Which Small-Sample Correction Should be Used When Analyzing Stepped-Wedge Designs With Time-Varying Treatment Effects?

Stepped-wedge cluster randomized trials (SW-CRTs) evaluate interventions that are sequentially rolled out across clusters. Standard analyses of SW-CRTs typically use immediate-treatment (IT) models, which assume the treatment effects begin at crossover and remain constant thereafter. When treatment effects vary with exposure duration, IT models may misrepresent the target effects. Exposure-time indicator (ETI) models address this by allowing treatment effects to differ by time since exposure and can properly target the time-averaged treatment effect (TATE) and long-term effect (LTE). Like IT models, ETI models require specification of a random-effects structure, which may be misspecified. While robust variance estimators (RVEs) theoretically protect against such misspecification, their empirical performance under ETI models is not well understood. We review RVEs for ETI models and evaluate them in comprehensive simulation studies with continuous and binary outcomes under correctly specified (binary only) and misspecified random-effects structures. We compare the classic sandwich variance, Kauermann-Carroll (KC), Mancl-DeRouen (MD), and Morel-Bokossa-Neerchal (MBN) bias-corrected sandwich variance estimators for inference on the TATE and LTE in primary simulations and additionally evaluate Fay-Graubard (FG) in a sub-study. Our simulations show that under misspecified random-effects structures, model-based standard errors (SE) produced undercoverage, whereas RVEs improved performance under the ETI models. For continuous outcomes, MD with a t-distribution and degrees of freedom equal to the number of clusters minus two gave the closest to nominal coverage probabilities. Surprisingly, however, MBN was the only consistently reliable option for binary outcomes. MD, however, could be unstable in one-cluster-per-sequence designs because of data sparsity. Across scenarios, both model-based SE and RVE for LTE were unstable, indicating that greater caution is needed when targeting LTE under ETI models.