Analysis of cluster randomised stepped wedge trials with repeated cross-sectional samples

Abstract

Background: The stepped wedge cluster randomised trial (SW-CRT) is increasingly being used to evaluate policy or service delivery interventions. However, there is a dearth of trials literature addressing analytical approaches to the SW-CRT. Perhaps as a result, a significant number of published trials have major methodological shortcomings, including failure to adjust for secular trends at the analysis stage. Furthermore, the commonly used analytical framework proposed by Hussey and Hughes makes several assumptions.

Methods: We highlight the assumptions implicit in the basic SW-CRT analytical model proposed by Hussey and Hughes. We consider how simple modifications of the basic model, using both random and fixed effects, can be used to accommodate deviations from the underlying assumptions. We consider the implications of these modifications for the intracluster correlation coefficients. In a case study, the importance of adjusting for the secular trend is illustrated.

Results: The basic SW-CRT model includes a fixed effect for time, implying a common underlying secular trend across steps and clusters. It also includes a single term for treatment, implying a constant shift in this trend under the treatment. When these assumptions are not realistic, simple modifications can be implemented to allow the secular trend to vary across clusters and the treatment effect to vary across clusters or time. In our case study, the naïve treatment effect estimate (adjusted for clustering but unadjusted for time) suggests a beneficial effect. However, after adjusting for the underlying secular trend, we demonstrate a reversal of the treatment effect.

Conclusion: Due to the inherent confounding of the treatment effect with time, analysis of a SW-CRT should always account for secular trends or risk-biased estimates of the treatment effect. Furthermore, the basic model proposed by Hussey and Hughes makes a number of important assumptions. Consideration needs to be given to the appropriate model choice at the analysis stage. We provide a Stata code to implement the proposed analyses in the illustrative case study.

Keywords: Analysis; Cluster randomised trial; Secular trends; Stepped wedge.

Fig. 1

Schematic illustration of the stepped wedge cluster randomised trial

Fig. 2

Schematic representation of study design for case study

Fig. 3

Model-based estimate of underlying temporal trend in primary outcome over duration of trial in unexposed clusters (black line) and model-based estimated of outcome in intervention periods (red line) – basic model for the case study. Point estimates and 95% CI for each step with smoothed (LOWESS) line overlaid (black control; red intervention)

Fig. 4

Model-based estimate of treatment effect (ln odds ratio, OR) over duration of trial. Point estimates and 95% CI for each time period in which observations were both exposed and unexposed to intervention