1
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Stallard N. Adaptive enrichment designs with a continuous biomarker. Biometrics 2023; 79:9-19. [PMID: 35174875 DOI: 10.1111/biom.13644] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 09/23/2021] [Indexed: 12/01/2022]
Abstract
A popular design for clinical trials assessing targeted therapies is the two-stage adaptive enrichment design with recruitment in stage 2 limited to a biomarker-defined subgroup chosen based on data from stage 1. The data-dependent selection leads to statistical challenges if data from both stages are used to draw inference on treatment effects in the selected subgroup. If subgroups considered are nested, as when defined by a continuous biomarker, treatment effect estimates in different subgroups follow the same distribution as estimates in a group-sequential trial. This result is used to obtain tests controlling the familywise type I error rate (FWER) for six simple subgroup selection rules, one of which also controls the FWER for any selection rule. Two approaches are proposed: one based on multivariate normal distributions suitable if the number of possible subgroups, k, is small, and one based on Brownian motion approximations suitable for large k. The methods, applicable in the wide range of settings with asymptotically normal test statistics, are illustrated using survival data from a breast cancer trial.
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Affiliation(s)
- Nigel Stallard
- Statistics and Epidemiology, Division of Health Sciences, Warwick Medical School, University of Warwick, Coventry, UK
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2
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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: 11] [Impact Index Per Article: 11.0] [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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3
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Toyoizumi K, Matsui S. Bias correction based on weighted likelihood for conditional estimation of subgroup effects in randomized clinical trials. Stat Med 2022; 41:5276-5289. [PMID: 36055340 DOI: 10.1002/sim.9567] [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: 11/11/2021] [Revised: 07/07/2022] [Accepted: 08/18/2022] [Indexed: 11/10/2022]
Abstract
Currently, many confirmatory randomized clinical trials (RCTs) with predictive markers have taken the all-comers approach because of the difficulty in developing predictive markers that are biologically compelling enough to apply the enrichment approach to restrict the patient population to a marker-defined subgroup. However, such a RCT with weak marker credentials can conclude that the new treatment is efficacious only in the subgroup, especially when the primary analysis demonstrates some treatment efficacy in the subgroup, but the overall treatment efficacy is not significant under a control of study-wise alpha rate. In this article, we consider conditional estimation of subgroup treatment effects, given the negative result in testing the overall treatment efficacy in the trial. To address the problem of unstable estimation due to the truncation in the distribution of the test statistic on overall treatment efficacy, we propose a new approach based on a weighted likelihood for the truncated distribution. The weighted likelihood can be derived by invoking a randomized test with a smooth critical function for the overall test. Our approach allows for point and interval estimations of the conditional effects consistently based on the standard maximum likelihood inference. Numerical evaluations, including simulations and application to real clinical trials, and guidelines for implementing our methods with R-codes, are provided.
