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Cao W, Zhu H, Wang L, Zhang L, Yu J. Doubly adaptive biased coin design to improve Bayesian clinical trials with time-to-event endpoints. Stat Med 2024; 43:1743-1758. [PMID: 38387866 DOI: 10.1002/sim.10047] [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: 04/24/2023] [Revised: 02/05/2024] [Accepted: 02/12/2024] [Indexed: 02/24/2024]
Abstract
Clinical trialists often face the challenge of balancing scientific questions with other design features, such as improving efficiency, minimizing exposure to inferior treatments, and simultaneously comparing multiple treatments. While Bayesian response adaptive randomization (RAR) is a popular and effective method for achieving these objectives, it is known to have large variability and a lack of explicit theoretical results, making its use in clinical trials a subject of concern. It is desirable to propose a design that targets the same allocation proportion as Bayesian RAR and achieves the above objectives but addresses the concerns over Bayesian RAR. We propose the frequentist doubly adaptive biased coin designs (DBCD) targeting ethical allocation proportions from the Bayesian framework to satisfy different objectives in clinical trials with time-to-event endpoints. We derive the theoretical properties of the proposed adaptive randomization design and show through comprehensive numerical simulations that it can achieve ethical objectives without sacrificing efficiency. Our combined theoretical and numerical results offer a strong foundation for the practical use of RAR in real clinical trials.
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Affiliation(s)
- Wenhao Cao
- Division of Biostatistics and Health Data Science, University of Minnesota, Minneapolis, Minnesota, USA
| | - Hongjian Zhu
- Statistical Innovation Group, AbbVie Inc., Virtual Office, Sugar Land, Texas, USA
| | - Li Wang
- Statistical Innovation Group, AbbVie Inc., North Chicago, Illinois, USA
| | - Lixin Zhang
- Center for Data Science and School of Mathematical Sciences, Zhejiang University, Hangzhou, China
| | - Jun Yu
- Medical Affairs and Health Technology Assessment Statistics, AbbVie Inc., Virtual Office, Sugar Land, Texas, USA
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2
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Zhu H, Wong WK. An Overview of Adaptive Designs and Some of Their Challenges, Benefits, and Innovative Applications. J Med Internet Res 2023; 25:e44171. [PMID: 37843888 PMCID: PMC10616728 DOI: 10.2196/44171] [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: 11/08/2022] [Revised: 03/25/2023] [Accepted: 05/16/2023] [Indexed: 10/17/2023] Open
Abstract
Adaptive designs are increasingly developed and used to improve all phases of clinical trials and in biomedical studies in various ways to address different statistical issues. We first present an overview of adaptive designs and note their numerous advantages over traditional clinical trials. In particular, we provide a concrete demonstration that shows how recent adaptive design strategies can further improve an adaptive trial implemented 13 years ago. Despite their usefulness, adaptive designs are still not widely implemented in clinical trials. We offer a few possible reasons and propose some ways to use them more broadly in practice, which include greater availability of software tools and interactive websites to generate optimal adaptive trials freely and effectively, including the use of metaheuristics to facilitate the search for an efficient trial design. To this end, we present several web-based tools for finding various adaptive and nonadaptive optimal designs and discuss nature-inspired metaheuristics. Metaheuristics are assumptions-free general purpose optimization algorithms widely used in computer science and engineering to tackle all kinds of challenging optimization problems, and their use in designing clinical trials is just emerging. We describe a few recent such applications and some of their capabilities for designing various complex trials. Particle swarm optimization is an exemplary nature-inspired algorithm, and similar to others, it has a simple definition but many moving parts, making it hard to study its properties analytically. We investigated one of its hitherto unstudied issues on how to bring back out-of-range candidates during the search for the optimum of the search domain and show that different strategies can impact the success and time of the search. We conclude with a few caveats on the use of metaheuristics for a successful search.
