Designing psycho-oncology randomised trials and cluster randomised trials: variance components and intra-cluster correlation of commonly used psychosocial measures

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.

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

Statistical Methods in Medical Research ◽

10.1177/09622802211037073 ◽

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.

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