I/II clinical trial design to identify the optimal biological dose (OBD) of immunotherapy. We propose a nonparametric approach to derive the closed-form estimates of the joint toxicity-efficacy response probabilities under the monotonic increasing constraint for the toxicity outcomes. These estimates are then used to measure the immunotherapy's toxicity-efficacy profiles at each dose and guide the dose finding. The first stage of the design aims to explore the toxicity profile. The second stage aims to find the OBD, which can achieve the optimal therapeutic effect by considering both the toxicity and efficacy outcomes through a utility function. The closed-form estimates and concise dose-finding algorithm make the TSNP design appealing in practice. The simulation results show that the TSNP design yields superior operating characteristics than the existing Bayesian parametric designs. User-friendly computational software is freely available to facilitate the application of the proposed design to real trials. We provide comprehensive illustrations and examples about implementing the proposed design with associated software.
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Affiliation(s)
- Yan Han
- Department of Biostatistics, Indiana University, Indianapolis, Indiana, USA
| | - Hao Liu
- Department of Biostatistics, Indiana University, Indianapolis, Indiana, USA
| | - Sha Cao
- Department of Biostatistics, Indiana University, Indianapolis, Indiana, USA
- Center for Computational Biology and Bioinformatics, Indiana University, Indianapolis, Indiana, USA
| | - Chi Zhang
- Center for Computational Biology and Bioinformatics, Indiana University, Indianapolis, Indiana, USA
- Department of Medical and Molecular Genetics, Indiana University, Indianapolis, Indiana, USA
| | - Yong Zang
- Department of Biostatistics, Indiana University, Indianapolis, Indiana, USA
- Center for Computational Biology and Bioinformatics, Indiana University, Indianapolis, Indiana, USA
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24
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Tsimberidou AM, Müller P, Ji Y. Innovative trial design in precision oncology. Semin Cancer Biol 2020; 84:284-292. [DOI: 10.1016/j.semcancer.2020.09.006] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2020] [Accepted: 09/09/2020] [Indexed: 01/01/2023]
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25
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Kaneko S, Hirakawa A, Kakurai Y, Hamada C. A dose-finding approach for genomic patterns in phase I trials. J Biopharm Stat 2020; 30:834-853. [PMID: 32310707 DOI: 10.1080/10543406.2020.1744619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
Precision medicine is an emerging approach for disease treatment and prevention that accounts for individual variability in genes, environment, and lifestyle. Cancer is a genomic disease; therefore, the dose-efficacy and dose-toxicity relationships for molecularly targeted agents in cancer most likely differ, based on the genomic mutation pattern. The individualized optimal dose - the maximal efficacious dose with a clinically acceptable safety profile - may vary depending on the genomic mutation patterns and should be determined prior to the use of these agents in precision medicine. In addition, genes that influence the individualized optimal doses should be identified in early-phase development. In this study, we propose a novel dose-finding approach to identify the individualized optimal dose for molecularly targeted agents in phase I cancer trials. Individualized optimal dose determination and gene selection were conducted simultaneously based on L 1 and L 2 penalized regression. Similar to most reported dose-finding approaches, this study considers non-monotonic patterns for dose-efficacy and dose-toxicity relationships, as well as correlations between efficacy and toxicity outcomes based on multinomial distribution. Our dose-finding algorithm is based on the predictive probability calculated with an estimated penalized regression model. We compare the operating characteristics between the proposed and existing methods by simulation studies under various scenarios.
