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Cook JA, Julious SA, Sones W, Hampson LV, Hewitt C, Berlin JA, Ashby D, Emsley R, Fergusson DA, Walters SJ, Wilson EC, MacLennan G, Stallard N, Rothwell JC, Bland M, Brown L, Ramsay CR, Cook A, Armstrong D, Altman D, Vale LD. Practical help for specifying the target difference in sample size calculations for RCTs: the DELTA 2 five-stage study, including a workshop. Health Technol Assess 2019; 23:1-88. [PMID: 31661431 PMCID: PMC6843113 DOI: 10.3310/hta23600] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
BACKGROUND The randomised controlled trial is widely considered to be the gold standard study for comparing the effectiveness of health interventions. Central to its design is a calculation of the number of participants needed (the sample size) for the trial. The sample size is typically calculated by specifying the magnitude of the difference in the primary outcome between the intervention effects for the population of interest. This difference is called the 'target difference' and should be appropriate for the principal estimand of interest and determined by the primary aim of the study. The target difference between treatments should be considered realistic and/or important by one or more key stakeholder groups. OBJECTIVE The objective of the report is to provide practical help on the choice of target difference used in the sample size calculation for a randomised controlled trial for researchers and funder representatives. METHODS The Difference ELicitation in TriAls2 (DELTA2) recommendations and advice were developed through a five-stage process, which included two literature reviews of existing funder guidance and recent methodological literature; a Delphi process to engage with a wider group of stakeholders; a 2-day workshop; and finalising the core document. RESULTS Advice is provided for definitive trials (Phase III/IV studies). Methods for choosing the target difference are reviewed. To aid those new to the topic, and to encourage better practice, 10 recommendations are made regarding choosing the target difference and undertaking a sample size calculation. Recommended reporting items for trial proposal, protocols and results papers under the conventional approach are also provided. Case studies reflecting different trial designs and covering different conditions are provided. Alternative trial designs and methods for choosing the sample size are also briefly considered. CONCLUSIONS Choosing an appropriate sample size is crucial if a study is to inform clinical practice. The number of patients recruited into the trial needs to be sufficient to answer the objectives; however, the number should not be higher than necessary to avoid unnecessary burden on patients and wasting precious resources. The choice of the target difference is a key part of this process under the conventional approach to sample size calculations. This document provides advice and recommendations to improve practice and reporting regarding this aspect of trial design. Future work could extend the work to address other less common approaches to the sample size calculations, particularly in terms of appropriate reporting items. FUNDING Funded by the Medical Research Council (MRC) UK and the National Institute for Health Research as part of the MRC-National Institute for Health Research Methodology Research programme.
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Affiliation(s)
- Jonathan A Cook
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK
| | - Steven A Julious
- Medical Statistics Group, School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - William Sones
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK
| | - Lisa V Hampson
- Statistical Methodology and Consulting, Novartis Pharma AG, Basel, Switzerland
| | - Catherine Hewitt
- York Trials Unit, Department of Health Sciences, University of York, York, UK
| | | | - Deborah Ashby
- Imperial Clinical Trials Unit, Imperial College London, London, UK
| | - Richard Emsley
- Department of Biostatistics and Health Informatics, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - Dean A Fergusson
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
| | - Stephen J Walters
- Medical Statistics Group, School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Edward Cf Wilson
- Cambridge Centre for Health Services Research, Cambridge Clinical Trials Unit University of Cambridge, Cambridge, UK
- Health Economics Group, Norwich Medical School, University of East Anglia, Norwich, UK
| | - Graeme MacLennan
- Centre for Healthcare Randomised Trials, University of Aberdeen, Aberdeen, UK
| | - Nigel Stallard
- Warwick Medical School, Statistics and Epidemiology, University of Warwick, Coventry, UK
| | - Joanne C Rothwell
- Medical Statistics Group, School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Martin Bland
- Department of Health Sciences, University of York, York, UK
| | - Louise Brown
- MRC Clinical Trials Unit, Institute of Clinical Trials and Methodology, University College London, London, UK
| | - Craig R Ramsay
- Health Services Research Unit, University of Aberdeen, Aberdeen, UK
| | - Andrew Cook
- Wessex Institute, University of Southampton, Southampton, UK
| | - David Armstrong
- School of Population Health and Environmental Sciences, King's College London, London, UK
| | - Douglas Altman
