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

Findings from a pragmatic cluster randomised controlled feasibility trial of a music and dance programme for community dwelling older adults

INTRODUCTION

Functional decline, chronic illness, reduced quality of life and increased healthcare utilisation are common in older adults. Evidence suggests music and dance can support healthy ageing in older adults. This study explored the feasibility, potential for effect and cost effectiveness of the Music and Movement for Health (MMH) programme among community-dwelling older adults using a pragmatic cluster-randomised, controlled feasibility trial design.

METHODS

Community-dwelling adults aged 65 years or older were recruited to seven clusters in the Mid-West region of Ireland. Clusters were block randomised to either the MMH intervention or control. Primary feasibility outcomes included recruitment, retention, adherence, fidelity, and safety. Secondary outcomes measured physical activity, physical and cognitive performance, and psychosocial well-being, along with healthcare utilisation were assessed at baseline and after 12 weeks.

RESULTS

The study successfully met feasibility targets, with recruitment (n = 100), retention (91 %), adherence (71 %), data completeness (92 %) and intervention fidelity (21 out of 24) all meeting predetermined criteria. Both groups exhibited an increase in self-reported physical activity and improved physical function. Participants in the intervention group scored consistently better in psychosocial measures compared to the control group at follow-up. The health economic analysis confirmed the feasibility of the methodology employed and points to the potential cost-effectiveness of the MMH relative to the control or no organised programme.

DISCUSSION AND IMPLICATIONS

The MMH intervention and study design were found to be feasible and acceptable with important findings to inform future evaluation of the clinical and cost-effectiveness of a definitive randomised controlled trial.

The symbolic two-step method applied to cancer care delivery research: Safeguarding against designing an underpowered cluster randomized trial with a continuous outcome by accounting for the imprecision in the within- and between-center variation

BACKGROUND

Knowing the predictive factors of the variation in a center-level continuous outcome of interest is valuable in the design and analysis of parallel-arm cluster randomized trials. The symbolic two-step method for sample size planning that we present incorporates this knowledge while simultaneously accounting for patient-level characteristics. Our approach is illustrated through application to cluster randomized trials in cancer care delivery research. The required number of centers (clusters) depends on the between- and within-center variance; the within-center variance is a function of estimates obtained by regressing the log within-center variance on predictive factors. Obtaining accurate estimates of the components needed to characterize the within-center variation is challenging.

METHODS

Using our previously derived sample size formula, our objective in the current research is to directly account for the imprecision in these estimates, using a Bayesian approach, to safeguard against designing an underpowered study when using the symbolic two-step method. Using estimates of the required components, including the number of centers that contribute to those estimates, we make formal allowance for the imprecision in these estimates on which a sample size will be based.

RESULTS

The mean of the distribution for power is consistently smaller than the single point estimate that the sample size formula yields. The reduction in power is more pronounced in the presence of increased uncertainty about the estimates with the reduction becoming more attenuated with increased numbers of centers that contribute to the estimates.

CONCLUSIONS

Accounting for imprecision in the estimates of the components required for sample size estimation using the symbolic two-step method in the design of a cluster randomized trial yields conservative estimates of power.

Bayesian optimal stepped wedge design

Recently, there has been a growing interest in designing cluster trials using stepped wedge design (SWD). An SWD is a type of cluster-crossover design in which clusters of individuals are randomized unidirectional from a control to an intervention at certain time points. The intraclass correlation coefficient (ICC) that measures the dependency of subject within a cluster plays an important role in design and analysis of stepped wedge trials. In this paper, we discuss a Bayesian approach to address the dependency of SWD on the ICC and robust Bayesian SWDs are proposed. Bayesian design is shown to be more robust against the misspecification of the parameter values compared to the locally optimal design. Designs are obtained for the various choices of priors assigned to the ICC. A detailed sensitivity analysis is performed to assess the robustness of proposed optimal designs. The power superiority of Bayesian design against the commonly used balanced design is demonstrated numerically using hypothetical as well as real scenarios.

Determining the sample size for a cluster-randomised trial using knowledge elicitation: Bayesian hierarchical modelling of the intracluster correlation coefficient

BACKGROUND

The intracluster correlation coefficient is a key input parameter for sample size determination in cluster-randomised trials. Sample size is very sensitive to small differences in the intracluster correlation coefficient, so it is vital to have a robust intracluster correlation coefficient estimate. This is often problematic because either a relevant intracluster correlation coefficient estimate is not available or the available estimate is imprecise due to being based on small-scale studies with low numbers of clusters. Misspecification may lead to an underpowered or inefficiently large and potentially unethical trial.

