Relative efficiency of unequal cluster sizes for variance component estimation in cluster randomized and multicentre...

Area of Science:

• Biostatistics
• Clinical Trials

Background:

• Cluster randomized trials (CRTs) and multicentre trials (MCTs) are used to evaluate treatments on individuals within clusters (e.g., patients in clinics).
• Equal sample sizes per cluster are optimal for parameter estimation but often impractical in real-world studies.

Purpose of the Study:

• To investigate the relative efficiency (RE) of unequal versus equal cluster sizes for estimating variance components in CRTs and MCTs with quantitative outcomes.
• To develop and validate an approximate formula for calculating RE based on cluster size distribution and intraclass correlation.

Main Methods:

• Utilized maximum likelihood estimation to assess the relative efficiency of different cluster size distributions.
• Conducted numerical investigations across a range of cluster size variations.
• Derived and tested an approximate formula for RE as a function of mean cluster size, variance of cluster sizes, and intraclass correlation.

Main Results:

• The relative efficiency loss for variance component estimation due to unequal cluster sizes rarely exceeds 20%.
• An approximate formula for RE was developed and validated, showing good accuracy.
• Increased sampling of clusters (by 25%) can compensate for efficiency losses from unequal cluster sizes.

Conclusions:

• Variation in cluster sizes in CRTs and MCTs has a manageable impact on variance component estimation efficiency.
• The proposed approximation provides a practical tool for researchers to estimate efficiency losses and plan study designs.
• Researchers can balance efficiency and feasibility by adjusting the number of clusters and accounting for size variations.