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Affiliation(s)
- Kiichiro Toyoizumi
- Department of Biostatistics, Nagoya University Graduate School of Medicine, Nagoya, Japan.,Statistics & Decision Sciences Department, Janssen Pharmaceutical K. K, Tokyo, Japan
| | - Shigeyuki Matsui
- Department of Biostatistics, Nagoya University Graduate School of Medicine, Nagoya, Japan.,Department of Data Science, The Institute of Statistical Mathematics, Tokyo, Japan
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4
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Brügemann D, Lehner B, Kieser M, Krisam J, Hommertgen A, Jaekel C, Harrabi SB, Herfarth K, Mechtesheimer G, Sedlaczek O, Egerer G, Geisbüsch A, Uhl M, Debus J, Seidensaal K. Neoadjuvant irradiation of extremity soft tissue sarcoma with ions (Extrem-ion): study protocol for a randomized phase II pilot trial. BMC Cancer 2022; 22:538. [PMID: 35550036 PMCID: PMC9097299 DOI: 10.1186/s12885-022-09560-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2022] [Accepted: 04/17/2022] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND The standard of care treatment for soft tissue sarcoma of the extremities is a wide resection in combination with pre- or postoperative radiotherapy with high local control rates, sparing patients the necessity of amputation without compromising on overall survival rates. The currently preferred timing of radiotherapy is under debate. Albeit having higher rates of acute wound complications, late side effects like fibrosis, joint stiffness or edema are less frequent in preoperative compared to postoperative radiotherapy. This can be explained in smaller treatment volumes and a lower dose in the preoperative setting. Particles allow better sparing of surrounding tissues at risk, and carbon ions additionally offer biologic advantages and are preferred in less radiosensitive tumors. Hypofractionation allows for a significantly shorter treatment duration. METHODS Extrem-ion is a prospective, randomized, monocentric phase II trial. Patients with resectable or marginally resectable, histologically confirmed soft tissue sarcoma of the extremities will be randomized between neoadjuvant proton or neoadjuvant carbon ion radiotherapy in active scanning beam application technique (39 Gy [relative biological effectiveness, RBE] in 13 fractions [5-6 fractions per week] in each arm). The primary objective is the proportion of therapies without wound healing disorder the first 120 days after surgery or discontinuation of treatment for any reason related to the treatment. The secondary endpoints of the study consist of local control, local progression-free survival, disease-free survival, overall survival, and quality of life. DISCUSSION The aim of this study is to confirm that hypofractionated, preoperative radiotherapy is safe and feasible. The potential for reduced toxicity by the utilization of particle therapy is the rational of this trial. A subsequent randomized phase III trial will compare the hypofractionated proton and carbon ion irradiation in regards to local control. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT04946357 ; Retrospectively registered June 30, 2021.
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Affiliation(s)
- D Brügemann
- Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120, Heidelberg, Germany
- Heidelberg Institute of Radiation Oncology (HIRO), Heidelberg, Germany
- National Center for Tumor diseases (NCT), Heidelberg, Germany
- Department of Radiation Oncology, Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg University Hospital, Heidelberg, Germany
| | - B Lehner
- Center for Orthopedics, Trauma Surgery and Paraplegiology, University of Heidelberg, Heidelberg, Germany
| | - M Kieser
- Institute for Medical Biometry, University of Heidelberg, Heidelberg, Germany
| | - J Krisam
- Institute for Medical Biometry, University of Heidelberg, Heidelberg, Germany
| | - A Hommertgen
- Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120, Heidelberg, Germany
| | - C Jaekel
- Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120, Heidelberg, Germany
| | - S B Harrabi
- Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120, Heidelberg, Germany
- Heidelberg Institute of Radiation Oncology (HIRO), Heidelberg, Germany
- National Center for Tumor diseases (NCT), Heidelberg, Germany
- Department of Radiation Oncology, Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg University Hospital, Heidelberg, Germany
- Clinical Cooperation Unit Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg, Germany
| | - K Herfarth
- Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120, Heidelberg, Germany
- Heidelberg Institute of Radiation Oncology (HIRO), Heidelberg, Germany
- National Center for Tumor diseases (NCT), Heidelberg, Germany
- Department of Radiation Oncology, Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg University Hospital, Heidelberg, Germany
- Clinical Cooperation Unit Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg, Germany
| | - G Mechtesheimer
- Institute of Pathology, University of Heidelberg, Heidelberg, Germany
| | - O Sedlaczek
- Department of Radiology, University of Heidelberg, Heidelberg, Germany
- Department of Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany
| | - G Egerer
- Department of Hematology, Oncology and Rheumatology, Heidelberg University, Heidelberg, Germany
| | - A Geisbüsch
- Center for Orthopedics, Trauma Surgery and Paraplegiology, University of Heidelberg, Heidelberg, Germany
| | - M Uhl
- Department of Radiation Oncology, Klinikum Ludwigshafen, Ludwigshafen, Germany
| | - J Debus
- Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120, Heidelberg, Germany
- Heidelberg Institute of Radiation Oncology (HIRO), Heidelberg, Germany
- National Center for Tumor diseases (NCT), Heidelberg, Germany
- Department of Radiation Oncology, Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg University Hospital, Heidelberg, Germany
- Clinical Cooperation Unit Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg, Germany
- German Cancer Consortium (DKTK), Heidelberg, Germany
| | - K Seidensaal
- Department of Radiation Oncology, Heidelberg University Hospital, Im Neuenheimer Feld 400, 69120, Heidelberg, Germany.
