1
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Robertson DS, Choodari-Oskooei B, Dimairo M, Flight L, Pallmann P, Jaki T. Point estimation for adaptive trial designs II: Practical considerations and guidance. Stat Med 2023; 42:2496-2520. [PMID: 37021359 PMCID: PMC7614609 DOI: 10.1002/sim.9734] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Revised: 01/20/2023] [Accepted: 03/18/2023] [Indexed: 04/07/2023]
Abstract
In adaptive clinical trials, the conventional end-of-trial point estimate of a treatment effect is prone to bias, that is, a systematic tendency to deviate from its true value. As stated in recent FDA guidance on adaptive designs, it is desirable to report estimates of treatment effects that reduce or remove this bias. However, it may be unclear which of the available estimators are preferable, and their use remains rare in practice. This article is the second in a two-part series that studies the issue of bias in point estimation for adaptive trials. Part I provided a methodological review of approaches to remove or reduce the potential bias in point estimation for adaptive designs. In part II, we discuss how bias can affect standard estimators and assess the negative impact this can have. We review current practice for reporting point estimates and illustrate the computation of different estimators using a real adaptive trial example (including code), which we use as a basis for a simulation study. We show that while on average the values of these estimators can be similar, for a particular trial realization they can give noticeably different values for the estimated treatment effect. Finally, we propose guidelines for researchers around the choice of estimators and the reporting of estimates following an adaptive design. The issue of bias should be considered throughout the whole lifecycle of an adaptive design, with the estimation strategy prespecified in the statistical analysis plan. When available, unbiased or bias-reduced estimates are to be preferred.
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Affiliation(s)
| | - Babak Choodari-Oskooei
- MRC Clinical Trials Unit at UCL, Institute of Clinical Trials and Methodology, University College London, London, UK
| | - Munya Dimairo
- School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK
| | - Laura Flight
- School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK
| | | | - Thomas Jaki
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
- Faculty of Informatics and Data Science, University of Regensburg, Regensburg, Germany
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2
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Khan JN, Kimani PK, Glimm E, Stallard N. Adjusting for treatment selection in phase II/III clinical trials with time to event data. Stat Med 2023; 42:146-163. [PMID: 36419206 PMCID: PMC10098876 DOI: 10.1002/sim.9606] [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: 03/22/2022] [Revised: 09/25/2022] [Accepted: 11/01/2022] [Indexed: 11/26/2022]
Abstract
Phase II/III clinical trials are efficient two-stage designs that test multiple experimental treatments. In stage 1, patients are allocated to the control and all experimental treatments, with the data collected from them used to select experimental treatments to continue to stage 2. Patients recruited in stage 2 are allocated to the selected treatments and the control. Combined data of stage 1 and stage 2 are used for a confirmatory phase III analysis. Appropriate analysis needs to adjust for selection bias of the stage 1 data. Point estimators exist for normally distributed outcome data. Extending these estimators to time to event data is not straightforward because treatment selection is based on correlated treatment effects and stage 1 patients who do not get events in stage 1 are followed-up in stage 2. We have derived an approximately uniformly minimum variance conditional unbiased estimator (UMVCUE) and compared its biases and mean squared errors to existing bias adjusted estimators. In simulations, one existing bias adjusted estimator has similar properties as the practically unbiased UMVCUE while the others can have noticeable biases but they are less variable than the UMVCUE. For confirmatory phase II/III clinical trials where unbiased estimators are desired, we recommend the UMVCUE or the existing estimator with which it has similar properties.
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Affiliation(s)
| | - Peter K Kimani
- Warwick Medical School, University of Warwick, Coventry, UK
| | | | - Nigel Stallard
- Warwick Medical School, University of Warwick, Coventry, UK
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3
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Robertson DS, Choodari‐Oskooei B, Dimairo M, Flight L, Pallmann P, Jaki T. Point estimation for adaptive trial designs I: A methodological review. Stat Med 2023; 42:122-145. [PMID: 36451173 PMCID: PMC7613995 DOI: 10.1002/sim.9605] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Revised: 10/21/2022] [Accepted: 11/01/2022] [Indexed: 12/02/2022]
Abstract
Recent FDA guidance on adaptive clinical trial designs defines bias as "a systematic tendency for the estimate of treatment effect to deviate from its true value," and states that it is desirable to obtain and report estimates of treatment effects that reduce or remove this bias. The conventional end-of-trial point estimates of the treatment effects are prone to bias in many adaptive designs, because they do not take into account the potential and realized trial adaptations. While much of the methodological developments on adaptive designs have tended to focus on control of type I error rates and power considerations, in contrast the question of biased estimation has received relatively less attention. This article is the first in a two-part series that studies the issue of potential bias in point estimation for adaptive trials. Part I provides a comprehensive review of the methods to remove or reduce the potential bias in point estimation of treatment effects for adaptive designs, while part II illustrates how to implement these in practice and proposes a set of guidelines for trial statisticians. The methods reviewed in this article can be broadly classified into unbiased and bias-reduced estimation, and we also provide a classification of estimators by the type of adaptive design. We compare the proposed methods, highlight available software and code, and discuss potential methodological gaps in the literature.
