How important is randomisation in a stepped wedge trial?

James R Hargreaves, Audrey Prost, Katherine L. Fielding, Andrew J. Copas

In cluster randomised trials, randomisation increases internal study validity. If enough clusters are randomised, an unadjusted analysis should be unbiased. If a smaller number of clusters are included, stratified or matched randomisation can increase comparability between trial arms. In addition, an adjusted analysis may be required; nevertheless, randomisation removes the possibility for systematically biased allocation and increases transparency. In stepped wedge trials, clusters are randomised to receive an intervention at different start times ('steps'), and all clusters eventually receive it. In a recent study protocol for a 'modified stepped wedge trial', the investigators considered randomisation of the clusters (hospital wards), but decided against it for ethical and logistical reasons, and under the assumption that it would not add much to the rigour of the evaluation. We show that the benefits of randomisation for cluster randomised trials also apply to stepped wedge trials. The biggest additional issue for stepped wedge trials in relation to parallel cluster randomised trials is the need to control for secular trends in the outcome. Analysis of stepped wedge trials can in theory be based on 'horizontal' or 'vertical' comparisons. Horizontal comparisons are based on measurements taken before and after the intervention is introduced in each cluster, and are unbiased if there are no secular trends. Vertical comparisons are based on outcome measurements from clusters that have switched to the intervention condition and those from clusters that have yet to switch, and are unbiased under randomisation since at any time point, which clusters are in intervention and control conditions will have been determined at random. Secular outcome trends are a possibility in many settings. Many stepped wedge trials are analysed with a mixed model, including a random effect for cluster and fixed effects for time period to account for secular trends, thereby combining both vertical and horizontal comparisons of intervention and control clusters. The importance of randomisation in a stepped wedge trial is that the effects of time can be estimated from the data, and bias from secular trends that would otherwise arise can be controlled for, provided the trends are correctly specified in the model.