Statistical analysis of publicly funded cluster randomised controlled trials: a review of the National Institute for Health Research Journals Library

Re-analysis of data from cluster randomised trials to explore the impact of model choice on estimates of odds ratios: study protocol

BACKGROUND

There are numerous approaches available to analyse data from cluster randomised trials. These include cluster-level summary methods and individual-level methods accounting for clustering, such as generalised estimating equations and generalised linear mixed models. There has been much methodological work showing that estimates of treatment effects can vary depending on the choice of approach, particularly when estimating odds ratios, essentially because the different approaches target different estimands.

METHODS

In this manuscript, we describe the protocol for a planned re-analysis of data from a large number of cluster randomised trials. Our main objective is to examine empirically whether and how odds ratios estimated using different approaches (for both primary and secondary binary outcomes) vary in cluster randomised trials. We describe the methods that will be used to identify the datasets for inclusion and how they will be analysed and reported.

DISCUSSION

There have been a number of small comparisons of empirical differences between the different approaches to analysis for CRTs. The systematic approach outlined in this protocol will allow a much deeper understanding of when there are important choices around the model approach and in which settings. This will be of importance given the heightened awareness of the importance of estimands and the specification of statistical analysis plans.

What type of cluster randomized trial for which setting?

The cluster randomized trial allows a randomized evaluation when it is either not possible to randomize the individual or randomizing individuals would put the trial at high risk of contamination across treatment arms. There are many variations of the cluster randomized design, including the parallel design with or without baseline measures, the cluster randomized cross-over design, the stepped-wedge cluster randomized design, and more recently-developed variants such as the batched stepped-wedge design and the staircase design. Once it has been clearly established that there is a need for cluster randomization, one ever important question is which form the cluster design should take. If a design in which time is split into multiple trial periods is to be adopted (e.g. as in a stepped-wedge), researchers must decide whether the same participants should be measured in multiple trial periods (cohort sampling); or if different participants should be measured in each period (continual recruitment or cross-sectional sampling). Here we outline the different possible options and weigh up the pros and cons of the different design choices, which revolve around statistical efficiency, study logistics and the assumptions required.

Calculating power for multilevel implementation trials in mental health: Meaningful effect sizes, intraclass correlation coefficients, and proportions of variance explained by covariates

Background

Despite the ubiquity of multilevel sampling, design, and analysis in mental health implementation trials, few resources are available that provide reference values of design parameters (e.g., effect size, intraclass correlation coefficient [ICC], and proportion of variance explained by covariates [covariate R 2]) needed to accurately determine sample size. The aim of this study was to provide empirical reference values for these parameters by aggregating data on implementation and clinical outcomes from multilevel implementation trials, including cluster randomized trials and individually randomized repeated measures trials, in mental health. The compendium of design parameters presented here represents plausible values that implementation scientists can use to guide sample size calculations for future trials.

Method

We searched NIH RePORTER for all federally funded, multilevel implementation trials addressing mental health populations and settings from 2010 to 2020. For all continuous and binary implementation and clinical outcomes included in eligible trials, we generated values of effect size, ICC, and covariate R2 at each level via secondary analysis of trial data or via extraction of estimates from analyses in published research reports. Effect sizes were calculated as Cohen d; ICCs were generated via one-way random effects ANOVAs; covariate R2 estimates were calculated using the reduction in variance approach.

Results

Seventeen trials were eligible, reporting on 53 implementation and clinical outcomes and 81 contrasts between implementation conditions. Tables of effect size, ICC, and covariate R2 are provided to guide implementation researchers in power analyses for designing multilevel implementation trials in mental health settings, including two- and three-level cluster randomized designs and unit-randomized repeated-measures designs.

Conclusions

Researchers can use the empirical reference values reported in this study to develop meaningful sample size determinations for multilevel implementation trials in mental health. Discussion focuses on the application of the reference values reported in this study.

Analysing cluster randomised controlled trials using GLMM, GEE1, GEE2, and QIF: results from four case studies

BACKGROUND

Using four case studies, we aim to provide practical guidance and recommendations for the analysis of cluster randomised controlled trials.