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Affiliation(s)
| | | | - Munya Dimairo
- School of Health and Related Research (ScHARR)University of SheffieldSheffieldUK
| | - Laura Flight
- School of Health and Related Research (ScHARR)University of SheffieldSheffieldUK
| | | | - Thomas Jaki
- MRC Biostatistics UnitUniversity of CambridgeCambridgeUK
- Faculty of Informatics and Data ScienceUniversity of RegensburgRegensburgGermany
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4
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Marschner IC, Schou M, Martin AJ. Estimation of the treatment effect following a clinical trial that stopped early for benefit. Stat Methods Med Res 2022; 31:2456-2469. [PMID: 36065593 DOI: 10.1177/09622802221122445] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
When a clinical trial stops early for benefit, the maximum likelihood estimate (MLE) of the treatment effect may be subject to overestimation bias. Several authors have proposed adjusting for this bias using the conditional MLE, which is obtained by conditioning on early stopping. However, this approach has a fundamental problem in that the adjusted estimate may not be in the direction of benefit, even though the study has stopped early due to benefit. In this paper, we address this problem by embedding both the MLE and the conditional MLE within a broader class of penalised likelihood estimates, and choosing a member of the class that is a favourable compromise between the two. This penalised MLE, and its associated confidence interval, always lie in the direction of benefit when the study stops early for benefit. We study its properties using both simulations and analyses of the ENZAMET trial in metastatic prostate cancer. Conditional on stopping early for benefit, the method is found to have good unbiasedness and coverage properties, along with very favourable efficiency at earlier interim analyses. We recommend the penalised MLE as a supplementary analysis to a conventional primary analysis when a clinical trial stops early for benefit.
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Affiliation(s)
- Ian C Marschner
- 110588NHMRC Clinical Trials Centre, University of Sydney, Sydney, Australia
| | - Manjula Schou
- 110588NHMRC Clinical Trials Centre, University of Sydney, Sydney, Australia
| | - Andrew J Martin
- 110588NHMRC Clinical Trials Centre, University of Sydney, Sydney, Australia
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5
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A comparison of estimation methods adjusting for selection bias in adaptive enrichment designs with time‐to‐event endpoints. Stat Med 2022; 41:1767-1779. [DOI: 10.1002/sim.9327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Revised: 01/03/2022] [Accepted: 01/04/2022] [Indexed: 11/07/2022]
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6
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Kimani PK, Todd S, Renfro LA, Glimm E, Khan JN, Kairalla JA, Stallard N. Point and interval estimation in two-stage adaptive designs with time to event data and biomarker-driven subpopulation selection. Stat Med 2020; 39:2568-2586. [PMID: 32363603 PMCID: PMC7785132 DOI: 10.1002/sim.8557] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Revised: 03/31/2020] [Accepted: 04/06/2020] [Indexed: 02/02/2023]
Abstract
In personalized medicine, it is often desired to determine if all patients or only a subset of them benefit from a treatment. We consider estimation in two-stage adaptive designs that in stage 1 recruit patients from the full population. In stage 2, patient recruitment is restricted to the part of the population, which, based on stage 1 data, benefits from the experimental treatment. Existing estimators, which adjust for using stage 1 data for selecting the part of the population from which stage 2 patients are recruited, as well as for the confirmatory analysis after stage 2, do not consider time to event patient outcomes. In this work, for time to event data, we have derived a new asymptotically unbiased estimator for the log hazard ratio and a new interval estimator with good coverage probabilities and probabilities that the upper bounds are below the true values. The estimators are appropriate for several selection rules that are based on a single or multiple biomarkers, which can be categorical or continuous.
