Cluster randomized crossover trials with very few clusters but multiple periods: which analyses for continuous outcomes should be used?
Abstract
Cluster randomized crossover (CRXO) trials are often used when individual randomization is impractical and the number of available clusters is limited. However, statistical analysis of CRXO trials is complex because of the need to account for complex correlation structures over time. It becomes especially challenging when very few clusters are used because standard modeling assumptions may lead to unstable variance estimates, poor confidence interval coverage, and inflated type I error. This study evaluates individual-level mixed-effects and fixed-effects models with and without a cluster-period random effect, cluster-period summary analysis using normal- or t-based inference, and two-period crossover-difference estimators. Using extensive simulation studies under both nested exchangeable and discrete time decay correlation structures, we compare model performance in terms of bias, root mean squared error, coverage probability, type I error, and convergence. Across scenarios, all models produced approximately unbiased treatment effect estimates, but their inferential performance differed substantially. Models that explicitly accounted for cluster-period heterogeneity generally provided the most reliable control of coverage and type I error, whereas simpler exchangeable models performed adequately only when the true correlation structure closely matched their assumptions. Cluster-period level analysis performance improved with increasing numbers of periods but was unreliable in the sparsest designs. Overall, the findings suggest that in CRXO trials with very few clusters, accurate modeling of cluster-period correlation is more important than the choice between fixed and random cluster intercepts, and that results from extremely sparse designs should be interpreted with caution.
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BibTeX
@misc{tong2026cluster,
title = {{Cluster randomized crossover trials with very few clusters but multiple periods: which analyses for continuous outcomes should be used?}},
author = {Guangyu Tong and Qianzhe Sun and Jessica Kasza and Andrew Forbes and Monica Taljaard and Fan Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06868},
eprint = {2609.06868},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06868},
}
RIS
TY - UNPB
TI - Cluster randomized crossover trials with very few clusters but multiple periods: which analyses for continuous outcomes should be used?
AU - Guangyu Tong
AU - Qianzhe Sun
AU - Jessica Kasza
AU - Andrew Forbes
AU - Monica Taljaard
AU - Fan Li
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06868
UR - https://arxiv.org/abs/2609.06868
AB - Cluster randomized crossover (CRXO) trials are often used when individual randomization is impractical and the number of available clusters is limited. However, statistical analysis of CRXO trials is complex because of the need to account for complex correlation structures over time. It becomes especially challenging when very few clusters are used because standard modeling assumptions may lead to unstable variance estimates, poor confidence interval coverage, and inflated type I error. This study evaluates individual-level mixed-effects and fixed-effects models with and without a cluster-period random effect, cluster-period summary analysis using normal- or t-based inference, and two-period crossover-difference estimators. Using extensive simulation studies under both nested exchangeable and discrete time decay correlation structures, we compare model performance in terms of bias, root mean squared error, coverage probability, type I error, and convergence. Across scenarios, all models produced approximately unbiased treatment effect estimates, but their inferential performance differed substantially. Models that explicitly accounted for cluster-period heterogeneity generally provided the most reliable control of coverage and type I error, whereas simpler exchangeable models performed adequately only when the true correlation structure closely matched their assumptions. Cluster-period level analysis performance improved with increasing numbers of periods but was unreliable in the sparsest designs. Overall, the findings suggest that in CRXO trials with very few clusters, accurate modeling of cluster-period correlation is more important than the choice between fixed and random cluster intercepts, and that results from extremely sparse designs should be interpreted with caution.
ER -