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.

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

BACKGROUND: In cluster randomised controlled trials (cRCTs), groups of individuals (rather than individuals) are randomised to minimise the risk of contamination and/or efficiently use limited resources or solve logistic and administrative problems. A major concern in the primary analysis of cRCT is the use of appropriate statistical methods to account for correlation among outcomes from a particular group/cluster. This review aimed to investigate the statistical methods used in practice for analysing the primary outcomes in publicly funded cluster randomised controlled trials, adherence to the CONSORT (Consolidated Standards of Reporting Trials) reporting guidelines for cRCTs and the recruitment abilities of the cluster trials design. METHODS: We manually searched the United Kingdom's National Institute for Health Research (NIHR) online Journals Library, from 1 January 1997 to 15 July 2021 chronologically for reports of cRCTs. Information on the statistical methods used in the primary analyses was extracted. One reviewer conducted the search and extraction while the two other independent reviewers supervised and validated 25% of the total trials reviewed. RESULTS: A total of 1942 reports, published online in the NIHR Journals Library were screened for eligibility, 118 reports of cRCTs met the initial inclusion criteria, of these 79 reports containing the results of 86 trials with 100 primary outcomes analysed were finally included. Two primary outcomes were analysed at the cluster-level using a generalized linear model. At the individual-level, the generalized linear mixed model was the most used statistical method (80%, 80/100), followed by regression with robust standard errors (7%) then generalized estimating equations (6%). Ninety-five percent (95/100) of the primary outcomes in the trials were analysed with appropriate statistical methods that accounted for clustering while 5% were not. The mean observed intracluster correlation coefficient (ICC) was 0.06 (SD, 0.12; range, - 0.02 to 0.63), and the median value was 0.02 (IQR, 0.001-0.060), although 42% of the observed ICCs for the analysed primary outcomes were not reported. CONCLUSIONS: In practice, most of the publicly funded cluster trials adjusted for clustering using appropriate statistical method(s), with most of the primary analyses done at the individual level using generalized linear mixed models. However, the inadequate analysis and poor reporting of cluster trials published in the UK is still happening in recent times, despite the availability of the CONSORT reporting guidelines for cluster trials published over a decade ago.