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Affiliation(s)
- S Kaneko
- Japan Development, Biostatistics Pharma, Integrated Biostatistics Japan, Novartis Pharma K.K ., Minato-ku, Tokyo, Japan
| | - A Hirakawa
- Department of Biostatistics and Bioinformatics, Graduate School of Medicine, the University of Tokyo , Bunkyo-ku, Tokyo, Japan
| | - Y Kakurai
- R&D Division, Biostatistics & Data Management, Daiichi-Sankyo Co., Ltd ., Shinagawa-ku, Tokyo, Japan.,Department of Information and Computer Technology, Tokyo University of Science , Katsushika-ku, Tokyo, Japan
| | - C Hamada
- Department of Information and Computer Technology, Tokyo University of Science , Katsushika-ku, Tokyo, Japan
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26
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Lee J, F Thall P, Msaouel P. A phase I-II design based on periodic and continuous monitoring of disease status and the times to toxicity and death. Stat Med 2020; 39:2035-2050. [PMID: 32255206 DOI: 10.1002/sim.8528] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2019] [Revised: 01/28/2020] [Accepted: 02/22/2020] [Indexed: 11/10/2022]
Abstract
A Bayesian phase I-II dose-finding design is presented for a clinical trial with four coprimary outcomes that reflect the actual clinical observation process. During a prespecified fixed follow-up period, the times to disease progression, toxicity, and death are monitored continuously, and an ordinal disease status variable, including progressive disease (PD) as one level, is evaluated repeatedly by scheduled imaging. We assume a proportional hazards model with piecewise constant baseline hazard for each continuous variable and a longitudinal multinomial probit model for the ordinal disease status process and include multivariate patient frailties to induce association among the outcomes. A finite partition of the nonfatal outcome combinations during the follow-up period is constructed, and the utility of each set in the partition is elicited. Posterior mean utility is used to optimize each patient's dose, subject to a safety rule excluding doses with an unacceptably high rate of PD, severe toxicity, or death. A simulation study shows that, compared with the proposed design, a simpler design based on commonly used efficacy and toxicity outcomes obtained by combining the four variables described above performs poorly and has substantially smaller probabilities of correctly choosing truly optimal doses and excluding truly unsafe doses.
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Affiliation(s)
- Juhee Lee
- Department of Statistics, University of California Santa Cruz, Santa Cruz, California, USA
| | - Peter F Thall
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA
| | - Pavlos Msaouel
- Department of Genitourinary Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas, USA
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27
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Lin R, Thall PF, Yuan Y. An adaptive trial design to optimize dose-schedule regimes with delayed outcomes. Biometrics 2020; 76:304-315. [PMID: 31273750 PMCID: PMC6942642 DOI: 10.1111/biom.13116] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2018] [Accepted: 07/02/2019] [Indexed: 11/30/2022]
Abstract
This paper proposes a two-stage phase I-II clinical trial design to optimize dose-schedule regimes of an experimental agent within ordered disease subgroups in terms of the toxicity-efficacy trade-off. The design is motivated by settings where prior biological information indicates it is certain that efficacy will improve with ordinal subgroup level. We formulate a flexible Bayesian hierarchical model to account for associations among subgroups and regimes, and to characterize ordered subgroup effects. Sequentially adaptive decision-making is complicated by the problem, arising from the motivating application, that efficacy is scored on day 90 and toxicity is evaluated within 30 days from the start of therapy, while the patient accrual rate is fast relative to these outcome evaluation intervals. To deal with this in a practical manner, we take a likelihood-based approach that treats unobserved toxicity and efficacy outcomes as missing values, and use elicited utilities that quantify the efficacy-toxicity trade-off as a decision criterion. Adaptive randomization is used to assign patients to regimes while accounting for subgroups, with randomization probabilities depending on the posterior predictive distributions of utilities. A simulation study is presented to evaluate the design's performance under a variety of scenarios, and to assess its sensitivity to the amount of missing data, the prior, and model misspecification.
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Affiliation(s)
- Ruitao Lin
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Peter F Thall
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Ying Yuan
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
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28
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Li P, Taylor JM, Kong S, Jolly S, Schipper MJ. A utility approach to individualized optimal dose selection using biomarkers. Biom J 2019; 62:386-397. [DOI: 10.1002/bimj.201900030] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2019] [Revised: 09/02/2019] [Accepted: 09/08/2019] [Indexed: 11/07/2022]
Affiliation(s)
- Pin Li
- Department of BiostatisticsUniversity of MichiganAnn Arbor MI USA
| | | | - Spring Kong
- Department of Radiation OncologyCase Western Reserve UniversityCleveland OH USA
| | - Shruti Jolly
- Department of Radiation OncologyUniversity of MichiganAnn Arbor MI USA
| | - Matthew J. Schipper
- Department of BiostatisticsUniversity of MichiganAnn Arbor MI USA
- Department of Radiation OncologyUniversity of MichiganAnn Arbor MI USA
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29
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Park Y, Fullerton HJ, Elm JJ. A pragmatic, adaptive clinical trial design for a rare disease: The FOcal Cerebral Arteriopathy Steroid (FOCAS) trial. Contemp Clin Trials 2019; 86:105852. [PMID: 31614215 PMCID: PMC6857809 DOI: 10.1016/j.cct.2019.105852] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2019] [Revised: 09/16/2019] [Accepted: 09/17/2019] [Indexed: 11/25/2022]
Abstract
BACKGROUND Pediatric stroke investigators identified as their top research priority a clinical trial of corticosteroids for focal cerebral arteriopathy (FCA). However, FCA is both rare and an acute condition making it infeasible to enroll the large sample sizes needed for standard, confirmatory clinical trials. We present a pragmatic approach to clinical trial design that may inform the approach to other rare disorders. METHODS We surveyed pediatric stroke experts to determine the level of evidence that would impact their clinical management of FCA. Incorporating survey results, a randomized, group sequential Bayesian adaptive design was proposed based on a quantitative radiologic outcome measure (change from baseline in change in the FCA Severity Score). Using accumulating information, the design determines whether intervention is better than control with high probability. RESULTS Among 21 (100%) respondents, the probability of corticosteroid efficacy that would lead the experts to treat was 30% (median). The probability of efficacy that would make them unwilling to randomize (because they would feel all children should receive corticosteroids) was 70%. Simulation studies with the proposed design showed that a total of 42 subjects controls the type I error rate at the desired level 0.20 and yields a smaller average sample size and trial duration compared to a conventional design. CONCLUSIONS Designs in rare diseases require special considerations; this is especially true for this childhood disease, which is both uncommon and acute. This design has incorporated expert consensus to establish the criteria for success, formal monitoring rules for safety, and early stopping rules.