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Affiliation(s)
- Hongjian Zhu
- Statistical Innovation Group, AbbVie Inc., Virtual Office, Sugar Land, TX, United States
| | - Weng Kee Wong
- Department of Biostatistics, Fielding School of Public Health, University of California at Los Angeles, Los Angeles, CA, United States
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3
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Giovagnoli A, Verdinelli I. Bayesian Adaptive Randomization with Compound Utility Functions. Stat Sci 2023. [DOI: 10.1214/21-sts848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Alessandra Giovagnoli
- Alessandra Giovagnoli is retired Professor, Department of Statistical Sciences, Alma Mater Studiorum, Università di Bologna, Bologna, Italy
| | - Isabella Verdinelli
- Isabella Verdinelli is Professor in Residence, Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
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4
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Ogura T, Shiraishi C. Parameter estimation of Weibull distribution for the number of days between drug administration and early onset adverse event. J Biopharm Stat 2022; 33:386-399. [PMID: 36511635 DOI: 10.1080/10543406.2022.2154940] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The Weibull distribution is applied to the number of days between the start date of drug administration and the date of occurrence of an adverse event. The tendency of occurrence of adverse events can be clarified by estimating the two- or three-parameter Weibull distribution, using the data regarding the number of days. Our purpose is to estimate the parameters of the Weibull distribution with high accuracy, even in low-reported adverse events, such as new drugs, polypharmacy and small clinical trials. Furthermore, the two-sample Kolmogorov - Smirnov test (two-sided) is used to examine whether the tendency of occurrence of adverse events is different for two Weibull distributions estimated from two drugs with similar efficacy. We used discrete data derived from FDA Adverse Event Reporting System (FAERS), as the FAERS data are presented in years, months and days without hours and minutes. Because this study focuses on early onset adverse events, data may be contained 0 days. The discreteness of the data and the fact that it may include zero make this distribution different from the general Weibull distribution, which is defined for continuous data greater than zero. We search for the optimal parameter estimation method for the Weibull distribution under these two conditions, and verify its effectiveness using Monte Carlo simulations and FAERS data. Because the results obtained from FAERS data may differ depending on data handling, we describe the of data handling technique and the sample code that can reproduce the results.
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Affiliation(s)
- Toru Ogura
- Clinical Research Support Center, Mie University Hospital, Tsu, Mie, Japan
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5
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Yu Y, Xu C, Zhong J, Cheung SH. Comparison of treatments with ordinal responses in trials with sequential monitoring and response-adaptive randomization. Stat Med 2022; 41:5061-5083. [PMID: 35973712 DOI: 10.1002/sim.9554] [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: 04/15/2022] [Revised: 07/06/2022] [Accepted: 07/26/2022] [Indexed: 11/08/2022]
Abstract
In clinical trials, comparisons of treatments with ordinal responses are frequently conducted using the proportional odds model. However, the use of this model necessitates the adoption of the proportional odds assumption, which may not be appropriate. In particular, when responses are skewed, the use of the proportional odds model may result in a markedly inflated type I error rate. The latent Weibull distribution has recently been proposed to remedy this problem, and it has been demonstrated to be superior to the proportional odds model, especially when response-adaptive randomization is incorporated. However, there are several drawbacks associated with the latent Weibull model and the previously suggested response-adaptive treatment randomization scheme. In this paper, we propose the modified latent Weibull model to address these issues. Based on the modified latent Weibull model, the original response-adaptive design was also revised. In addition, the group sequential monitoring mechanism was included to enable interim analyses to be performed to determine, during a trial, whether a specific treatment is significantly more effective than another. If so, this will enable the trial to be terminated at a much earlier stage than a trial based on a fixed sample size. We performed a simulation study that clearly demonstrated the merits of our proposed framework. Furthermore, we redesigned a clinical study to further illustrate the advantages of our response-adaptive approach.
