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

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.

Association of intracluster correlation measures with outcome prevalence for binary outcomes in cluster randomised trials

In cluster randomised trials, a measure of intracluster correlation such as the intraclass correlation coefficient (ICC) should be reported for each primary outcome. Providing intracluster correlation estimates may help in calculating sample size of future cluster randomised trials and also in interpreting the results of the trial from which they are derived. For a binary outcome, the ICC is known to be associated with its prevalence, which raises at least two issues. First, it questions the use of ICC estimates obtained on a binary outcome in a trial for sample size calculations in a subsequent trial in which the same binary outcome is expected to have a different prevalence. Second, it challenges the interpretation of ICC estimates because they do not solely depend on clustering level. Other intracluster correlation measures proposed for clustered binary data settings include the variance partition coefficient, the median odds ratio and the tetrachoric correlation coefficient. Under certain assumptions, the theoretical maximum possible value for an ICC associated with a binary outcome can be derived, and we proposed the relative deviation of an ICC estimate to this maximum value as another measure of the intracluster correlation. We conducted a simulation study to explore the dependence of these intracluster correlation measures on outcome prevalence and found that all are associated with prevalence. Even if all depend on prevalence, the tetrachoric correlation coefficient computed with Kirk’s approach was less dependent on the outcome prevalence than the other measures when the intracluster correlation was about 0.05. We also observed that for lower values, such as 0.01, the analysis of variance estimator of the ICC is preferred.

Interim data monitoring in cluster randomised trials: Practical issues and a case study

Background There is an abundance of guidance for the interim monitoring of individually randomised trials. While methodological literature exists on how to extend these methods to cluster randomised trials, there is little guidance on practical implementation. Cluster trials have many features which make their monitoring needs different. We outline the methodological and practical challenges of interim monitoring of cluster trials; and apply these considerations to a case study. Case study The E-MOTIVE study is an 80-cluster randomised trial of a bundle of interventions to treat postpartum haemorrhage. The proposed data monitoring plan includes (1) monitor sample size assumptions, (2) monitor for evidence of selection bias, and (3) an interim assessment of the primary outcome, as well as monitoring data completeness. The timing of the sample size monitoring is chosen with both consideration of statistical precision and to allow time to recruit more clusters. Monitoring for selection bias involves comparing individual-level characteristics and numbers recruited between study arms to identify any post-randomisation participant identification bias. An interim analysis of outcomes presented with 99.9% confidence intervals using the Haybittle–Peto approach should mitigate any concern regarding the inflation of type-I error. The pragmatic nature of the trial means monitoring for adherence is not relevant, as it is built into a process evaluation. Conclusions The interim analyses of cluster trials have a number of important differences to monitoring individually randomised trials. In cluster trials, there will often be a greater need to monitor nuisance parameters, yet there will often be considerable uncertainty in their estimation. This means the utility of sample size re-estimation can be questionable particularly when there are practical or funding difficulties associated with making any changes to planned sample sizes. Perhaps most importantly interim monitoring has the potential to identify selection bias, particularly in trials with post-randomisation identification or recruitment. Finally, the pragmatic nature of cluster trials might mean that the utility of methods to allow for interim monitoring of outcomes based on statistical testing, or monitoring for adherence to study interventions, are less relevant. Our intention is to facilitate the planning of future cluster randomised trials and to promote discussion and debate to improve monitoring of these studies.

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

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.

Optimal design of cluster randomised trials with continuous recruitment and prospective baseline period

Background: Cluster randomised trials, like individually randomised trials, may benefit from a baseline period of data collection. We consider trials in which clusters prospectively recruit or identify participants as a continuous process over a given calendar period, and ask whether and for how long investigators should collect baseline data as part of the trial, in order to maximise precision. Methods: We show how to calculate and plot the variance of the treatment effect estimator for different lengths of baseline period in a range of scenarios, and offer general advice. Results: In some circumstances it is optimal not to include a baseline, while in others there is an optimal duration for the baseline. All other things being equal, the circumstances where it is preferable not to include a baseline period are those with a smaller recruitment rate, smaller intracluster correlation, greater decay in the intracluster correlation over time, or wider transition period between recruitment under control and intervention conditions. Conclusion: The variance of the treatment effect estimator can be calculated numerically, and plotted against the duration of baseline to inform design. It would be of interest to extend these investigations to cluster randomised trial designs with more than two randomised sequences of control and intervention condition, including stepped wedge designs.