METHODS

Four modelling approaches (Generalized Linear Mixed Models with parameters estimated by maximum likelihood/restricted maximum likelihood; Generalized Linear Models with parameters estimated by Generalized Estimating Equations (1st order or second order) and Quadratic Inference Function, for analysing correlated individual participant level outcomes in cluster randomised controlled trials were identified after we reviewed the literature. We systematically searched the online bibliography databases of MEDLINE, EMBASE, PsycINFO (via OVID), CINAHL (via EBSCO), and SCOPUS. We identified the above-mentioned four statistical analytical approaches and applied them to four case studies of cluster randomised controlled trials with the number of clusters ranging from 10 to 100, and individual participants ranging from 748 to 9,207. Results were obtained for both continuous and binary outcomes using R and SAS statistical packages.

RESULTS

The intracluster correlation coefficient (ICC) estimates for the case studies were less than 0.05 and are consistent with the observed ICC values commonly reported in primary care and community-based cluster randomised controlled trials. In most cases, the four methods produced similar results. However, in a few analyses, quadratic inference function produced different results compared to the generalized linear mixed model, first-order generalized estimating equations, and second-order generalized estimating equations, especially in trials with small to moderate numbers of clusters.

CONCLUSION

This paper demonstrates the analysis of cluster randomised controlled trials with four modelling approaches. The results obtained were similar in most cases, however, for trials with few clusters we do recommend that the quadratic inference function should be used with caution, and where possible a small sample correction should be used. The generalisability of our results is limited to studies with similar features to our case studies, for example, studies with a similar-sized ICC. It is important to conduct simulation studies to comprehensively evaluate the performance of the four modelling approaches.

Key considerations for designing, conducting and analysing a cluster randomized trial

Not only do cluster randomized trials require a larger sample size than individually randomized trials, they also face many additional complexities. The potential for contamination is the most commonly used justification for using cluster randomization, but the risk of contamination should be carefully weighed against the more serious problem of questionable scientific validity in settings with post-randomization identification or recruitment of participants unblinded to the treatment allocation. In this paper we provide some simple guidelines to help researchers conduct cluster trials in a way that minimizes potential biases and maximizes statistical efficiency. The overarching theme of this guidance is that methods that apply to individually randomized trials rarely apply to cluster randomized trials. We recommend that cluster randomization be only used when necessary-balancing the benefits of cluster randomization with its increased risks of bias and increased sample size. Researchers should also randomize at the lowest possible level-balancing the risks of contamination with ensuring an adequate number of randomization units-as well as exploring other options for statistically efficient designs. Clustering should always be allowed for in the sample size calculation; and the use of restricted randomization (and adjustment in the analysis for covariates used in the randomization) should be considered. Where possible, participants should be recruited before randomizing clusters and, when recruiting (or identifying) participants post-randomization, recruiters should be masked to the allocation. In the analysis, the target of inference should align with the research question, and adjustment for clustering and small sample corrections should be used when the trial includes less than about 40 clusters.

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.

Alternative Designs for Testing Speech, Language, and Hearing Interventions: Cluster-Randomized Trials and Stepped-Wedge Designs

PURPOSE

Individual-randomized trials are the gold standard for testing the efficacy and effectiveness of drugs, devices, and behavioral interventions. Health care delivery, educational, and programmatic interventions are often complex, involving multiple levels of change and measurement precluding individual randomization for testing. Cluster-randomized trials and cluster-randomized stepped-wedge trials are alternatives where the intervention is allocated at the group level, such as a clinic or a school, and the outcomes are measured at the person level. These designs are introduced along with the statistical implications of similarities among individuals within the same cluster. We also illustrate the parameters that have the most impact on the likelihood of detecting intervention effects, which must be considered when planning these trials.

CONCLUSION

Cluster-randomized and stepped-wedge designs should be considered by researchers as experimental alternatives to individual-randomized trials when testing speech, language, and hearing care interventions in real-world settings.