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Affiliation(s)
| | - Susan Todd
- Department of Mathematics and Statistics, University of Reading, Reading, UK
| | - Lindsay A. Renfro
- Division of Biostatistics, University of Southern California, Los Angeles, CA
| | | | | | - John A. Kairalla
- Department of Biostatistics, University of Florida, Gainesville, Florida
| | - Nigel Stallard
- Warwick Medical School, University of Warwick, Coventry, UK
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7
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Stallard N, Hampson L, Benda N, Brannath W, Burnett T, Friede T, Kimani PK, Koenig F, Krisam J, Mozgunov P, Posch M, Wason J, Wassmer G, Whitehead J, Williamson SF, Zohar S, Jaki T. Efficient Adaptive Designs for Clinical Trials of Interventions for COVID-19. Stat Biopharm Res 2020; 12:483-497. [PMID: 34191981 PMCID: PMC8011600 DOI: 10.1080/19466315.2020.1790415] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Revised: 06/23/2020] [Accepted: 06/24/2020] [Indexed: 02/06/2023]
Abstract
The COVID-19 pandemic has led to an unprecedented response in terms of clinical research activity. An important part of this research has been focused on randomized controlled clinical trials to evaluate potential therapies for COVID-19. The results from this research need to be obtained as rapidly as possible. This presents a number of challenges associated with considerable uncertainty over the natural history of the disease and the number and characteristics of patients affected, and the emergence of new potential therapies. These challenges make adaptive designs for clinical trials a particularly attractive option. Such designs allow a trial to be modified on the basis of interim analysis data or stopped as soon as sufficiently strong evidence has been observed to answer the research question, without compromising the trial's scientific validity or integrity. In this article, we describe some of the adaptive design approaches that are available and discuss particular issues and challenges associated with their use in the pandemic setting. Our discussion is illustrated by details of four ongoing COVID-19 trials that have used adaptive designs.
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Affiliation(s)
- Nigel Stallard
- Statistics and Epidemiology, Division of Health Sciences, Warwick Medical School, University of Warwick, Coventry, UK
| | - Lisa Hampson
- Advanced Methodology and Data Science, Novartis Pharma AG, Basel, Switzerland
| | - Norbert Benda
- The Federal Institute for Drugs and Medical Devices (BfArM), Bonn, Germany
| | - Werner Brannath
- Institute for Statistics, University of Bremen, Bremen, Germany
| | - Thomas Burnett
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Peter K. Kimani
- Statistics and Epidemiology, Division of Health Sciences, Warwick Medical School, University of Warwick, Coventry, UK
| | - Franz Koenig
- Section for Medical Statistics, CeMSIIS, Medical University of Vienna, Vienna, Austria
| | - Johannes Krisam
- Institute of Medical Biometry and Informatics, University of Heidelberg, Heidelberg, Germany
| | - Pavel Mozgunov
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - Martin Posch
- Section for Medical Statistics, CeMSIIS, Medical University of Vienna, Vienna, Austria
| | - James Wason
- Population Health Sciences Institute, Newcastle University, Newcastle upon Tyne, UK
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | | | - John Whitehead
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - S. Faye Williamson
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - Sarah Zohar
- INSERM, Centre de Recherche des Cordeliers, Sorbonne Université, Université de Paris, Paris, France
| | - Thomas Jaki
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
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8
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Whitehead J, Desai Y, Jaki T. Estimation of treatment effects following a sequential trial of multiple treatments. Stat Med 2020; 39:1593-1609. [PMID: 32207166 PMCID: PMC7217198 DOI: 10.1002/sim.8497] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Revised: 11/23/2019] [Accepted: 12/16/2019] [Indexed: 11/13/2022]
Abstract
When a clinical trial is subject to a series of interim analyses as a result of which the study may be terminated or modified, final frequentist analyses need to take account of the design used. Failure to do so may result in overstated levels of significance, biased effect estimates and confidence intervals with inadequate coverage probabilities. A wide variety of valid methods of frequentist analysis have been devised for sequential designs comparing a single experimental treatment with a single control treatment. It is less clear how to perform the final analysis of a sequential or adaptive design applied in a more complex setting, for example, to determine which treatment or set of treatments amongst several candidates should be recommended. This article has been motivated by consideration of a trial in which four treatments for sepsis are to be compared, with interim analyses allowing the dropping of treatments or termination of the trial to declare a single winner or to conclude that there is little difference between the treatments that remain. The approach taken is based on the method of Rao‐Blackwellization which enhances the accuracy of unbiased estimates available from the first interim analysis by taking their conditional expectations given final sufficient statistics. Analytic approaches to determine such expectations are difficult and specific to the details of the design: instead “reverse simulations” are conducted to construct replicate realizations of the first interim analysis from the final test statistics. The method also provides approximate confidence intervals for the differences between treatments.