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Affiliation(s)
- Yian Yu
- Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, China
| | - Cong Xu
- Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, China
| | - Junjiang Zhong
- School of Mathematics and Statistics, Xiamen University of Technology, Xiamen, China
| | - Siu Hung Cheung
- Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China
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Bandyopadhyay U, Bhattacharya R. A Randomized Two Stage Adaptively Censored Design With Application to Testing. REVISTA COLOMBIANA DE ESTADÍSTICA 2019. [DOI: 10.15446/rce.v42n2.65344] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Abstract
A two stage randomized design is developed for two treatment clinical trials in which response variables are exponential and the observations are censored by using failure censoring and time censoring in the first and second stages respectively. The censoring time for the second stage is determined from the outcomes of the first stage. An application to testing for the equality of treatment effects is given along with a comparative study with relevant properties.
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Ryeznik Y, Sverdlov O, Hooker AC. Implementing Optimal Designs for Dose-Response Studies Through Adaptive Randomization for a Small Population Group. AAPS JOURNAL 2018; 20:85. [PMID: 30027336 DOI: 10.1208/s12248-018-0242-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Accepted: 06/18/2018] [Indexed: 11/30/2022]
Abstract
In dose-response studies with censored time-to-event outcomes, D-optimal designs depend on the true model and the amount of censored data. In practice, such designs can be implemented adaptively, by performing dose assignments according to updated knowledge of the dose-response curve at interim analysis. It is also essential that treatment allocation involves randomization-to mitigate various experimental biases and enable valid statistical inference at the end of the trial. In this work, we perform a comparison of several adaptive randomization procedures that can be used for implementing D-optimal designs for dose-response studies with time-to-event outcomes with small to moderate sample sizes. We consider single-stage, two-stage, and multi-stage adaptive designs. We also explore robustness of the designs to experimental (chronological and selection) biases. Simulation studies provide evidence that both the choice of an allocation design and a randomization procedure to implement the target allocation impact the quality of dose-response estimation, especially for small samples. For best performance, a multi-stage adaptive design with small cohort sizes should be implemented using a randomization procedure that closely attains the targeted D-optimal design at each stage. The results of the current work should help clinical investigators select an appropriate randomization procedure for their dose-response study.
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Affiliation(s)
- Yevgen Ryeznik
- Department of Mathematics, Uppsala University, Room Å14133 Lägerhyddsvägen 1, Hus 1, 6 och 7, 751 06, Uppsala, Sweden. .,Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden.
| | - Oleksandr Sverdlov
- Early Development Biostatistics, Novartis Institutes for Biomedical Research, East Hannover, New Jersey, USA
| | - Andrew C Hooker
- Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
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Ryeznik Y, Sverdlov O, Hooker AC. Adaptive Optimal Designs for Dose-Finding Studies with Time-to-Event Outcomes. AAPS JOURNAL 2017; 20:24. [PMID: 29285730 DOI: 10.1208/s12248-017-0166-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2017] [Accepted: 10/28/2017] [Indexed: 11/30/2022]
Abstract
We consider optimal design problems for dose-finding studies with censored Weibull time-to-event outcomes. Locally D-optimal designs are investigated for a quadratic dose-response model for log-transformed data subject to right censoring. Two-stage adaptive D-optimal designs using maximum likelihood estimation (MLE) model updating are explored through simulation for a range of different dose-response scenarios and different amounts of censoring in the model. The adaptive optimal designs are found to be nearly as efficient as the locally D-optimal designs. A popular equal allocation design can be highly inefficient when the amount of censored data is high and when the Weibull model hazard is increasing. The issues of sample size planning/early stopping for an adaptive trial are investigated as well. The adaptive D-optimal design with early stopping can potentially reduce study size while achieving similar estimation precision as the fixed allocation design.