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Affiliation(s)
- Yeonhee Park
- Department of Public Health Sciences, Medical University of South Carolina, Charleston, SC, United States
| | - Heather J Fullerton
- Departments of Neurology & Pediatrics, University of California, San Francisco, San Francisco, CA, United States
| | - Jordan J Elm
- Department of Public Health Sciences, Medical University of South Carolina, Charleston, SC, United States.
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30
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Zhou Y, Lee JJ, Yuan Y. A utility-based Bayesian optimal interval (U-BOIN) phase I/II design to identify the optimal biological dose for targeted and immune therapies. Stat Med 2019; 38:5299-5316. [PMID: 31621952 DOI: 10.1002/sim.8361] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Revised: 05/15/2019] [Accepted: 08/12/2019] [Indexed: 11/08/2022]
Abstract
In the era of targeted therapy and immunotherapy, the objective of dose finding is often to identify the optimal biological dose (OBD), rather than the maximum tolerated dose. We develop a utility-based Bayesian optimal interval (U-BOIN) phase I/II design to find the OBD. We jointly model toxicity and efficacy using a multinomial-Dirichlet model, and employ a utility function to measure dose risk-benefit trade-off. The U-BOIN design consists of two seamless stages. In stage I, the Bayesian optimal interval design is used to quickly explore the dose space and collect preliminary toxicity and efficacy data. In stage II, we continuously update the posterior estimate of the utility for each dose after each cohort, using accumulating efficacy and toxicity from both stages I and II, and then use the posterior estimate to direct the dose assignment and selection. Compared to existing phase I/II designs, one prominent advantage of the U-BOIN design is its simplicity for implementation. Once the trial is designed, it can be easily applied using predetermined decision tables, without complex model fitting and estimation. Our simulation study shows that, despite its simplicity, the U-BOIN design is robust and has high accuracy to identify the OBD. We extend the design to accommodate delayed efficacy by leveraging the short-term endpoint (eg, immune activity or other biological activity of targeted agents), and using it to predict the delayed efficacy outcome to facilitate real-time decision making. A user-friendly software to implement the U-BOIN is freely available at www.trialdesign.org.
