Optimal allocation of clusters in stepped wedge designs with a decaying correlation structure.

Area of Science:

• Epidemiology
• Biostatistics
• Clinical Trials

Background:

• The cluster randomized stepped wedge design is a powerful tool for evaluating interventions.
• Uniform allocation is commonly used but may not be the most statistically efficient.
• Optimizing cluster allocation can enhance study power and resource utilization.

Purpose of the Study:

• To derive the optimal allocation of clusters to treatment sequences in the cluster randomized stepped wedge design.
• To compare optimal allocation with uniform allocation for both cohort and cross-sectional designs.
• To investigate the impact of autocorrelation structures on optimal cluster allocation.

Main Methods:

• Derivation of optimal cluster allocation formulas for stepped wedge designs.
• Analysis under an exponential decay correlation structure.
• Evaluation of sensitivity to intraclass correlation and autocorrelation coefficients.

Main Results:

• Optimal allocation depends on intraclass correlation, subjects per cluster-period, and autocorrelation coefficients.
• For small to moderate autocorrelations, sequences with early or late switches receive more clusters.
• As autocorrelations increase, clusters tend towards more equal distribution across sequences.

Conclusions:

• The optimal cluster allocation in stepped wedge designs is not always uniform.
• Uniform allocation demonstrates high efficiency (≥0.8) across most studied scenarios.
• R code is provided to implement the derived optimal allocation strategies.