Robust inference for the stepped wedge design

Stepped wedge designed trials are a type of cluster-randomized study in which the intervention is introduced to each cluster in a random order over time. This design is often used to assess the effect of a new intervention as it is rolled out across a series of clinics or communities. Based on a permutation argument, we derive a closed-form expression for an estimate of the intervention effect, along with its standard error, for a stepped wedge design trial. We show that these estimates are robust to misspecification of both the mean and covariance structure of the underlying data-generating mechanism, thereby providing a robust approach to inference for the intervention effect in stepped wedge designs. We use simulations to evaluate the type 1 error and power of the proposed estimate and to compare the performance of the proposed estimate to the optimal estimate when the correct model specification is known. The limitations, possible extensions, and open problems regarding the method are discussed.