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Affiliation(s)
- Yanhong Zhou
- Quantitative Science, The University of Texas MD Anderson Cancer Center UTHealth Graduate School of Biomedical Sciences, Houston, Texas.,Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - J Jack Lee
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Ying Yuan
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
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31
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Domenicano I, Ventz S, Cellamare M, Mak RH, Trippa L. Bayesian uncertainty‐directed dose finding designs. J R Stat Soc Ser C Appl Stat 2019. [DOI: 10.1111/rssc.12355] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- I. Domenicano
- University of Rome “La Sapienza” Italy
- Dana–Farber Cancer Institute Boston USA
| | - S. Ventz
- Dana–Farber Cancer Institute Boston
- Harvard School of Public Health Boston USA
| | - M. Cellamare
- Dana–Farber Cancer Institute Boston
- Harvard School of Public Health Boston USA
| | - R. H. Mak
- Dana–Farber Cancer Institute Boston
- Harvard Medical School Boston USA
| | - L. Trippa
- Dana–Farber Cancer Institute Boston
- Harvard School of Public Health Boston USA
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32
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Tarantino P, Trapani D, Morganti S, Ferraro E, Viale G, D’Amico P, Duso BA, Curigliano G. Opportunities and challenges of implementing Pharmacogenomics in cancer drug development. CANCER DRUG RESISTANCE (ALHAMBRA, CALIF.) 2019; 2:43-52. [PMID: 35582141 PMCID: PMC9019172 DOI: 10.20517/cdr.2018.22] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/31/2018] [Revised: 02/01/2019] [Accepted: 02/15/2019] [Indexed: 11/12/2022]
Abstract
Cancer drug development is a time and resources consuming process. Around 90% of drugs entering clinical trials fail due to lack of efficacy and/or safety issues, more often after conspicuous research and economic efforts. Part of the discarded drugs might be beneficial only in a subgroup of the study patients, and some adverse events might be prevented by identifying those patients more vulnerable to toxicities. The implementation of pharmacogenomic biomarkers allows the categorization of patients, to predict efficacy and toxicity and to optimize the drug development process. Around seventy FDA approved drugs currently present one or more genetic biomarker to keep in consideration, and with the progress of Precision Medicine tailoring therapies on individuals' genomic landscape promises to become a new standard of cancer care. In the current article we review the role of pharmacogenomics in cancer drug development, underlying the advantages and challenges of their implementation.
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Affiliation(s)
- Paolo Tarantino
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
| | - Dario Trapani
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
| | - Stefania Morganti
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
| | - Emanuela Ferraro
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
| | - Giulia Viale
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
| | - Paolo D’Amico
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
| | - Bruno Achutti Duso
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
| | - Giuseppe Curigliano
- Division of Early Drug Development for Innovative Therapies, IEO, European Institute of Oncology IRCCS, Milan 20141, Italy
- Department of Oncology and Haematology (DIPO), University of Milan, Milan 20122, Italy
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33
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Lee J, Thall PF, Rezvani K. Optimizing natural killer cell doses for heterogeneous cancer patients on the basis of multiple event times. J R Stat Soc Ser C Appl Stat 2019; 68:461-474. [PMID: 31105345 PMCID: PMC6521706 DOI: 10.1111/rssc.12271] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A sequentially adaptive Bayesian design is presented for a clinical trial of cord blood derived natural killer cells to treat severe hematologic malignancies. Given six prognostic subgroups defined by disease type and severity, the goal is to optimize cell dose in each subgroup. The trial has five co-primary outcomes, the times to severe toxicity, cytokine release syndrome, disease progression or response, and death. The design assumes a multivariate Weibull regression model, with marginals depending on dose, subgroup, and patient frailties that induce association among the event times. Utilities of all possible combinations of the nonfatal outcomes over the first 100 days following cell infusion are elicited, with posterior mean utility used as a criterion to optimize dose. For each subgroup, the design stops accrual to doses having an unacceptably high death rate, and at the end of the trial selects the optimal safe dose. A simulation study is presented to validate the design's safety, ability to identify optimal doses, and robustness, and to compare it to a simplified design that ignores patient heterogeneity.
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Affiliation(s)
- Juhee Lee
- Department of Applied Mathematics and Statistics, University of California at Santa Cruz, Santa Cruz, CA
| | - Peter F. Thall
- Department of Biostatistics, M.D. Anderson Cancer Center, Houston, TX
| | - Katy Rezvani
- Department of Stem Cell Transplantation and Cellular Therapy, M.D. Anderson Cancer Center, Houston, TX
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Kakurai Y, Kaneko S, Hamada C, Hirakawa A. Dose individualization and variable selection by using the Bayesian lasso in early phase dose finding trials. J R Stat Soc Ser C Appl Stat 2018. [DOI: 10.1111/rssc.12326] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
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Guo B, Zang Y. A Bayesian adaptive phase II clinical trial design accounting for spatial variation. Stat Methods Med Res 2018; 28:3187-3204. [DOI: 10.1177/0962280218797149] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Conventional phase II clinical trials evaluate the treatment effects under the assumption of patient homogeneity. However, due to inter-patient heterogeneity, the effect of a treatment may differ remarkably among subgroups of patients. Besides patient’s individual characteristics such as age, gender, and biomarker status, a substantial amount of this heterogeneity could be due to the spatial variation across geographic regions because of unmeasured or unknown spatially varying environmental and social exposures. In this article, we propose a hierarchical Bayesian adaptive design for two-arm randomized phase II clinical trials that accounts for the spatial variation as well as patient’s individual characteristics. We treat the treatment efficacy as an ordinal outcome and quantify the desirability of each possible category of the ordinal efficacy using a utility function. A cumulative probit mixed model is used to relate efficacy to patient-specific covariates and geographic region spatial effects. Spatial dependence between regions is induced through the conditional autoregressive priors on the spatial effects. A two-stage design is proposed to adaptively assign patients to desirable treatments according to each patient’s spatial information and individual covariates and make treatment recommendations at the end of the trial based on the overall treatment effect. Simulation studies show that our proposed design has good operating characteristics and significantly outperforms an alternative phase II trial design that ignores the spatial variation.