- Heidelberg Institute of Radiation Oncology (HIRO), Heidelberg, Germany.
- National Center for Tumor diseases (NCT), Heidelberg, Germany.
- Department of Radiation Oncology, Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg University Hospital, Heidelberg, Germany.
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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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Nguyen Duc A, Heinzmann D, Berge C, Wolbers M. A pragmatic adaptive enrichment design for selecting the right target population for cancer immunotherapies. Pharm Stat 2020; 20:202-211. [PMID: 32869509 DOI: 10.1002/pst.2066] [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: 03/18/2020] [Revised: 06/09/2020] [Accepted: 08/11/2020] [Indexed: 02/02/2023]
Abstract
One of the challenges in the design of confirmatory trials is to deal with uncertainties regarding the optimal target population for a novel drug. Adaptive enrichment designs (AED) which allow for a data-driven selection of one or more prespecified biomarker subpopulations at an interim analysis have been proposed in this setting but practical case studies of AEDs are still relatively rare. We present the design of an AED with a binary endpoint in the highly dynamic setting of cancer immunotherapy. The trial was initiated as a conventional trial in early triple-negative breast cancer but amended to an AED based on emerging data external to the trial suggesting that PD-L1 status could be a predictive biomarker. Operating characteristics are discussed including the concept of a minimal detectable difference, that is, the smallest observed treatment effect that would lead to a statistically significant result in at least one of the target populations at the interim or the final analysis, respectively, in the setting of AED.
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Affiliation(s)
- Anh Nguyen Duc
- Biostatistics, Hoffmann-La Roche Pharma AG, Basel, Switzerland
| | | | - Claude Berge
- Biostatistics, Hoffmann-La Roche Pharma AG, Basel, Switzerland
| | - Marcel Wolbers
- Biostatistics, Hoffmann-La Roche Pharma AG, Basel, Switzerland
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7
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Dimairo M, Pallmann P, Wason J, Todd S, Jaki T, Julious SA, Mander AP, Weir CJ, Koenig F, Walton MK, Nicholl JP, Coates E, Biggs K, Hamasaki T, Proschan MA, Scott JA, Ando Y, Hind D, Altman DG. The adaptive designs CONSORT extension (ACE) statement: a checklist with explanation and elaboration guideline for reporting randomised trials that use an adaptive design. Trials 2020; 21:528. [PMID: 32546273 PMCID: PMC7298968 DOI: 10.1186/s13063-020-04334-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Adaptive designs (ADs) allow pre-planned changes to an ongoing trial without compromising the validity of conclusions and it is essential to distinguish pre-planned from unplanned changes that may also occur. The reporting of ADs in randomised trials is inconsistent and needs improving. Incompletely reported AD randomised trials are difficult to reproduce and are hard to interpret and synthesise. This consequently hampers their ability to inform practice as well as future research and contributes to research waste. Better transparency and adequate reporting will enable the potential benefits of ADs to be realised.This extension to the Consolidated Standards Of Reporting Trials (CONSORT) 2010 statement was developed to enhance the reporting of randomised AD clinical trials. We developed an Adaptive designs CONSORT Extension (ACE) guideline through a two-stage Delphi process with input from multidisciplinary key stakeholders in clinical trials research in the public and private sectors from 21 countries, followed by a consensus meeting. Members of the CONSORT Group were involved during the development process.The paper presents the ACE checklists for AD randomised trial reports and abstracts, as well as an explanation with examples to aid the application of the guideline. The ACE checklist comprises seven new items, nine modified items, six unchanged items for which additional explanatory text clarifies further considerations for ADs, and 20 unchanged items not requiring further explanatory text. The ACE abstract checklist has one new item, one modified item, one unchanged item with additional explanatory text for ADs, and 15 unchanged items not requiring further explanatory text.The intention is to enhance transparency and improve reporting of AD randomised trials to improve the interpretability of their results and reproducibility of their methods, results and inference. We also hope indirectly to facilitate the much-needed knowledge transfer of innovative trial designs to maximise their potential benefits. In order to encourage its wide dissemination this article is freely accessible on the BMJ and Trials journal websites."To maximise the benefit to society, you need to not just do research but do it well" Douglas G Altman.
