scholarly journals Sample size calculation for stepped wedge and other longitudinal cluster randomised trials

2016 ◽  
Vol 35 (26) ◽  
pp. 4718-4728 ◽  
Author(s):  
Richard Hooper ◽  
Steven Teerenstra ◽  
Esther de Hoop ◽  
Sandra Eldridge
Keyword(s):  
Sample Size ◽  
Sample Size Calculation ◽  
Randomised Trials ◽  
Stepped Wedge ◽  
Cluster Randomised Trials ◽  
Cluster Randomised

scholarly journals Unequal cluster sizes in stepped-wedge cluster randomised trials: a systematic review

BMJ Open ◽  
2017 ◽  
Vol 7 (11) ◽  
pp. e017151 ◽  
Author(s):  
Caroline Kristunas ◽  
Tom Morris ◽  
Laura Gray
Keyword(s):  
Sample Size ◽  
Statistical Power ◽  
Sample Size Calculation ◽  
Secondary Outcome ◽  
Randomised Trials ◽  
Stepped Wedge ◽  
Cluster Randomised Trials ◽  
Cluster Randomised ◽  
The Difference ◽  
Unequal Cluster

ObjectivesTo investigate the extent to which cluster sizes vary in stepped-wedge cluster randomised trials (SW-CRT) and whether any variability is accounted for during the sample size calculation and analysis of these trials.SettingAny, not limited to healthcare settings.ParticipantsAny taking part in an SW-CRT published up to March 2016.Primary and secondary outcome measuresThe primary outcome is the variability in cluster sizes, measured by the coefficient of variation (CV) in cluster size. Secondary outcomes include the difference between the cluster sizes assumed during the sample size calculation and those observed during the trial, any reported variability in cluster sizes and whether the methods of sample size calculation and methods of analysis accounted for any variability in cluster sizes.ResultsOf the 101 included SW-CRTs, 48% mentioned that the included clusters were known to vary in size, yet only 13% of these accounted for this during the calculation of the sample size. However, 69% of the trials did use a method of analysis appropriate for when clusters vary in size. Full trial reports were available for 53 trials. The CV was calculated for 23 of these: the median CV was 0.41 (IQR: 0.22–0.52). Actual cluster sizes could be compared with those assumed during the sample size calculation for 14 (26%) of the trial reports; the cluster sizes were between 29% and 480% of that which had been assumed.ConclusionsCluster sizes often vary in SW-CRTs. Reporting of SW-CRTs also remains suboptimal. The effect of unequal cluster sizes on the statistical power of SW-CRTs needs further exploration and methods appropriate to studies with unequal cluster sizes need to be employed.

scholarly journals Systematic review finds major deficiencies in sample size methodology and reporting for stepped-wedge cluster randomised trials

BMJ Open ◽  
2016 ◽  
Vol 6 (2) ◽  
pp. e010166 ◽  
Author(s):  
James Martin ◽  
Monica Taljaard ◽  
Alan Girling ◽  
Karla Hemming
Keyword(s):  
Systematic Review ◽  
Sample Size ◽  
Randomised Trials ◽  
Stepped Wedge ◽  
Cluster Randomised Trials ◽  
Cluster Randomised

scholarly journals Cluster randomised trials with different numbers of measurements at baseline and endline: Sample size and optimal allocation

2019 ◽  
Vol 17 (1) ◽  
pp. 69-76
Author(s):  
Andrew J Copas ◽  
Richard Hooper
Keyword(s):  
Sample Size ◽  
Cluster Size ◽  
Randomised Trial ◽  
Sample Size Calculation ◽  
Baseline Data ◽  
Cluster Randomised Trial ◽  
Randomised Trials ◽  
Cluster Randomised Trials ◽  
Cluster Randomised ◽  
The Impact

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.

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

2017 ◽  
Vol 28 (3) ◽  
pp. 703-716 ◽  
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.

scholarly journals Sample sizes for cluster-randomised trials with continuous outcomes: Accounting for uncertainty in a single intra-cluster correlation estimate

2021 ◽  
pp. 096228022110370
Author(s):  
Jen Lewis ◽  
Steven A Julious
Keyword(s):  
Sample Size ◽  
Correlation Coefficient ◽  
Randomised Trial ◽  
Sample Size Calculation ◽  
Coefficient Estimate ◽  
Randomised Trials ◽  
Main Trial ◽  
Cluster Randomised Trials ◽  
Cluster Randomised ◽  
Cluster Correlation