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Affiliation(s)
- Beibei Guo
- Department of Experimental Statistics, Louisiana State University, Baton Rouge, LA, USA
| | - Yong Zang
- Department of Biostatistics, School of Medicine, Indiana University, Indianapolis, IN, USA
- Center for Computational Biology and Bioinformatics, Indiana University, Indianapolis, IN, USA
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Murray TA, Yuan Y, Thall PF, Elizondo JH, Hofstetter WL. A utility-based design for randomized comparative trials with ordinal outcomes and prognostic subgroups. Biometrics 2018; 74:1095-1103. [PMID: 29359314 PMCID: PMC6054910 DOI: 10.1111/biom.12842] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Revised: 11/01/2018] [Accepted: 11/01/2017] [Indexed: 11/28/2022]
Abstract
A design is proposed for randomized comparative trials with ordinal outcomes and prognostic subgroups. The design accounts for patient heterogeneity by allowing possibly different comparative conclusions within subgroups. The comparative testing criterion is based on utilities for the levels of the ordinal outcome and a Bayesian probability model. Designs based on two alternative models that include treatment-subgroup interactions are considered, the proportional odds model and a non-proportional odds model with a hierarchical prior that shrinks toward the proportional odds model. A third design that assumes homogeneity and ignores possible treatment-subgroup interactions also is considered. The three approaches are applied to construct group sequential designs for a trial of nutritional prehabilitation versus standard of care for esophageal cancer patients undergoing chemoradiation and surgery, including both untreated patients and salvage patients whose disease has recurred following previous therapy. A simulation study is presented that compares the three designs, including evaluation of within-subgroup type I and II error probabilities under a variety of scenarios including different combinations of treatment-subgroup interactions.
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Affiliation(s)
- Thomas A Murray
- Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota, U.S.A
| | - Ying Yuan
- Department of Biostatistics, The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Peter F Thall
- Department of Biostatistics, The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Joan H Elizondo
- Department of Clinical Nutrition, The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Wayne L Hofstetter
- Department of Thoracic and Cardiovascular Surgery, The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
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Cotterill A, Jaki T. Dose-escalation strategies which use subgroup information. Pharm Stat 2018; 17:414-436. [PMID: 29900666 PMCID: PMC6175353 DOI: 10.1002/pst.1860] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Revised: 01/30/2018] [Accepted: 02/26/2018] [Indexed: 12/04/2022]
Abstract
Dose-escalation trials commonly assume a homogeneous trial population to identify a single recommended dose of the experimental treatment for use in future trials. Wrongly assuming a homogeneous population can lead to a diluted treatment effect. Equally, exclusion of a subgroup that could in fact benefit from the treatment can cause a beneficial treatment effect to be missed. Accounting for a potential subgroup effect (ie, difference in reaction to the treatment between subgroups) in dose-escalation can increase the chance of finding the treatment to be efficacious in a larger patient population. A standard Bayesian model-based method of dose-escalation is extended to account for a subgroup effect by including covariates for subgroup membership in the dose-toxicity model. A stratified design performs well but uses available data inefficiently and makes no inferences concerning presence of a subgroup effect. A hypothesis test could potentially rectify this problem but the small sample sizes result in a low-powered test. As an alternative, the use of spike and slab priors for variable selection is proposed. This method continually assesses the presence of a subgroup effect, enabling efficient use of the available trial data throughout escalation and in identifying the recommended dose(s). A simulation study, based on real trial data, was conducted and this design was found to be both promising and feasible.
