Understanding between-cluster variation in prevalence and limits for how much variation is plausible

Area of Science:

• Biostatistics
• Clinical Trial Design
• Epidemiology

Background:

• Understanding between-cluster variation is essential for analyzing clustered binary data in clinical trials and observational studies.
• The intra-cluster correlation coefficient (ICC), commonly used in sample size and power calculations for cluster randomized trials, can be unintuitive.
• Low ICC values may mask substantial between-cluster differences, complicating interpretation.

Purpose of the Study:

• To propose more interpretable and transportable methods for quantifying between-cluster variation in clustered binary data.
• To provide practical guidance for clinical trialists in assessing and specifying between-cluster variation.
• To introduce bounds for key variation metrics based on maximum entropy theory.

Main Methods:

• Visualizing the distribution of true cluster prevalences, potentially assuming a beta distribution.
• Calculating the standard deviation of true cluster prevalences as a more interpretable alternative to ICC.
• Applying maximum entropy theory to derive rule-of-thumb bounds for ICC, standard deviation, coefficient of variation, and log odds scale metrics.

Main Results:

• The standard deviation of true cluster prevalences is more interpretable than ICC.
• Plausible ICC and standard deviation values are bounded by overall prevalence, its complement, and one-third.
• Metrics on the log odds scale demonstrated greater transportability across studies with varying prevalences compared to ICC and coefficient of variation.

Conclusions:

• Visualizing cluster prevalence distributions and using log odds scale metrics improve the understanding of between-cluster variation.
• The proposed bounds offer practical guidance for avoiding implausibly high ICC values in sample size calculations.
• This work enhances the interpretability and transportability of between-cluster variation measures in clustered binary data analysis.