Variance formulae for multiphase stepped wedge cluster randomized trial

In a multiphase stepped wedge cluster randomized trial (MSW-CRT), more than one intervention will be initiated on each sequence in a fixed order. Hence, with the MSW-CRT design, the effect of the first intervention can be evaluated when compared to control, as well as the added-on effects of the subsequent interventions. Studies that use MSW-CRT have been proposed, but properties of this design have not been explicitly studied. We derive closed-form variance formulae to test the interventions' effects, which can be readily used for sample size and power calculation. Additionally, we provide relationships between variances to test the interventions' effects and design parameters. Under special conditions, some important properties include: (i) the variances to test different interventions' effects (ie, the first intervention effect and the second intervention effect) may be same; (ii) as the cluster-period mean autocorrelation increases, the variance to test an intervention effect may first increase and then decrease; (iii) as the amount of periods between the initiations of two interventions (ie, lag) increases, the variance to test an intervention effect may remain unchanged. We illustrate the relationships between power and design parameters using the variance formulae. From a few illustrative examples, we observe that the statistical test that uses data only relevant to a specific intervention has inferior power (relative power loss <15%) compared to the test when using all the study data. Also, power is reduced when both the total number of periods and lag are decreased simultaneously (relative power loss <20%).