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Affiliation(s)
- Amy Cotterill
- Cancer Research UK Clinical Trials Unit, Institute of Cancer and Genomic SciencesUniversity of BirminghamBirminghamUK
| | - Thomas Jaki
- Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and StatisticsLancaster UniversityLancasterUK
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Liu S, Guo B, Yuan Y. A Bayesian Phase I/II Trial Design for Immunotherapy. J Am Stat Assoc 2018; 113:1016-1027. [PMID: 31741544 PMCID: PMC6860919 DOI: 10.1080/01621459.2017.1383260] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Revised: 04/01/2017] [Indexed: 10/18/2022]
Abstract
Immunotherapy is an innovative treatment approach that stimulates a patient's immune system to fight cancer. It demonstrates characteristics distinct from conventional chemotherapy and stands to revolutionize cancer treatment. We propose a Bayesian phase I/II dosefinding design that incorporates the unique features of immunotherapy by simultaneously considering three outcomes: immune response, toxicity and efficacy. The objective is to identify the biologically optimal dose, defined as the dose with the highest desirability in the risk-benefit tradeoff. An Emax model is utilized to describe the marginal distribution of the immune response. Conditional on the immune response, we jointly model toxicity and efficacy using a latent variable approach. Using the accumulating data, we adaptively randomize patients to experimental doses based on the continuously updated model estimates. A simulation study shows that our proposed design has good operating characteristics in terms of selecting the target dose and allocating patients to the target dose.
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Affiliation(s)
- Suyu Liu
- Assistant Professor, Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, TX 77030-4009
| | - Beibei Guo
- Assistant Professor, Department of Experimental Statistics, Louisiana State University, Baton Rouge, LA 70803
| | - Ying Yuan
- Professor, Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, TX 77030-4009,
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Guo B, Li D, Yuan Y. SPIRIT: A seamless phase I/II randomized design for immunotherapy trials. Pharm Stat 2018; 17:527-540. [DOI: 10.1002/pst.1869] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2017] [Revised: 02/16/2018] [Accepted: 04/19/2018] [Indexed: 01/24/2023]
Affiliation(s)
- Beibei Guo
- Department of Experimental Statistics; Louisiana State University; Baton Rouge LA 70803 USA
| | | | - Ying Yuan
- Department of Biostatistics; The University of Texas MD Anderson Cancer Center; Houston TX 77030 USA
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40
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Guo B, Park Y, Liu S. A utility‐based Bayesian phase I–II design for immunotherapy trials with progression‐free survival end point. J R Stat Soc Ser C Appl Stat 2018. [DOI: 10.1111/rssc.12288] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Beibei Guo
- Louisiana State University Baton Rouge USA
| | - Yeonhee Park
- University of Texas MD Anderson Cancer Center Houston USA
| | - Suyu Liu
- University of Texas MD Anderson Cancer Center Houston USA
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Yan F, Thall PF, Lu KH, Gilbert MR, Yuan Y. Phase I-II clinical trial design: a state-of-the-art paradigm for dose finding. Ann Oncol 2018; 29:694-699. [PMID: 29267863 PMCID: PMC5888967 DOI: 10.1093/annonc/mdx795] [Citation(s) in RCA: 52] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
Background Conventional phase I algorithms for finding a phase-2 recommended dose (P2RD) based on toxicity alone is problematic because the maximum tolerated dose (MTD) is not necessarily the optimal dose with the most desirable risk-benefit trade-off. Moreover, the increasingly common practice of treating an expansion cohort at a chosen MTD has undesirable consequences that may not be obvious. Patients and methods We review the phase I-II paradigm and the EffTox design, which utilizes both efficacy and toxicity to choose optimal doses for successive patient cohorts and find the optimal P2RD. We conduct a computer simulation study to compare the performance of the EffTox design with the traditional 3 + 3 design and the continuous reassessment method. Results By accounting for the risk-benefit trade-off, the EffTox phase I-II design overcomes the limitations of conventional toxicity-based phase I designs. Numerical simulations show that the EffTox design has higher probabilities of identifying the optimal dose and treats more patients at the optimal dose. Conclusions Phase I-II designs, such as the EffTox design, provide a coherent and efficient approach to finding the optimal P2RD by explicitly accounting for risk-benefit trade-offs underlying medical decisions.
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Affiliation(s)
- F Yan
- Division of Biostatistics, China Pharmaceutical University, Nanjing, China
| | - P F Thall
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, USA
| | - K H Lu
- Department of Gynecologic Oncology and Reproductive Medicine, The University of Texas MD Anderson Cancer Center, Houston, USA
| | - M R Gilbert
- Center for Cancer Research, National Cancer Institute, Bethesda, USA
| | - Y Yuan
- Division of Biostatistics, China Pharmaceutical University, Nanjing, China; Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, USA.
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