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK
| | - Luke D Vale
- Health Economics Group, Institute of Health & Society, Newcastle University, Newcastle upon Tyne, UK
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Cook JA, Julious SA, Sones W, Hampson LV, Hewitt C, Berlin JA, Ashby D, Emsley R, Fergusson DA, Walters SJ, Wilson ECF, Maclennan G, Stallard N, Rothwell JC, Bland M, Brown L, Ramsay CR, Cook A, Armstrong D, Altman D, Vale LD. DELTA 2 guidance on choosing the target difference and undertaking and reporting the sample size calculation for a randomised controlled trial. Trials 2018; 19:606. [PMID: 30400926 PMCID: PMC6218987 DOI: 10.1186/s13063-018-2884-0] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Accepted: 08/29/2018] [Indexed: 12/29/2022] Open
Abstract
Background A key step in the design of a RCT is the estimation of the number of participants needed in the study. The most common approach is to specify a target difference between the treatments for the primary outcome and then calculate the required sample size. The sample size is chosen to ensure that the trial will have a high probability (adequate statistical power) of detecting a target difference between the treatments should one exist. The sample size has many implications for the conduct and interpretation of the study. Despite the critical role that the target difference has in the design of a RCT, the way in which it is determined has received little attention. In this article, we summarise the key considerations and messages from new guidance for researchers and funders on specifying the target difference, and undertaking and reporting a RCT sample size calculation. This article on choosing the target difference for a randomised controlled trial (RCT) and undertaking and reporting the sample size calculation has been dual published in the BMJ and BMC Trials journals Methods The DELTA2 (Difference ELicitation in TriAls) project comprised five major components: systematic literature reviews of recent methodological developments (stage 1) and existing funder guidance (stage 2); a Delphi study (stage 3); a two-day consensus meeting bringing together researchers, funders and patient representatives (stage 4); and the preparation and dissemination of a guidance document (stage 5). Results and Discussion The key messages from the DELTA2 guidance on determining the target difference and sample size calculation for a randomised caontrolled trial are presented. Recommendations for the subsequent reporting of the sample size calculation are also provided.
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Affiliation(s)
- Jonathan A Cook
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Windmill Rd, Oxford, OX3 7LD, UK.
| | - Steven A Julious
- Medical Statistics Group, ScHARR, The University of Sheffield, Regent Court, 30 Regent Street, Sheffield, S1 4DA, UK
| | - William Sones
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Windmill Rd, Oxford, OX3 7LD, UK
| | - Lisa V Hampson
- Statistical Methodology and Consulting, Novartis, Basel, Switzerland.,Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK
| | - Catherine Hewitt
- Department of Health Sciences, Seebohm Rowntree Building, University of York, Heslington, York, YO10 5DD, UK
| | - Jesse A Berlin
- Johnson & Johnson, 1125 Trenton-Harbourton Road, Titusville, NJ, 08933, USA
| | - Deborah Ashby
- Imperial Clinical Trials Unit, School of Public Health, Imperial College London, Stadium House, 68 Wood Lane, London, W12 7RH, UK
| | - Richard Emsley
- Department of Biostatistics and Health Informatics, Institute of Psychiatry, Psychology and Neuroscience, King's College London, De Crespigny Park, Denmark Hill, London, SE5 8AF, UK
| | - Dean A Fergusson
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
| | - Stephen J Walters
- Medical Statistics Group, ScHARR, The University of Sheffield, Regent Court, 30 Regent Street, Sheffield, S1 4DA, UK
| | - Edward C F Wilson
- Cambridge Centre for Health Services Research & Cambridge Clinical Trials Unit, University of Cambridge, Institute of Public Health, Forvie Site, Robinson Way, Cambridge, CB2 0SR, UK
| | - Graeme Maclennan
- The Centre for Healthcare Randomised Trials (CHaRT), Health Sciences Building, University of Aberdeen, Foresterhill, Aberdeen, AB25 2D, UK
| | - Nigel Stallard
- Warwick Medical School - Statistics and Epidemiology, University of Warwick, Coventry, CV4 7AL, UK
| | - Joanne C Rothwell
- Medical Statistics Group, ScHARR, The University of Sheffield, Regent Court, 30 Regent Street, Sheffield, S1 4DA, UK
| | - Martin Bland
- Department of Health Sciences, Seebohm Rowntree Building, University of York, Heslington, York, YO10 5DD, UK
| | - Louise Brown
- MRC Clinical Trials Unit at UCL, Institute of Clinical Trials & Methodology, 2nd Floor 90 High Holborn, London, WC1V 6LJ, UK
| | - Craig R Ramsay
- Health Services Research Unit, University of Aberdeen, Health Sciences Building Foresterhill, Aberdeen, AB25 2ZD, UK
| | - Andrew Cook
- Public Health Medicine and Fellow in Health Technology Assessment, Wessex Institute, University of Southampton, Alpha House, Enterprise Road, Southampton, SO16 7NS, UK
| | - David Armstrong
- School of Population Health & Environmental Sciences, Faculty of Life Sciences and Medicine, Kings College London, Addison House, Guy's Campus, London, SE1 1UL, UK
| | - Doug Altman