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Affiliation(s)
- Munyaradzi Dimairo
- School of Health and Related Research, University of Sheffield, Sheffield, S1 4DA, UK.
| | | | - James Wason
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
- Institute of Health and Society, Newcastle University, Newcastle, UK
| | - Susan Todd
- Department of Mathematics and Statistics, University of Reading, Reading, UK
| | - Thomas Jaki
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - Steven A Julious
- School of Health and Related Research, University of Sheffield, Sheffield, S1 4DA, UK
| | - Adrian P Mander
- Centre for Trials Research, Cardiff University, Cardiff, UK
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - Christopher J Weir
- Edinburgh Clinical Trials Unit, Usher Institute, University of Edinburgh, Edinburgh, UK
| | - Franz Koenig
- Centre for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Vienna, Austria
| | - Marc K Walton
- Janssen Pharmaceuticals, Titusville, New Jersey, USA
| | - Jon P Nicholl
- School of Health and Related Research, University of Sheffield, Sheffield, S1 4DA, UK
| | - Elizabeth Coates
- School of Health and Related Research, University of Sheffield, Sheffield, S1 4DA, UK
| | - Katie Biggs
- School of Health and Related Research, University of Sheffield, Sheffield, S1 4DA, UK
| | | | - Michael A Proschan
- National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, USA
| | - John A Scott
- Division of Biostatistics in the Center for Biologics Evaluation and Research, Food and Drug Administration, Rockville, USA
| | - Yuki Ando
- Pharmaceuticals and Medical Devices Agency, Tokyo, Japan
| | - Daniel Hind
- School of Health and Related Research, University of Sheffield, Sheffield, S1 4DA, UK
| | - Douglas G Altman
- Centre for Statistics in Medicine, University of Oxford, Oxford, UK
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8
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Dimairo M, Pallmann P, Wason J, Todd S, Jaki T, Julious SA, Mander AP, Weir CJ, Koenig F, Walton MK, Nicholl JP, Coates E, Biggs K, Hamasaki T, Proschan MA, Scott JA, Ando Y, Hind D, Altman DG. The Adaptive designs CONSORT Extension (ACE) statement: a checklist with explanation and elaboration guideline for reporting randomised trials that use an adaptive design. BMJ 2020; 369:m115. [PMID: 32554564 PMCID: PMC7298567 DOI: 10.1136/bmj.m115] [Citation(s) in RCA: 55] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 11/19/2019] [Indexed: 12/11/2022]
Abstract
Adaptive designs (ADs) allow pre-planned changes to an ongoing trial without compromising the validity of conclusions and it is essential to distinguish pre-planned from unplanned changes that may also occur. The reporting of ADs in randomised trials is inconsistent and needs improving. Incompletely reported AD randomised trials are difficult to reproduce and are hard to interpret and synthesise. This consequently hampers their ability to inform practice as well as future research and contributes to research waste. Better transparency and adequate reporting will enable the potential benefits of ADs to be realised.This extension to the Consolidated Standards Of Reporting Trials (CONSORT) 2010 statement was developed to enhance the reporting of randomised AD clinical trials. We developed an Adaptive designs CONSORT Extension (ACE) guideline through a two-stage Delphi process with input from multidisciplinary key stakeholders in clinical trials research in the public and private sectors from 21 countries, followed by a consensus meeting. Members of the CONSORT Group were involved during the development process.The paper presents the ACE checklists for AD randomised trial reports and abstracts, as well as an explanation with examples to aid the application of the guideline. The ACE checklist comprises seven new items, nine modified items, six unchanged items for which additional explanatory text clarifies further considerations for ADs, and 20 unchanged items not requiring further explanatory text. The ACE abstract checklist has one new item, one modified item, one unchanged item with additional explanatory text for ADs, and 15 unchanged items not requiring further explanatory text.The intention is to enhance transparency and improve reporting of AD randomised trials to improve the interpretability of their results and reproducibility of their methods, results and inference. We also hope indirectly to facilitate the much-needed knowledge transfer of innovative trial designs to maximise their potential benefits.
