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      Recommendations for the analysis of individually randomised controlled trials with clustering in one arm – a case of continuous outcomes

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          Abstract

          Background

          In an individually randomised controlled trial where the treatment is delivered by a health professional it seems likely that the effectiveness of the treatment, independent of any treatment effect, could depend on the skill, training or even enthusiasm of the health professional delivering it. This may then lead to a potential clustering of the outcomes for patients treated by the same health professional, but similar clustering may not occur in the control arm. Using four case studies, we aim to provide practical guidance and recommendations for the analysis of trials with some element of clustering in one arm.

          Methods

          Five approaches to the analysis of outcomes from an individually randomised controlled trial with clustering in one arm are identified in the literature. Some of these methods are applied to four case studies of completed randomised controlled trials with clustering in one arm with sample sizes ranging from 56 to 539. Results are obtained using the statistical packages R and Stata and summarised using a forest plot.

          Results

          The intra-cluster correlation coefficient (ICC) for each of the case studies was small (<0.05) indicating little dependence on the outcomes related to cluster allocations. All models fitted produced similar results, including the simplest approach of ignoring clustering for the case studies considered.

          Conclusions

          A partially clustered approach, modelling the clustering in just one arm, most accurately represents the trial design and provides valid results. Modelling homogeneous variances between the clustered and unclustered arm is adequate in scenarios similar to the case studies considered. We recommend treating each participant in the unclustered arm as a single cluster. This approach is simple to implement in R and Stata and is recommended for the analysis of trials with clustering in one arm only. However, the case studies considered had small ICC values, limiting the generalisability of these results.

          Electronic supplementary material

          The online version of this article (doi:10.1186/s12874-016-0249-5) contains supplementary material, which is available to authorized users.

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          Most cited references 22

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              Small sample inference for fixed effects from restricted maximum likelihood.

              Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.
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                Author and article information

                Contributors
                l.flight@sheffield.ac.uk
                annabel.allison@mrc-bsu.cam.ac.uk
                m.dimairo@sheffield.ac.uk
                e.lee@sheffield.ac.uk
                l.mandefield@sheffield.ac.uk
                s.j.walters@sheffield.ac.uk
                Journal
                BMC Med Res Methodol
                BMC Med Res Methodol
                BMC Medical Research Methodology
                BioMed Central (London )
                1471-2288
                29 November 2016
                29 November 2016
                2016
                : 16
                Affiliations
                [1 ]ScHARR, University of Sheffield, 30 Regent Street, Sheffield, S1 4DA UK
                [2 ]MRC Biostatistics Unit, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge, CB2 0SR UK
                Article
                249
                10.1186/s12874-016-0249-5
                5129671
                27899073
                © The Author(s) 2016

                Open Access This 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.

                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100000272, National Institute for Health Research;
                Funded by: FundRef http://dx.doi.org/10.13039/501100000272, National Institute for Health Research;
                Categories
                Research Article
                Custom metadata
                © The Author(s) 2016

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