The fixed-effects model for robust analysis of stepped-wedge cluster trials with a small number of clusters and continuous outcomes: a simulation study

Background: Stepped-wedge cluster trials (SW-CTs) describe a cluster trial design where treatment rollout is staggered over the course of the trial. Clusters are commonly randomized to receive treatment beginning at different time points in this study design (commonly referred to as a Stepped-wedge cluster randomized trial; SW-CRT), but they can also be non-randomized. Trials with this design regularly have a low number of clusters and can be vulnerable to covariate imbalance. To address such covariate imbalance, previous work has examined covariate-constrained randomization and analysis adjustment for imbalanced covariates in mixed-effects models. These methods require the imbalanced covariate to always be known and measured. In contrast, the fixed-effects model automatically adjusts for all imbalanced time-invariant covariates, both measured and unmeasured, and has been implicated to have proper type I error control in SW-CTs with a small number of clusters and binary outcomes.

Methods: We present a simulation study comparing the performance of the fixed-effects model against the mixed-effects model in randomized and non-randomized SW-CTs with small numbers of clusters and continuous outcomes. Additionally, we compare these models in scenarios with cluster-level covariate imbalances or confounding.

Results: We found that the mixed-effects model can have low coverage probabilities and inflated type I error rates in SW-CTs with continuous outcomes, especially with a small number of clusters or when the ICC is low. Furthermore, mixed-effects models with a Satterthwaite or Kenward-Roger small sample correction can still result in inflated or overly conservative type I error rates, respectively. In contrast, the fixed-effects model consistently produced the target level of coverage probability and type I error rates without dramatically compromising power. Furthermore, the fixed-effects model was able to automatically account for all time-invariant cluster-level covariate imbalances and confounding to robustly yield unbiased estimates.

Conclusions: We recommend the fixed-effects model for robust analysis of SW-CTs with a small number of clusters and continuous outcomes, due to its proper type I error control and ability to automatically adjust for all potential imbalanced time-invariant cluster-level covariates and confounders.