Which Small-Sample Correction Should be Used When Analyzing Stepped-Wedge Designs With Time-Varying Treatment Effects?
7 affiliations
- 1Department of Biostatistics and Bioinformatics, Roswell Park Comprehensive Cancer Center, Buffalo, New York, USA.
- 2Roswell Park Graduate Division, State University of New York at Buffalo, Buffalo, New York, USA.
- 3Methodological and Implementation Research, Ottawa Hospital Research Institute, Ottawa, Ontario, Canada.
- 4School of Epidemiology and Public Health, University of Ottawa, Ottawa, Ontario, Canada.
- 5Department of Biostatistics, School of Public Health, University of Washington, Seattle, Washington, USA.
- 6Department of Biostatistics, Yale University, New Haven, Connecticut, USA.
- 7Center for Methods in Implementation and Prevention Science, Yale University, New Haven, Connecticut, USA.
Abstract
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.
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BibTeX
@article{ouyang2026which,
title = {{Which Small-Sample Correction Should be Used When Analyzing Stepped-Wedge Designs With Time-Varying Treatment Effects?}},
author = {Yongdong Ouyang and Monica Taljaard and James P Hughes and Fan Li},
journal = {Statistics in medicine},
year = {2026},
month = oct,
doi = {10.1002/sim.70782},
url = {https://europepmc.org/article/MED/42910555},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Which Small-Sample Correction Should be Used When Analyzing Stepped-Wedge Designs With Time-Varying Treatment Effects?
AU - Yongdong Ouyang
AU - Monica Taljaard
AU - James P Hughes
AU - Fan Li
PY - 2026
DA - 2026/10/30
JO - Statistics in medicine
DO - 10.1002/sim.70782
UR - https://europepmc.org/article/MED/42910555
AB - 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.
SN - 0277-6715
SN - 1097-0258
ER -