METHODS

We apply a Bayesian approach to produce an intracluster correlation coefficient estimate and hence propose sample size for a planned cluster-randomised trial of the effectiveness of a systematic voiding programme for post-stroke incontinence. A Bayesian hierarchical model is used to combine intracluster correlation coefficient estimates from other relevant trials making use of the wealth of intracluster correlation coefficient information available in published research. We employ knowledge elicitation process to assess the relevance of each intracluster correlation coefficient estimate to the planned trial setting. The team of expert reviewers assigned relevance weights to each study, and each outcome within the study, hence informing parameters of Bayesian modelling. To measure the performance of experts, agreement and reliability methods were applied.

RESULTS

The 34 intracluster correlation coefficient estimates extracted from 16 previously published trials were combined in the Bayesian hierarchical model using aggregated relevance weights elicited from the experts. The intracluster correlation coefficients available from external sources were used to construct a posterior distribution of the targeted intracluster correlation coefficient which was summarised as a posterior median with a 95% credible interval informing researchers about the range of plausible sample size values. The estimated intracluster correlation coefficient determined a sample size of between 450 (25 clusters) and 480 (20 clusters), compared to 500-600 from a classical approach. The use of quantiles, and other parameters, from the estimated posterior distribution is illustrated and the impact on sample size described.

CONCLUSION

Accounting for uncertainty in an unknown intracluster correlation coefficient, trials can be designed with a more robust sample size. The approach presented provides the possibility of incorporating intracluster correlation coefficients from various cluster-randomised trial settings which can differ from the planned study, with the difference being accounted for in the modelling. By using expert knowledge to elicit relevance weights and synthesising the externally available intracluster correlation coefficient estimates, information is used more efficiently than in a classical approach, where the intracluster correlation coefficient estimates tend to be less robust and overly conservative. The intracluster correlation coefficient estimate constructed is likely to produce a smaller sample size on average than the conventional strategy of choosing a conservative intracluster correlation coefficient estimate. This may therefore result in substantial time and resources savings.

A hybrid approach to comparing parallel-group and stepped-wedge cluster-randomized trials with a continuous primary outcome when there is uncertainty in the intra-cluster correlation

BACKGROUND/AIMS

To evaluate how uncertainty in the intra-cluster correlation impacts whether a parallel-group or stepped-wedge cluster-randomized trial design is more efficient in terms of the required sample size, in the case of cross-sectional stepped-wedge cluster-randomized trials and continuous outcome data.

METHODS

We motivate our work by reviewing how the intra-cluster correlation and standard deviation were justified in 54 health technology assessment reports on cluster-randomized trials. To enable uncertainty at the design stage to be incorporated into the design specification, we then describe how sample size calculation can be performed for cluster- randomized trials in the 'hybrid' framework, which places priors on design parameters and controls the expected power in place of the conventional frequentist power. Comparison of the parallel-group and stepped-wedge cluster-randomized trial designs is conducted by placing Beta and truncated Normal priors on the intra-cluster correlation, and a Gamma prior on the standard deviation.

RESULTS

Many Health Technology Assessment reports did not adhere to the Consolidated Standards of Reporting Trials guideline of indicating the uncertainty around the assumed intra-cluster correlation, while others did not justify the assumed intra-cluster correlation or standard deviation. Even for a prior intra-cluster correlation distribution with a small mode, moderate prior densities on high intra-cluster correlation values can lead to a stepped-wedge cluster-randomized trial being more efficient because of the degree to which a stepped-wedge cluster-randomized trial is more efficient for high intra-cluster correlations. With careful specification of the priors, the designs in the hybrid framework can become more robust to, for example, an unexpectedly large value of the outcome variance.

CONCLUSION

When there is difficulty obtaining a reliable value for the intra-cluster correlation to assume at the design stage, the proposed methodology offers an appealing approach to sample size calculation. Often, uncertainty in the intra-cluster correlation will mean a stepped-wedge cluster-randomized trial is more efficient than a parallel-group cluster-randomized trial design.