The stepped wedge cluster randomized trial (SW-CRT) design is now preferred for many health- related trials because of its flexibility on resource allocation and clinical ethics concerns. However, as a necessary extension of studying multiple interventions, multiphase stepped wedge designs (MSW-CRT) have not been studied adequately. Since estimated intervention effect from Generalized estimating equations (GEE) has a population-average interpretation, valid inference methods for binary outcomes based on GEE are preferred by public health policy makers.
We form hypothesis testing of add-on effect of a second treatment based on GEE analysis in an MSW-CRT design with limited number of clusters. Four variance-correction estimators are used to adjust the bias of the sandwich estimator. Simulation studies have been used to compare the statistical power and type I error rate of these methods under different correlation matrices.
We demonstrate that an average estimator with t(I-3) can stably maintain type I error close to the nominal level with limited sample sizes in our settings. We show that power of testing the add-on effect depends on the baseline event rate, effect sizes of two interventions and the number of clusters. Moreover, by changing the design with including more sequences, power benefit can be achieved.
For designing the MSW-CRT, we suggest using more sequences and checking event rate after initiating the first intervention via interim analysis. When the number of clusters is not very large in MSW-CRTs, inference can be conduct using GEE analysis with an average estimator with t(I-3) sampling distribution.