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      DELTA 2 guidance on choosing the target difference and undertaking and reporting the sample size calculation for a randomised controlled trial

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          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 DELTA 2 (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 DELTA 2 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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          Most cited references21

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          The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results.

          Although there is a growing understanding of the importance of statistical power considerations when designing studies and of the value of confidence intervals when interpreting data, confusion exists about the reverse arrangement: the role of confidence intervals in study design and of power in interpretation. Confidence intervals should play an important role when setting sample size, and power should play no role once the data have been collected, but exactly the opposite procedure is widely practiced. In this commentary, we present the reasons why the calculation of power after a study is over is inappropriate and how confidence intervals can be used during both study design and study interpretation.
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            Many faces of the minimal clinically important difference (MCID): a literature review and directions for future research.

            The minimal clinically important difference (MCID) for an instrument is a much sought after, but elusive figure. In this review we will highlight new findings in this area, including taxonomy of MCID, methods used to ascertain MCID, the perspective taken for evaluating importance, and other sources of variation for MCID values. In the end we believe the MCID will be a context-specific value rather than a fixed number. The review highlights the need to do methodological research in this area, especially concurrent comparisons between approaches, or across different patient groups. There are many faces to the MCID, it is not a simple concept, nor simple to calculate.
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              Reporting of sample size calculation in randomised controlled trials: review

              Objectives To assess quality of reporting of sample size calculation, ascertain accuracy of calculations, and determine the relevance of assumptions made when calculating sample size in randomised controlled trials. Design Review. Data sources We searched MEDLINE for all primary reports of two arm parallel group randomised controlled trials of superiority with a single primary outcome published in six high impact factor general medical journals between 1 January 2005 and 31 December 2006. All extra material related to design of trials (other articles, online material, online trial registration) was systematically assessed. Data extracted by use of a standardised form included parameters required for sample size calculation and corresponding data reported in results sections of articles. We checked completeness of reporting of the sample size calculation, systematically replicated the sample size calculation to assess its accuracy, then quantified discrepancies between a priori hypothesised parameters necessary for calculation and a posteriori estimates. Results Of the 215 selected articles, 10 (5%) did not report any sample size calculation and 92 (43%) did not report all the required parameters. The difference between the sample size reported in the article and the replicated sample size calculation was greater than 10% in 47 (30%) of the 157 reports that gave enough data to recalculate the sample size. The difference between the assumptions for the control group and the observed data was greater than 30% in 31% (n=45) of articles and greater than 50% in 17% (n=24). Only 73 trials (34%) reported all data required to calculate the sample size, had an accurate calculation, and used accurate assumptions for the control group. Conclusions Sample size calculation is still inadequately reported, often erroneous, and based on assumptions that are frequently inaccurate. Such a situation raises questions about how sample size is calculated in randomised controlled trials.
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                Author and article information

