Abstract
BackgroundCluster randomised trials with unequal sized clusters often have lower precision than with clusters of equal size. To allow for this, sample sizes are inflated by a modified version of the design effect for clustering. These inflation factors are valid under the assumption that randomisation is stratified by cluster size. We investigate the impact of unequal cluster size when that constraint is relaxed, with particular focus on the stepped-wedge cluster randomised trial, where this is more difficult to achieve.MethodsAssuming a multi-level mixed effect model with exchangeable correlation structure for a cross-sectional design, we use simulation methods to compare the precision for a trial with clusters of unequal size to a trial with clusters of equal size (relative efficiency). For a range of scenarios we illustrate the impact of various design features (the cluster-mean correlation – a function of the intracluster correlation and the cluster size, the number of clusters, number of randomisation sequences) on the average and distribution of the relative efficiency.ResultsSimulations confirm that the average reduction in precision, due to varying cluster sizes, is smaller in a stepped-wedge trial compared to the parallel trial. However, the variance of the distribution of the relative efficiency is large; and is larger under the stepped-wedge design compared to the parallel design. This can result in large variations in actual power, depending on the allocation of clusters to sequences. Designs with larger variations in cluster sizes, smaller number of clusters and studies with smaller cluster-mean correlations (smaller cluster sizes or smaller intra-cluster correlation) are particularly at risk.ConclusionThe actual realised power in a stepped-wedge trial might be substantially higher or lower than that estimated. This is particularly important when there are a small number of clusters or the variability in cluster sizes is large. Constraining the randomisation on cluster size, where feasible, might mitigate this effect.
Highlights
Cluster randomised trials with unequal sized clusters often have lower precision than with clusters of equal size
We explore which of a SW-Cluster randomised trial (CRT) and a parallel CRT (PCRT) is most affected by varying cluster size; and to a limited extent explore whether randomisation schemes which constrain the randomisation so that total sample sizes under intervention and control conditions are balanced might help minimise any loss in power due to varying cluster sizes
We present estimates of the relative efficiency, which compares the precision of a stepped-wedge CRT (SW-CRT) with unequal cluster sizes to the precision in a SW-CRT with equal cluster sizes; under the prerequisite than both designs have the same total sample size
Summary
Cluster randomised trials with unequal sized clusters often have lower precision than with clusters of equal size. To allow for this, sample sizes are inflated by a modified version of the design effect for clustering. These inflation factors are valid under the assumption that randomisation is stratified by cluster size. There have been many suggested modifications to the conventional cluster design effect (DE) to allow for unequal cluster sizes in a P-CRT. The stepped-wedge CRT (SW-CRT) is an alternative form of the CRT Under this design, clusters are typically randomly allocated to one of a number of sequences which dictate how many time periods the cluster will spend in the control condition, followed by periods under the intervention condition (Fig. 1) [7, 9]. Outcomes can be assessed on the same cohort of participants who are followed-up for the study duration, on a new cross-section of participants at each time-period, or Martin et al BMC Medical Research Methodology (2019) 19:123 explore the influence of varying cluster sizes in the SW-CRTs in absence of stratification by cluster size; and importantly consider the distribution of possible realisations of power across all randomisation orders
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