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# The optimal design of stepped wedge trials with equal allocation to sequences and a comparison to other trial designs.

### Author information

- 1
- 1 Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK.
- 2
- 2 London Hub for Trials Methodology Research, MRC Clinical Trials Unit at University College London, London, UK.
- 3
- 3 Department of Social and Environmental Health Research, London School of Hygiene & Tropical Medicine, London, UK.

### Abstract

Background/Aims We sought to optimise the design of stepped wedge trials with an equal allocation of clusters to sequences and explored sample size comparisons with alternative trial designs. Methods We developed a new expression for the design effect for a stepped wedge trial, assuming that observations are equally correlated within clusters and an equal number of observations in each period between sequences switching to the intervention. We minimised the design effect with respect to (1) the fraction of observations before the first and after the final sequence switches (the periods with all clusters in the control or intervention condition, respectively) and (2) the number of sequences. We compared the design effect of this optimised stepped wedge trial to the design effects of a parallel cluster-randomised trial, a cluster-randomised trial with baseline observations, and a hybrid trial design (a mixture of cluster-randomised trial and stepped wedge trial) with the same total cluster size for all designs. Results We found that a stepped wedge trial with an equal allocation to sequences is optimised by obtaining all observations after the first sequence switches and before the final sequence switches to the intervention; this means that the first sequence remains in the control condition and the last sequence remains in the intervention condition for the duration of the trial. With this design, the optimal number of sequences is [Formula: see text], where [Formula: see text] is the cluster-mean correlation, [Formula: see text] is the intracluster correlation coefficient, and m is the total cluster size. The optimal number of sequences is small when the intracluster correlation coefficient and cluster size are small and large when the intracluster correlation coefficient or cluster size is large. A cluster-randomised trial remains more efficient than the optimised stepped wedge trial when the intracluster correlation coefficient or cluster size is small. A cluster-randomised trial with baseline observations always requires a larger sample size than the optimised stepped wedge trial. The hybrid design can always give an equally or more efficient design, but will be at most 5% more efficient. We provide a strategy for selecting a design if the optimal number of sequences is unfeasible. For a non-optimal number of sequences, the sample size may be reduced by allowing a proportion of observations before the first or after the final sequence has switched. Conclusion The standard stepped wedge trial is inefficient. To reduce sample sizes when a hybrid design is unfeasible, stepped wedge trial designs should have no observations before the first sequence switches or after the final sequence switches.

#### KEYWORDS:

Stepped wedge trial; cluster randomised trial; design effect; hybrid trial; power; sample size; study design

- PMID:
- 28797179
- PMCID:
- PMC5718336
- DOI:
- 10.1177/1740774517723921

- [Indexed for MEDLINE]