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Windmill Rd, Oxford, OX3 7LD, UK
| | - Luke D Vale
- Health Economics Group, Institute of Health & Society, Newcastle University, Newcastle upon Tyne, NE2 4AX, UK
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Cook JA, Julious SA, Sones W, Hampson LV, Hewitt C, Berlin JA, Ashby D, Emsley R, Fergusson DA, Walters SJ, Wilson ECF, MacLennan G, Stallard N, Rothwell JC, Bland M, Brown L, Ramsay CR, Cook A, Armstrong D, Altman D, Vale LD. DELTA 2 guidance on choosing the target difference and undertaking and reporting the sample size calculation for a randomised controlled trial. BMJ 2018; 363:k3750. [PMID: 30560792 PMCID: PMC6216070 DOI: 10.1136/bmj.k3750] [Citation(s) in RCA: 85] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 08/09/2018] [Indexed: 11/17/2022]
Affiliation(s)
- Jonathan A Cook
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Oxford OX3 7LD, UK
| | - Steven A Julious
- Medical Statistics Group, ScHARR, University of Sheffield, Sheffield, UK
| | - William Sones
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Oxford OX3 7LD, UK
| | - Lisa V Hampson
- Statistical Methodology and Consulting, Novartis, Basel, Switzerland
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
| | - Catherine Hewitt
- Department of Health Sciences, University of York, Heslington, York, UK
| | | | - Deborah Ashby
- Imperial Clinical Trials Unit, School of Public Health, Imperial College London, London, UK
| | - Richard Emsley
- Department of Biostatistics and Health Informatics, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - Dean A Fergusson
- Clinical Epidemiology Programme, Ottawa Hospital Research Institute, Ottawa, ON, Canada
| | - Stephen J Walters
- Medical Statistics Group, ScHARR, University of Sheffield, Sheffield, UK
| | - Edward C F Wilson
- Cambridge Centre for Health Services Research and Cambridge Clinical Trials Unit, University of Cambridge, Institute of Public Health, Cambridge, UK
| | - Graeme MacLennan
- Centre for Healthcare Randomised Trials (CHaRT), University of Aberdeen, Aberdeen, UK
| | - Nigel Stallard
- Warwick Medical School-Statistics and Epidemiology, University of Warwick, Coventry, UK
| | - Joanne C Rothwell
- Medical Statistics Group, ScHARR, University of Sheffield, Sheffield, UK
| | - Martin Bland
- Department of Health Sciences, University of York, Heslington, York, UK
| | - Louise Brown
- MRC Clinical Trials Unit at University College London, Institute of Clinical Trials and Methodology, London, UK
| | - Craig R Ramsay
- Health Services Research Unit, University of Aberdeen, Aberdeen, UK
| | - Andrew Cook
- Wessex Institute, University of Southampton, Southampton, UK
| | - David Armstrong
- School of Population Health and Environmental Sciences, Faculty of Life Sciences and Medicine, King's College London, London, UK
| | - Doug Altman
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Oxford OX3 7LD, UK
| | - Luke D Vale
- Health Economics Group, Institute of Health and Society, Newcastle University, Newcastle upon Tyne, UK
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Cook JA, Julious SA, Sones W, Hampson LV, Hewitt C, Berlin JA, Ashby D, Emsley R, Fergusson DA, Walters SJ, Wilson ECF, Maclennan G, Stallard N, Rothwell JC, Bland M, Brown L, Ramsay CR, Cook A, Armstrong D, Altman D, Vale LD. DELTA 2 guidance on choosing the target difference and undertaking and reporting the sample size calculation for a randomised controlled trial. Trials 2018. [PMID: 30400926 DOI: 10.1186/s13063‐018‐2884‐0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND A key step in the design of a RCT is the estimation of the number of participants needed in the study. The most common approach is to specify a target difference between the treatments for the primary outcome and then calculate the required sample size. The sample size is chosen to ensure that the trial will have a high probability (adequate statistical power) of detecting a target difference between the treatments should one exist. The sample size has many implications for the conduct and interpretation of the study. Despite the critical role that the target difference has in the design of a RCT, the way in which it is determined has received little attention. In this article, we summarise the key considerations and messages from new guidance for researchers and funders on specifying the target difference, and undertaking and reporting a RCT sample size calculation. This article on choosing the target difference for a randomised controlled trial (RCT) and undertaking and reporting the sample size calculation has been dual published in the BMJ and BMC Trials journals METHODS: The DELTA2 (Difference ELicitation in TriAls) project comprised five major components: systematic literature reviews of recent methodological developments (stage 1) and existing funder guidance (stage 2); a Delphi study (stage 3); a two-day consensus meeting bringing together researchers, funders and patient representatives (stage 4); and the preparation and dissemination of a guidance document (stage 5). RESULTS AND DISCUSSION The key messages from the DELTA2 guidance on determining the target difference and sample size calculation for a randomised caontrolled trial are presented. Recommendations for the subsequent reporting of the sample size calculation are also provided.
