Abstract
BackgroundThe current methodology for sample size calculations for stepped-wedge cluster randomised trials (SW-CRTs) is based on the assumption of equal cluster sizes. However, as is often the case in cluster randomised trials (CRTs), the clusters in SW-CRTs are likely to vary in size, which in other designs of CRT leads to a reduction in power. The effect of an imbalance in cluster size on the power of SW-CRTs has not previously been reported, nor what an appropriate adjustment to the sample size calculation should be to allow for any imbalance. We aimed to assess the impact of an imbalance in cluster size on the power of a cross-sectional SW-CRT and recommend a method for calculating the sample size of a SW-CRT when there is an imbalance in cluster size.MethodsThe effect of varying degrees of imbalance in cluster size on the power of SW-CRTs was investigated using simulations. The sample size was calculated using both the standard method and two proposed adjusted design effects (DEs), based on those suggested for CRTs with unequal cluster sizes. The data were analysed using generalised estimating equations with an exchangeable correlation matrix and robust standard errors.ResultsAn imbalance in cluster size was not found to have a notable effect on the power of SW-CRTs. The two proposed adjusted DEs resulted in trials that were generally considerably over-powered.ConclusionsWe recommend that the standard method of sample size calculation for SW-CRTs be used, provided that the assumptions of the method hold. However, it would be beneficial to investigate, through simulation, what effect the maximum likely amount of inequality in cluster sizes would be on the power of the trial and whether any inflation of the sample size would be required.
Highlights
The current methodology for sample size calculations for stepped-wedge cluster randomised trials (SW-Cluster randomised trial (CRT)) is based on the assumption of equal cluster sizes
Unlike other designs of CRTs, where sample size calculations have been developed to adjust for unequal cluster sizes, no such calculations have been proposed for use in stepped-wedge cluster randomised trials (SW-CRTs) with unequal cluster sizes
The cluster weights adjusted design effect (DE) is: and the minimum variance weights adjusted DE is: where ρ is the intracluster correlation coefficient (ICC), k is the number of steps, t is the number of measurements taken after each step, m is the average cluster size, b is the number of measurements taken at baseline, Coefficient of variation (CV) is the coefficient of variation in cluster size, I is the number of cluster and mi is the size of the ith cluster
Summary
The current methodology for sample size calculations for stepped-wedge cluster randomised trials (SW-CRTs) is based on the assumption of equal cluster sizes. Hussey and Hughes [8] suggest that these studies should be analysed using generalised linear mixed models, linear mixed models or generalised estimating equations (GEEs); the performance of these models depends on the number of clusters, as well as whether the cluster sizes are equal or unequal [8] These trials face the same problems as other cluster randomised trials (CRTs), with issues of unequal recruitment to clusters and the potential for entire clusters to drop out of the study. The effect of an imbalance in cluster sizes on the power of SW-CRTs has yet to be reported
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