Minimum number of clusters and comparison of analysis methods for cross sectional stepped wedge cluster randomised trials with binary outcomes: A simulation study

Daniel Barker,Patrick Mcelduff,Michael J Campbell,Catherine D’Este

doi:10.1186/s13063-017-1862-2

Abstract

BackgroundStepped wedge cluster randomised trials frequently involve a relatively small number of clusters. The most common frameworks used to analyse data from these types of trials are generalised estimating equations and generalised linear mixed models. A topic of much research into these methods has been their application to cluster randomised trial data and, in particular, the number of clusters required to make reasonable inferences about the intervention effect. However, for stepped wedge trials, which have been claimed by many researchers to have a statistical power advantage over the parallel cluster randomised trial, the minimum number of clusters required has not been investigated.MethodsWe conducted a simulation study where we considered the most commonly used methods suggested in the literature to analyse cross-sectional stepped wedge cluster randomised trial data. We compared the per cent bias, the type I error rate and power of these methods in a stepped wedge trial setting with a binary outcome, where there are few clusters available and when the appropriate adjustment for a time trend is made, which by design may be confounding the intervention effect.ResultsWe found that the generalised linear mixed modelling approach is the most consistent when few clusters are available. We also found that none of the common analysis methods for stepped wedge trials were both unbiased and maintained a 5% type I error rate when there were only three clusters.ConclusionsOf the commonly used analysis approaches, we recommend the generalised linear mixed model for small stepped wedge trials with binary outcomes. We also suggest that in a stepped wedge design with three steps, at least two clusters be randomised at each step, to ensure that the intervention effect estimator maintains the nominal 5% significance level and is also reasonably unbiased.

Highlights

Stepped wedge cluster randomised trials frequently involve a relatively small number of clusters
Which of the currently used methods of analysis is best for an SW-cluster randomised trial (CRT) with a binary outcome when the number of clusters is small? Second, what is the minimum number of clusters required for the consistent and unbiased estimation of the treatment effect in a stepped wedge cluster randomised trial (SW-CRT)? To help answer these questions we present a simulation study for a SW-CRT with a binary outcome, with the simulation study designed according to the guidelines provided by Burton et al [19]
Bias All intervention effect estimates were normally distributed; for the generalised estimating equation (GEE), the Generalised Linear Mixed Model (GLMM) and the fixed effects model this was on the logit scale and for the cluster summaries method this was on the proportion scale

Summary

Introduction

Stepped wedge cluster randomised trials frequently involve a relatively small number of clusters. If the incidence of a disease decreases over time independently of the intervention, failure to adjust for time would result in a biased estimate of the treatment effect This is because randomisation into a SW-CRT causes an association between the intervention and time via an increase in the number of clusters allocated to the intervention as the study progresses. It has been suggested that a SW-CRT will require fewer clusters than a parallel CRT [7, 9,10,11] and recent literature has shown that this is the case when the intra-cluster correlation coefficient (ICC) is high and clusters are large [12] This is perhaps one of the reasons for the increased use of the SW-CRT in recent years [2, 13]

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Conclusion