The impact of varying cluster size in cross-sectional stepped-wedge cluster randomised trials

Background/Aims: Published methods for sample size calculation for cluster randomised trials with baseline data are inflexible and primarily assume an equal amount of data collected at baseline and endline, that is, before and after the intervention has been implemented in some clusters. We extend these methods to any amount of baseline and endline data. We explain how to explore sample size for a trial if some baseline data from the trial clusters have already been collected as part of a separate study. Where such data aren’t available, we show how to choose the proportion of data collection devoted to the baseline within the trial, when a particular cluster size or range of cluster sizes is proposed. Methods: We provide a design effect given the cluster size and correlation parameters, assuming different participants are assessed at baseline and endline in the same clusters. We show how to produce plots to identify the impact of varying the amount of baseline data accounting for the inevitable uncertainty in the cluster autocorrelation. We illustrate the methodology using an example trial. Results: Baseline data provide more power, or allow a greater reduction in trial size, with greater values of the cluster size, intracluster correlation and cluster autocorrelation. Conclusion: Investigators should think carefully before collecting baseline data in a cluster randomised trial if this is at the expense of endline data. In some scenarios, this will increase the sample size required to achieve given power and precision.

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Inference for the treatment effect in multiple-period cluster randomised trials when random effect correlation structure is misspecified

Statistical Methods in Medical Research ◽

10.1177/0962280218797151 ◽

2018 ◽

Vol 28 (10-11) ◽

pp. 3112-3122 ◽

Cited By ~ 9

Author(s):

Jessica Kasza ◽

Andrew B Forbes

Keyword(s):

Treatment Effect ◽

Random Effect ◽

Correlation Structure ◽

Randomised Trials ◽

Stepped Wedge ◽

Cluster Randomised Trials ◽

Cluster Randomised ◽

Complex Models ◽

The Impact ◽

Cluster Correlation

Multiple-period cluster randomised trials, such as stepped wedge or cluster cross-over trials, are being conducted with increasing frequency. In the design and analysis of these trials, it is necessary to specify the form of the within-cluster correlation structure, and a common assumption is that the correlation between the outcomes of any pair of subjects within a cluster is identical. More complex models that allow for correlations within a cluster to decay over time have recently been suggested. However, most software packages cannot fit these models. As a result, practitioners may choose a simpler model. We analytically examine the impact of incorrectly omitting a decay in correlation on the variance of the treatment effect estimator and show that misspecification of the within-cluster correlation structure can lead to incorrect conclusions regarding estimated treatment effects for stepped wedge and cluster crossover trials.

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Impact of non-uniform correlation structure on sample size and power in multiple-period cluster randomised trials

Statistical Methods in Medical Research ◽

10.1177/0962280217734981 ◽

2017 ◽

Vol 28 (3) ◽

pp. 703-716 ◽

Cited By ~ 29

Author(s):

J Kasza ◽

K Hemming ◽

R Hooper ◽

JNS Matthews ◽

AB Forbes

Keyword(s):

Sample Size ◽

Treatment Effect ◽

Correlation Structure ◽

Randomised Trials ◽

Stepped Wedge ◽

Correlation Decay ◽

Cluster Randomised Trials ◽

Cluster Randomised ◽

The Impact ◽

Cluster Correlation

Stepped wedge and cluster randomised crossover trials are examples of cluster randomised designs conducted over multiple time periods that are being used with increasing frequency in health research. Recent systematic reviews of both of these designs indicate that the within-cluster correlation is typically taken account of in the analysis of data using a random intercept mixed model, implying a constant correlation between any two individuals in the same cluster no matter how far apart in time they are measured: within-period and between-period intra-cluster correlations are assumed to be identical. Recently proposed extensions allow the within- and between-period intra-cluster correlations to differ, although these methods require that all between-period intra-cluster correlations are identical, which may not be appropriate in all situations. Motivated by a proposed intensive care cluster randomised trial, we propose an alternative correlation structure for repeated cross-sectional multiple-period cluster randomised trials in which the between-period intra-cluster correlation is allowed to decay depending on the distance between measurements. We present results for the variance of treatment effect estimators for varying amounts of decay, investigating the consequences of the variation in decay on sample size planning for stepped wedge, cluster crossover and multiple-period parallel-arm cluster randomised trials. We also investigate the impact of assuming constant between-period intra-cluster correlations instead of decaying between-period intra-cluster correlations. Our results indicate that in certain design configurations, including the one corresponding to the proposed trial, a correlation decay can have an important impact on variances of treatment effect estimators, and hence on sample size and power. An R Shiny app allows readers to interactively explore the impact of correlation decay.

