Comparison of small-sample standard-error corrections for generalised estimating equations in stepped wedge cluster...

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Epidemiology

Background:

• Generalised estimating equations (GEE) with sandwich standard-error estimators are used for stepped wedge cluster randomised trials.
• A common issue is inflated type-one error when the number of clusters is small.

Purpose of the Study:

• To compare bias-corrected standard errors for stepped wedge cluster randomised trials with binary outcomes.
• To evaluate different methods for constructing confidence intervals.

Main Methods:

• A large simulation study was conducted.
• Binary outcomes were analyzed using GEE.
• Bias-corrected standard errors from Fay and Graubard, Mancl and DeRouen, Kauermann and Carroll, Morel et al., and Mackinnon and White were compared.
• Independent and exchangeable working correlation matrices were used.
• Confidence intervals were constructed using various degrees of freedom estimators.

Main Results:

• Fay and Graubard and an approximation to Kauermann and Carroll (with simpler matrix inversion) were unbiased with an independent working correlation matrix and >12 clusters.
• These methods provided confidence intervals with near 95% coverage with DF_FG (≥12 clusters) or DF_C-P (≥18 clusters).
• Both methods were conservative with fewer than 12 clusters.
• With an exchangeable working correlation matrix, approximated Kauermann and Carroll and Fay and Graubard showed slight under-coverage.

Conclusions:

• Fay and Graubard and approximated Kauermann and Carroll standard errors are recommended for stepped wedge cluster randomised trials with independent correlation and sufficient clusters.
• Careful consideration of the working correlation matrix and degrees of freedom is crucial for accurate inference.