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Affiliation(s)
- John Whitehead
- Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - Yasin Desai
- Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - Thomas Jaki
- Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
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9
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Kimani PK, Todd S, Renfro LA, Stallard N. Point estimation following two-stage adaptive threshold enrichment clinical trials. Stat Med 2018; 37:3179-3196. [PMID: 29855066 PMCID: PMC6175016 DOI: 10.1002/sim.7831] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Revised: 03/16/2018] [Accepted: 04/30/2018] [Indexed: 11/11/2022]
Abstract
Recently, several study designs incorporating treatment effect assessment in biomarker-based subpopulations have been proposed. Most statistical methodologies for such designs focus on the control of type I error rate and power. In this paper, we have developed point estimators for clinical trials that use the two-stage adaptive enrichment threshold design. The design consists of two stages, where in stage 1, patients are recruited in the full population. Stage 1 outcome data are then used to perform interim analysis to decide whether the trial continues to stage 2 with the full population or a subpopulation. The subpopulation is defined based on one of the candidate threshold values of a numerical predictive biomarker. To estimate treatment effect in the selected subpopulation, we have derived unbiased estimators, shrinkage estimators, and estimators that estimate bias and subtract it from the naive estimate. We have recommended one of the unbiased estimators. However, since none of the estimators dominated in all simulation scenarios based on both bias and mean squared error, an alternative strategy would be to use a hybrid estimator where the estimator used depends on the subpopulation selected. This would require a simulation study of plausible scenarios before the trial.
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Affiliation(s)
- Peter K. Kimani
- Warwick Medical SchoolUniversity of WarwickCoventry CV4 7ALUK
| | - Susan Todd
- Department of Mathematics and StatisticsUniversity of ReadingReading RG6 6AXUK
| | - Lindsay A. Renfro
- Division of Biomedical Statistics and InformaticsMayo ClinicRochesterMN 55905USA
| | - Nigel Stallard
- Warwick Medical SchoolUniversity of WarwickCoventry CV4 7ALUK
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10
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Chiu YD, Koenig F, Posch M, Jaki T. Design and estimation in clinical trials with subpopulation selection. Stat Med 2018; 37:4335-4352. [PMID: 30088280 PMCID: PMC6282861 DOI: 10.1002/sim.7925] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2017] [Revised: 05/23/2018] [Accepted: 07/06/2018] [Indexed: 11/10/2022]
Abstract
Population heterogeneity is frequently observed among patients' treatment responses in clinical trials because of various factors such as clinical background, environmental, and genetic factors. Different subpopulations defined by those baseline factors can lead to differences in the benefit or safety profile of a therapeutic intervention. Ignoring heterogeneity between subpopulations can substantially impact on medical practice. One approach to address heterogeneity necessitates designs and analysis of clinical trials with subpopulation selection. Several types of designs have been proposed for different circumstances. In this work, we discuss a class of designs that allow selection of a predefined subgroup. Using the selection based on the maximum test statistics as the worst‐case scenario, we then investigate the precision and accuracy of the maximum likelihood estimator at the end of the study via simulations. We find that the required sample size is chiefly determined by the subgroup prevalence and show in simulations that the maximum likelihood estimator for these designs can be substantially biased.
