A weighted Jackknife method for clustered data

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.

A weighted Jackknife approach utilizing linear model based-estimators for clustered data

Small number of clusters combined with cluster level heterogeneity poses a great challenge for the data analysis. We have published a weighted Jackknife approach to address this issue applying weighted cluster means as the basic estimators. The current study proposes a new version of the weighted delete-one-cluster Jackknife analytic framework, which employs Ordinary Least Squares or Generalized Least Squares estimators as the fundamentals. Algorithms for computing estimated variances of the study estimators have also been derived. Wald test statistics can be further obtained, and the statistical comparison in the outcome means of two conditions is determined using the cluster permutation procedure. The simulation studies show that the proposed framework produces estimates with higher precision and improved power for statistical hypothesis testing compared to other methods.