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An imbalance in cluster sizes does not lead to notable loss of power in cross-sectional, stepped-wedge cluster randomised trials with a continuous outcome

Trials ◽

10.1186/s13063-017-1832-8 ◽

2017 ◽

Vol 18 (1) ◽

Cited By ~ 7

Author(s):

Caroline A. Kristunas ◽

Karen L. Smith ◽

Laura J. Gray

Keyword(s):

Randomised Trials ◽

Stepped Wedge ◽

Cross Sectional ◽

Continuous Outcome ◽

Cluster Randomised Trials ◽

Cluster Randomised

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Minimum number of clusters and comparison of analysis methods for cross sectional stepped wedge cluster randomised trials with binary outcomes: A simulation study

Trials ◽

10.1186/s13063-017-1862-2 ◽

2017 ◽

Vol 18 (1) ◽

Cited By ~ 9

Author(s):

Daniel Barker ◽

Catherine D’Este ◽

Michael J. Campbell ◽

Patrick McElduff

Keyword(s):

Simulation Study ◽

Binary Outcomes ◽

Randomised Trials ◽

Stepped Wedge ◽

Cross Sectional ◽

Number Of Clusters ◽

Cluster Randomised Trials ◽

Cluster Randomised ◽

Analysis Methods ◽

Minimum Number

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The role of cluster size and intra-cluster correlations when adjusting for covariates in the analysis of cluster randomised trials

Trials ◽

10.1186/1745-6215-16-s2-p154 ◽

2015 ◽

Vol 16 (S2) ◽

Author(s):

Neil Wright

Keyword(s):

Cluster Size ◽

Randomised Trials ◽

Cluster Randomised Trials ◽

Cluster Randomised

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Group sequential designs for stepped-wedge cluster randomised trials

Clinical Trials ◽

10.1177/1740774517716937 ◽

2017 ◽

Vol 14 (5) ◽

pp. 507-517 ◽

Cited By ~ 5

Author(s):

Michael J Grayling ◽

James MS Wason ◽

Adrian P Mander

Keyword(s):

Randomised Trial ◽

Cluster Randomised Trial ◽

Type I ◽

Randomised Trials ◽

Early Stopping ◽

Stepped Wedge ◽

Group Sequential ◽

Interim Analyses ◽

Cluster Randomised Trials ◽

Cluster Randomised

Background/Aims: The stepped-wedge cluster randomised trial design has received substantial attention in recent years. Although various extensions to the original design have been proposed, no guidance is available on the design of stepped-wedge cluster randomised trials with interim analyses. In an individually randomised trial setting, group sequential methods can provide notable efficiency gains and ethical benefits. We address this by discussing how established group sequential methodology can be adapted for stepped-wedge designs. Methods: Utilising the error spending approach to group sequential trial design, we detail the assumptions required for the determination of stepped-wedge cluster randomised trials with interim analyses. We consider early stopping for efficacy, futility, or efficacy and futility. We describe first how this can be done for any specified linear mixed model for data analysis. We then focus on one particular commonly utilised model and, using a recently completed stepped-wedge cluster randomised trial, compare the performance of several designs with interim analyses to the classical stepped-wedge design. Finally, the performance of a quantile substitution procedure for dealing with the case of unknown variance is explored. Results: We demonstrate that the incorporation of early stopping in stepped-wedge cluster randomised trial designs could reduce the expected sample size under the null and alternative hypotheses by up to 31% and 22%, respectively, with no cost to the trial’s type-I and type-II error rates. The use of restricted error maximum likelihood estimation was found to be more important than quantile substitution for controlling the type-I error rate. Conclusion: The addition of interim analyses into stepped-wedge cluster randomised trials could help guard against time-consuming trials conducted on poor performing treatments and also help expedite the implementation of efficacious treatments. In future, trialists should consider incorporating early stopping of some kind into stepped-wedge cluster randomised trials according to the needs of the particular trial.

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