Sample size calculations for cluster-randomised trials require inclusion of an inflation factor taking into account the intra-cluster correlation coefficient. Often, estimates of the intra-cluster correlation coefficient are taken from pilot trials, which are known to have uncertainty about their estimation. Given that the value of the intra-cluster correlation coefficient has a considerable influence on the calculated sample size for a main trial, the uncertainty in the estimate can have a large impact on the ultimate sample size and consequently, the power of a main trial. As such, it is important to account for the uncertainty in the estimate of the intra-cluster correlation coefficient. While a commonly adopted approach is to utilise the upper confidence limit in the sample size calculation, this is a largely inefficient method which can result in overpowered main trials. In this paper, we present a method of estimating the sample size for a main cluster-randomised trial with a continuous outcome, using numerical methods to account for the uncertainty in the intra-cluster correlation coefficient estimate. Despite limitations with this initial study, the findings and recommendations in this paper can help to improve sample size estimations for cluster randomised controlled trials by accounting for uncertainty in the estimate of the intra-cluster correlation coefficient. We recommend this approach be applied to all trials where there is uncertainty in the intra-cluster correlation coefficient estimate, in conjunction with additional sources of information to guide the estimation of the intra-cluster correlation coefficient.

scholarly journals Intra-cluster correlations from the CLustered OUtcome Dataset bank to inform the design of longitudinal cluster trials

2021 ◽  
pp. 174077452110208
Author(s):  
Elizabeth Korevaar ◽  
Jessica Kasza ◽  
Monica Taljaard ◽  
Karla Hemming ◽  
Terry Haines ◽  
...  
Keyword(s):  
Sample Size ◽  
Discrete Time ◽  
Correlation Coefficients ◽  
Time Decay ◽  
Randomised Trials ◽  
Cluster Randomised Trials ◽  
Cluster Randomised ◽  
Sample Size Calculations ◽  
Correlation Structures ◽  
Cluster Correlation

Background: Sample size calculations for longitudinal cluster randomised trials, such as crossover and stepped-wedge trials, require estimates of the assumed correlation structure. This includes both within-period intra-cluster correlations, which importantly differ from conventional intra-cluster correlations by their dependence on period, and also cluster autocorrelation coefficients to model correlation decay. There are limited resources to inform these estimates. In this article, we provide a repository of correlation estimates from a bank of real-world clustered datasets. These are provided under several assumed correlation structures, namely exchangeable, block-exchangeable and discrete-time decay correlation structures. Methods: Longitudinal studies with clustered outcomes were collected to form the CLustered OUtcome Dataset bank. Forty-four available continuous outcomes from 29 datasets were obtained and analysed using each correlation structure. Patterns of within-period intra-cluster correlation coefficient and cluster autocorrelation coefficients were explored by study characteristics. Results: The median within-period intra-cluster correlation coefficient for the discrete-time decay model was 0.05 (interquartile range: 0.02–0.09) with a median cluster autocorrelation of 0.73 (interquartile range: 0.19–0.91). The within-period intra-cluster correlation coefficients were similar for the exchangeable, block-exchangeable and discrete-time decay correlation structures. Within-period intra-cluster correlation coefficients and cluster autocorrelations were found to vary with the number of participants per cluster-period, the period-length, type of cluster (primary care, secondary care, community or school) and country income status (high-income country or low- and middle-income country). The within-period intra-cluster correlation coefficients tended to decrease with increasing period-length and slightly decrease with increasing cluster-period sizes, while the cluster autocorrelations tended to move closer to 1 with increasing cluster-period size. Using the CLustered OUtcome Dataset bank, an RShiny app has been developed for determining plausible values of correlation coefficients for use in sample size calculations. Discussion: This study provides a repository of intra-cluster correlations and cluster autocorrelations for longitudinal cluster trials. This can help inform sample size calculations for future longitudinal cluster randomised trials.

scholarly journals Group sequential designs for stepped-wedge cluster randomised trials

2017 ◽  
Vol 14 (5) ◽  
pp. 507-517 ◽  
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.

Re-estimating sample size in cluster randomised trials with active recruitment within clusters

2014 ◽  
Vol 33 (19) ◽  
pp. 3253-3268 ◽  
Author(s):  
S. van Schie ◽  
M. Moerbeek
Keyword(s):  
Sample Size ◽  
Randomised Trials ◽  
Cluster Randomised Trials ◽  
Cluster Randomised
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