Comparison of analysis methods and design choices for treatment-by-period interaction in unidirectional switch designs: a simulation study

Background: Due to identifiability problems, statistical inference about treatment-by-period interactions has not been discussed for stepped wedge designs in the literature thus far. Unidirectional switch designs (USDs) generalize the stepped wedge designs and allow for estimation and testing of treatment-by-period interaction in its many flexible design forms. Methods: Under different forms of the USDs, we simulated binary data at both aggregated and individual levels and studied the performances of the generalized linear mixed model (GLMM) and the marginal model with generalized estimation equations (GEE) for estimating and testing treatment-by-period interactions. Results: The parallel group design had the highest power for detecting the treatment-by-period interactions. While there was no substantial difference between aggregated-level and individual-level analysis, the GLMM had better point estimates than the marginal model with GEE. Furthermore, the optimal USD for estimating the average treatment effect was not efficient for treatment-by-period interaction and the marginal model with GEE required a substantial number of clusters to yield unbiased estimates of the interaction parameters when the correlation structure is autoregressive of order 1 (AR1). On the other hand, marginal model with GEE had better coverages than GLMM under the AR1 correlation structure. Conclusion: From the designs and methods evaluated, in general, parallel group design with a GLMM is, preferred for estimation and testing of treatment-by-period interaction in a clustered randomized controlled trial for a binary outcome.