                Contributors
                jonathan.cook@ndorms.ox.ac.uk
                s.a.julious@sheffield.ac.uk
                William.sones@ndorms.ox.ac.uk
                lisa.hampson@novartis.com
                catherine.hewitt@york.ac.uk
                jberlin@its.jnj.com
                deborah.ashby@imperial.ac.uk
                Richard.Emsley@kcl.ac.uk
                dafergusson@ohri.ca
                s.j.walters@sheffield.ac.uk
                ed.wilson@medschl.cam.ac.uk
                g.maclennan@abdn.ac.uk
                N.Stallard@warwick.ac.uk
                j.c.rothwell@sheffield.ac.uk
                martin.bland@york.ac.uk
                l.brown@ucl.ac.uk
                c.r.ramsay@abdn.ac.uk
                andrewc@soton.ac.uk
                david.armstrong@kcl.ac.uk
                doug.altman@csm.ox.ac.uk
                luke.vale@newcastle.ac.uk
                Journal
                Trials
                Trials
                Trials
                BioMed Central (London )
                1745-6215
                5 November 2018
                5 November 2018
                2018
                : 19
                : 606
                Affiliations
                [1 ]ISNI 0000 0004 1936 8948, GRID grid.4991.5, 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
                [2 ]ISNI 0000 0004 1936 9262, GRID grid.11835.3e, Medical Statistics Group, ScHARR, , The University of Sheffield, ; Regent Court, 30 Regent Street, Sheffield, S1 4DA UK
                [3 ]ISNI 0000 0001 1515 9979, GRID grid.419481.1, Statistical Methodology and Consulting, Novartis, ; Basel, Switzerland
                [4 ]ISNI 0000 0000 8190 6402, GRID grid.9835.7, Department of Mathematics and Statistics, , Lancaster University, ; Lancaster, LA1 4YF UK
                [5 ]ISNI 0000 0004 1936 9668, GRID grid.5685.e, Department of Health Sciences, Seebohm Rowntree Building, , University of York, ; Heslington, York, YO10 5DD UK
                [6 ]GRID grid.417429.d, Johnson & Johnson, ; 1125 Trenton-Harbourton Road, Titusville, NJ 08933 USA
                [7 ]ISNI 0000 0001 2113 8111, GRID grid.7445.2, Imperial Clinical Trials Unit, School of Public Health, , Imperial College London, ; Stadium House, 68 Wood Lane, London, W12 7RH UK
                [8 ]ISNI 0000 0001 2322 6764, GRID grid.13097.3c, 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
                [9 ]ISNI 0000 0000 9606 5108, GRID grid.412687.e, Clinical Epidemiology Program, Ottawa Hospital Research Institute, ; Ottawa, ON Canada
                [10 ]ISNI 0000000121885934, GRID grid.5335.0, 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
                [11 ]ISNI 0000 0004 1936 7291, GRID grid.7107.1, The Centre for Healthcare Randomised Trials (CHaRT), Health Sciences Building, , University of Aberdeen, ; Foresterhill, Aberdeen, AB25 2D UK
                [12 ]ISNI 0000 0000 8809 1613, GRID grid.7372.1, Warwick Medical School - Statistics and Epidemiology, , University of Warwick, ; Coventry, CV4 7AL UK
                [13 ]MRC Clinical Trials Unit at UCL, Institute of Clinical Trials & Methodology, 2nd Floor 90 High Holborn, London, WC1V 6LJ UK
                [14 ]ISNI 0000 0004 1936 7291, GRID grid.7107.1, Health Services Research Unit, , University of Aberdeen, ; Health Sciences Building Foresterhill, Aberdeen, AB25 2ZD UK
                [15 ]ISNI 0000 0004 1936 9297, GRID grid.5491.9, Public Health Medicine and Fellow in Health Technology Assessment, Wessex Institute, University of Southampton, ; Alpha House, Enterprise Road, Southampton, SO16 7NS UK
                [16 ]ISNI 0000 0001 2322 6764, GRID grid.13097.3c, School of Population Health & Environmental Sciences, Faculty of Life Sciences and Medicine, , Kings College London, ; Addison House, Guy’s Campus, London, SE1 1UL UK
                [17 ]ISNI 0000 0001 0462 7212, GRID grid.1006.7, Health Economics Group, Institute of Health & Society, , Newcastle University, ; Newcastle upon Tyne, NE2 4AX UK
                Author information
                http://orcid.org/0000-0002-4156-6989
                Article
                2884
                10.1186/s13063-018-2884-0
                6218987
                30400926
                75a43ded-00e3-4f27-b215-49375d632378
                © The Author(s). 2018

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

                History
                : 20 August 2018
                : 29 August 2018
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100000265, Medical Research Council;
                Award ID: N/A
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100000272, National Institute for Health Research;
                Award ID: N/A
                Award Recipient :
                Categories
                Methodology
                Custom metadata
                © The Author(s) 2018

                Medicine
                Medicine

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