Sample size calculations for cluster randomised trials, with a focus on ordinal outcomes.

Abstract

Background A common approach to sample size calculation for cluster randomised trials (CRTs) is to calculate the sample size assuming individual randomisation and multiply it by an inflation factor, the design effect. This approach is well established for binary and continuous outcomes, but less so for ordinal. As the variety in trial design increases alternative or more complex methods are required. There is currently no single resource that provides a comprehensive summary of methods. This thesis aims to provide a unique contribution towards the review and development of sample size methods for CRTs, with a focus on ordinal outcomes. Methods I provide a comprehensive review of sample size methods for CRTs and summarise the methodological gaps that remain. Through simulation I evaluate the power performance, under realistic trial scenarios, of the design effect for ordinal outcomes calculated using a kappa-type intracluster correlation coefficient (ICC), the ICC on an assumed underlying variable and an ANOVA ICC. I provide practical guidance for sample size calculation for ordinal outcomes in CRTs. Results Simulation results showed when the number of clusters was large the ANOVA and kappa-type estimates were equivalent, and smaller than the latent variable ICC. Use of the ANOVA ICC in the design effect produced adequately powered trials and power was marginally reduced under a minor deviation from the common assumption of proportional odds used in ordered regression. Conclusions For outcomes with three to five categories the ANOVA ICC, calculated by assigning numerical equally spaced scores to the ordinal categories, can be used in the simple design effect to produce an adequately powered trial. The method assumes an analysis by random effects ordered regression with proportional odds, a reasonable number of clusters, and clusters of the same size.