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Affiliation(s)
- Yevgen Ryeznik
- Department of Mathematics, Uppsala University, Room Å14133 Lägerhyddsvägen 1, Hus 1, 6 och 7, 751 06, Uppsala, Sweden. .,Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden.
| | - Oleksandr Sverdlov
- Early Development Biostatistics - Translational Medicine, Novartis Pharmaceuticals Corporation, East Hanover, New Jersey, USA
| | - Andrew C Hooker
- Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
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Hyun SW, Wong WK. Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels. Int J Biostat 2015; 11:253-71. [PMID: 26565557 DOI: 10.1515/ijb-2015-0044] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
We construct an optimal design to simultaneously estimate three common interesting features in a dose-finding trial with possibly different emphasis on each feature. These features are (1) the shape of the dose-response curve, (2) the median effective dose and (3) the minimum effective dose level. A main difficulty of this task is that an optimal design for a single objective may not perform well for other objectives. There are optimal designs for dual objectives in the literature but we were unable to find optimal designs for 3 or more objectives to date with a concrete application. A reason for this is that the approach for finding a dual-objective optimal design does not work well for a 3 or more multiple-objective design problem. We propose a method for finding multiple-objective optimal designs that estimate the three features with user-specified higher efficiencies for the more important objectives. We use the flexible 4-parameter logistic model to illustrate the methodology but our approach is applicable to find multiple-objective optimal designs for other types of objectives and models. We also investigate robustness properties of multiple-objective optimal designs to mis-specification in the nominal parameter values and to a variation in the optimality criterion. We also provide computer code for generating tailor made multiple-objective optimal designs.
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Moatti M, Chevret S, Zohar S, Rosenberger WF. A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes. Methods Inf Med 2015; 55:4-13. [PMID: 26404511 DOI: 10.3414/me14-01-0132] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Accepted: 05/21/2015] [Indexed: 01/26/2023]
Abstract
BACKGROUND Response-adaptive randomisation designs have been proposed to improve the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosenberger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. OBJECTIVES The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the estimated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by redesigning a clinical trial on multiple myeloma. METHODS To handle continuous monitoring of data, we propose a Bayesian response-adaptive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simulation study to assess and compare the performance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive - either frequentist or fully Bayesian - designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior distribution of the log hazard ratio were computed. The method is then illustrated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. RESULTS As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mixture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. CONCLUSIONS Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.
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Affiliation(s)
| | - S Chevret
- Sylvie Chevret, Biostatistics and Clinical Epidemiology (ECSTRA) Team, Paris Diderot University, Saint-Louis hospital, 1, avenue Claude Vellefaux, 75475 Paris Cedex 10, France, E-mail:
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Ryeznik Y, Sverdlov O, Wong WK. RARtool: A MATLAB Software Package for Designing Response-Adaptive Randomized Clinical Trials with Time-to-Event Outcomes. J Stat Softw 2015; 66. [PMID: 26997924 DOI: 10.18637/jss.v066.i01] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022] Open
Abstract
Response-adaptive randomization designs are becoming increasingly popular in clinical trial practice. In this paper, we present RARtool, a user interface software developed in MATLAB for designing response-adaptive randomized comparative clinical trials with censored time-to-event outcomes. The RARtool software can compute different types of optimal treatment allocation designs, and it can simulate response-adaptive randomization procedures targeting selected optimal allocations. Through simulations, an investigator can assess design characteristics under a variety of experimental scenarios and select the best procedure for practical implementation. We illustrate the utility of our RARtool software by redesigning a survival trial from the literature.
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Affiliation(s)
- Yevgen Ryeznik
- Department of Mathematics, Uppsala University, Lägerhyddsvägen 1, Hus 1, 5 och 7, Box 480, 751 06, Uppsala, Sweden,
| | - Oleksandr Sverdlov
- R&D Global Biostatistics, EMD Serono, Inc., 45A Middlesex Turnpike, Billerica, MA 01821, United States of America,
| | - Weng Kee Wong
- Department of Biostatistics, Fielding School of Public Health, University of California, Los Angeles, Los Angeles, CA 90095, United States of America,
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