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Affiliation(s)
- Munyaradzi Dimairo
- School of Health and Related Research, University of Sheffield, Sheffield S1 4DA, UK
| | | | - James Wason
- MRC Biostatistics Unit, University of Cambridge, UK
- Institute of Health and Society, Newcastle University, UK
| | - Susan Todd
- Department of Mathematics and Statistics, University of Reading, UK
| | - Thomas Jaki
- Department of Mathematics and Statistics, Lancaster University, UK
| | - Steven A Julious
- School of Health and Related Research, University of Sheffield, Sheffield S1 4DA, UK
| | - Adrian P Mander
- Centre for Trials Research, Cardiff University, UK
- MRC Biostatistics Unit, University of Cambridge, UK
| | - Christopher J Weir
- Edinburgh Clinical Trials Unit, Usher Institute, University of Edinburgh, UK
| | - Franz Koenig
- Centre for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Austria
| | | | - Jon P Nicholl
- School of Health and Related Research, University of Sheffield, Sheffield S1 4DA, UK
| | - Elizabeth Coates
- School of Health and Related Research, University of Sheffield, Sheffield S1 4DA, UK
| | - Katie Biggs
- School of Health and Related Research, University of Sheffield, Sheffield S1 4DA, UK
| | | | - Michael A Proschan
- National Institute of Allergy and Infectious Diseases, National Institutes of Health, USA
| | - John A Scott
- Division of Biostatistics in the Center for Biologics Evaluation and Research, Food and Drug Administration, USA
| | - Yuki Ando
- Pharmaceuticals and Medical Devices Agency, Japan
| | - Daniel Hind
- School of Health and Related Research, University of Sheffield, Sheffield S1 4DA, UK
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9
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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] [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)
- Peter K Kimani
- Warwick Medical School, University of Warwick, Coventry, UK
| | - 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, USA
| | | | | | - John A Kairalla
- Department of Biostatistics, University of Florida, Gainesville, Florida, USA
| | - Nigel Stallard
- Warwick Medical School, University of Warwick, Coventry, UK
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10
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Placzek M, Friede T. A conditional error function approach for adaptive enrichment designs with continuous endpoints. Stat Med 2019; 38:3105-3122. [PMID: 31066093 DOI: 10.1002/sim.8154] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Revised: 02/22/2019] [Accepted: 03/09/2019] [Indexed: 12/15/2022]
Abstract
Adaptive enrichment designs offer an efficient and flexible way to demonstrate the efficacy of a treatment in a clinically defined full population or in, eg, biomarker-defined subpopulations while controlling the family-wise Type I error rate in the strong sense. Frequently used testing strategies in designs with two or more stages include the combination test and the conditional error function approach. Here, we focus on the latter and present some extensions. In contrast to previous work, we allow for multiple subgroups rather than one subgroup only. For nested as well as nonoverlapping subgroups with normally distributed endpoints, we explore the effect of estimating the variances in the subpopulations. Instead of using a normal approximation, we derive new t-distribution-based methods for two different scenarios. First, in the case of equal variances across the subpopulations, we present exact results using a multivariate t-distribution. Second, in the case of potentially varying variances across subgroups, we provide some improved approximations compared to the normal approximation. The performance of the proposed conditional error function approaches is assessed and compared to the combination test in a simulation study. The proposed methods are motivated by an example in pulmonary arterial hypertension.
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Affiliation(s)
- Marius Placzek
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany
| | - Tim Friede
- Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Germany.,DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Göttingen, Germany
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11
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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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