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Affiliation(s)
- Yi-Da Chiu
- Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancashire, UK
| | - Franz Koenig
- Center for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Vienna, Austria
| | - Martin Posch
- Center for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Vienna, Austria
| | - Thomas Jaki
- Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancashire, UK
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11
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Pallmann P, Bedding AW, Choodari-Oskooei B, Dimairo M, Flight L, Hampson LV, Holmes J, Mander AP, Odondi L, Sydes MR, Villar SS, Wason JMS, Weir CJ, Wheeler GM, Yap C, Jaki T. Adaptive designs in clinical trials: why use them, and how to run and report them. BMC Med 2018; 16:29. [PMID: 29490655 PMCID: PMC5830330 DOI: 10.1186/s12916-018-1017-7] [Citation(s) in RCA: 361] [Impact Index Per Article: 60.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Accepted: 01/30/2018] [Indexed: 12/11/2022] Open
Abstract
Adaptive designs can make clinical trials more flexible by utilising results accumulating in the trial to modify the trial's course in accordance with pre-specified rules. Trials with an adaptive design are often more efficient, informative and ethical than trials with a traditional fixed design since they often make better use of resources such as time and money, and might require fewer participants. Adaptive designs can be applied across all phases of clinical research, from early-phase dose escalation to confirmatory trials. The pace of the uptake of adaptive designs in clinical research, however, has remained well behind that of the statistical literature introducing new methods and highlighting their potential advantages. We speculate that one factor contributing to this is that the full range of adaptations available to trial designs, as well as their goals, advantages and limitations, remains unfamiliar to many parts of the clinical community. Additionally, the term adaptive design has been misleadingly used as an all-encompassing label to refer to certain methods that could be deemed controversial or that have been inadequately implemented.We believe that even if the planning and analysis of a trial is undertaken by an expert statistician, it is essential that the investigators understand the implications of using an adaptive design, for example, what the practical challenges are, what can (and cannot) be inferred from the results of such a trial, and how to report and communicate the results. This tutorial paper provides guidance on key aspects of adaptive designs that are relevant to clinical triallists. We explain the basic rationale behind adaptive designs, clarify ambiguous terminology and summarise the utility and pitfalls of adaptive designs. We discuss practical aspects around funding, ethical approval, treatment supply and communication with stakeholders and trial participants. Our focus, however, is on the interpretation and reporting of results from adaptive design trials, which we consider vital for anyone involved in medical research. We emphasise the general principles of transparency and reproducibility and suggest how best to put them into practice.
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Affiliation(s)
- Philip Pallmann
- Department of Mathematics & Statistics, Lancaster University, Lancaster, LA1 4YF UK
| | | | - Babak Choodari-Oskooei
- MRC Clinical Trials Unit at UCL, Institute of Clinical Trials and Methodology, University College London, London, UK
| | | | - Laura Flight
- Medical Statistics Group, University of Sheffield, Sheffield, UK
| | - Lisa V. Hampson
- Department of Mathematics & Statistics, Lancaster University, Lancaster, LA1 4YF UK
- Statistical Innovation Group, Advanced Analytics Centre, AstraZeneca, Cambridge, UK
| | - Jane Holmes
- Centre for Statistics in Medicine, University of Oxford, Oxford, UK
| | | | - Lang’o Odondi
- Centre for Statistics in Medicine, University of Oxford, Oxford, UK
| | - Matthew R. Sydes
- MRC Clinical Trials Unit at UCL, Institute of Clinical Trials and Methodology, University College London, London, UK
| | - Sofía S. Villar
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - James M. S. Wason
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
- Institute of Health and Society, Newcastle University, Newcastle, UK
| | - Christopher J. Weir
- Usher Institute of Population Health Sciences and Informatics, University of Edinburgh, Edinburgh, UK
| | - Graham M. Wheeler
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
- Cancer Research UK & UCL Cancer Trials Centre, University College London, London, UK
| | - Christina Yap
- Cancer Research UK Clinical Trials Unit, University of Birmingham, Birmingham, UK
| | - Thomas Jaki
- Department of Mathematics & Statistics, Lancaster University, Lancaster, LA1 4YF UK
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12
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Brückner M, Titman A, Jaki T. Estimation in multi-arm two-stage trials with treatment selection and time-to-event endpoint. Stat Med 2017; 36:3137-3153. [PMID: 28612371 PMCID: PMC5575545 DOI: 10.1002/sim.7367] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Revised: 05/08/2017] [Accepted: 05/12/2017] [Indexed: 12/29/2022]
Abstract
We consider estimation of treatment effects in two‐stage adaptive multi‐arm trials with a common control. The best treatment is selected at interim, and the primary endpoint is modeled via a Cox proportional hazards model. The maximum partial‐likelihood estimator of the log hazard ratio of the selected treatment will overestimate the true treatment effect in this case. Several methods for reducing the selection bias have been proposed for normal endpoints, including an iterative method based on the estimated conditional selection biases and a shrinkage approach based on empirical Bayes theory. We adapt these methods to time‐to‐event data and compare the bias and mean squared error of all methods in an extensive simulation study and apply the proposed methods to reconstructed data from the FOCUS trial. We find that all methods tend to overcorrect the bias, and only the shrinkage methods can reduce the mean squared error. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
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Affiliation(s)
- Matthias Brückner
- Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K
| | - Andrew Titman
- Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K
| | - Thomas Jaki
- Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K
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