Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating...

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Epidemiology

Background:

• Cluster randomized trials (CRTs) are increasingly used in research.
• Sample size calculations in CRTs typically assume equal cluster sizes for simplicity.
• In practice, cluster sizes often vary, potentially impacting statistical power and efficiency.

Purpose of the Study:

• To investigate the relative efficiency (RE) of unequal versus equal cluster sizes in CRTs.
• To develop methods for sample size adjustment in CRTs with unequal cluster sizes.
• To propose optimal sample size estimation strategies under budget constraints.

Main Methods:

• Utilized generalized estimating equation (GEE) models for analyzing correlated data in CRTs.
• Derived variances of the treatment effect estimator for continuous, binary, and count data.
• Defined and calculated Relative Efficiency (RE) as the ratio of variances under equal versus unequal cluster sizes.
• Employed simulation studies to evaluate RE across various cluster size distributions.

Main Results:

• Quantified the efficiency loss associated with unequal cluster sizes in CRTs.
• Derived simpler formulas for RE under the exchangeable working correlation structure for different data types.
• Simulation studies demonstrated the impact of cluster size distribution on RE.
• Proposed an adjusted sample size formula to account for efficiency loss.

Conclusions:

• Unequal cluster sizes in CRTs lead to a loss of statistical efficiency compared to equal sizes.
• GEE models provide a robust framework for analyzing CRTs with unequal cluster sizes.
• The proposed methods offer practical tools for accurate sample size determination in CRTs, considering varying cluster sizes and budget limitations.