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Affiliation(s)
- Jonathan A Cook
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Windmill Rd, Oxford, OX3 7LD, UK.
| | - Steven A Julious
- Medical Statistics Group, ScHARR, The University of Sheffield, Regent Court, 30 Regent Street, Sheffield, S1 4DA, UK
| | - William Sones
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Windmill Rd, Oxford, OX3 7LD, UK
| | - Lisa V Hampson
- Statistical Methodology and Consulting, Novartis, Basel, Switzerland.,Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK
| | - Catherine Hewitt
- Department of Health Sciences, Seebohm Rowntree Building, University of York, Heslington, York, YO10 5DD, UK
| | - Jesse A Berlin
- Johnson & Johnson, 1125 Trenton-Harbourton Road, Titusville, NJ, 08933, USA
| | - Deborah Ashby
- Imperial Clinical Trials Unit, School of Public Health, Imperial College London, Stadium House, 68 Wood Lane, London, W12 7RH, UK
| | - Richard Emsley
- Department of Biostatistics and Health Informatics, Institute of Psychiatry, Psychology and Neuroscience, King's College London, De Crespigny Park, Denmark Hill, London, SE5 8AF, UK
| | - Dean A Fergusson
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
| | - Stephen J Walters
- Medical Statistics Group, ScHARR, The University of Sheffield, Regent Court, 30 Regent Street, Sheffield, S1 4DA, UK
| | - Edward C F Wilson
- Cambridge Centre for Health Services Research & Cambridge Clinical Trials Unit, University of Cambridge, Institute of Public Health, Forvie Site, Robinson Way, Cambridge, CB2 0SR, UK
| | - Graeme Maclennan
- The Centre for Healthcare Randomised Trials (CHaRT), Health Sciences Building, University of Aberdeen, Foresterhill, Aberdeen, AB25 2D, UK
| | - Nigel Stallard
- Warwick Medical School - Statistics and Epidemiology, University of Warwick, Coventry, CV4 7AL, UK
| | - Joanne C Rothwell
- Medical Statistics Group, ScHARR, The University of Sheffield, Regent Court, 30 Regent Street, Sheffield, S1 4DA, UK
| | - Martin Bland
- Department of Health Sciences, Seebohm Rowntree Building, University of York, Heslington, York, YO10 5DD, UK
| | - Louise Brown
- MRC Clinical Trials Unit at UCL, Institute of Clinical Trials & Methodology, 2nd Floor 90 High Holborn, London, WC1V 6LJ, UK
| | - Craig R Ramsay
- Health Services Research Unit, University of Aberdeen, Health Sciences Building Foresterhill, Aberdeen, AB25 2ZD, UK
| | - Andrew Cook
- Public Health Medicine and Fellow in Health Technology Assessment, Wessex Institute, University of Southampton, Alpha House, Enterprise Road, Southampton, SO16 7NS, UK
| | - David Armstrong
- School of Population Health & Environmental Sciences, Faculty of Life Sciences and Medicine, Kings College London, Addison House, Guy's Campus, London, SE1 1UL, UK
| | - Doug Altman
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Botnar Research Centre, Nuffield Orthopaedic Centre, Windmill Rd, Oxford, OX3 7LD, UK
| | - Luke D Vale
- Health Economics Group, Institute of Health & Society, Newcastle University, Newcastle upon Tyne, NE2 4AX, UK
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