A comparison of confidence interval methods for the intraclass correlation coefficient in cluster randomized trials

Area of Science:

• Biostatistics
• Clinical Trials
• Statistical Methods

Background:

• Intraclass correlation coefficient (rho) is crucial for estimating variance inflation factors in cluster randomized trials.
• Accurate confidence intervals for rho are essential for robust trial planning and sample size calculations.
• Existing methods for calculating confidence intervals for rho have varying performance characteristics.

Purpose of the Study:

• To compare different methods for assigning confidence intervals to the intraclass correlation coefficient (rho).
• To evaluate these methods in the context of planning cluster randomized trials using variance inflation factors.
• To assess the impact of data characteristics, including normality of random effects, on interval performance.

Main Methods:

• Monte Carlo simulations were employed using unbalanced clustered data and real-world cluster randomized trial data.
• Coverage and precision of confidence intervals were compared across varying numbers of clusters, subjects per cluster, and rho values.
• Performance was assessed for both Normal and non-Normally distributed cluster-specific effects.

Main Results:

• Variance ratio statistic-based methods demonstrated superior coverage levels compared to large sample approximations.
• Searle's method achieved near-nominal coverage with Normally distributed random effects.
• Non-normality in cluster-level random effects significantly compromised the performance of all evaluated methods.
• Confidence intervals were generally wide, suggesting substantial uncertainty in sample size estimations for cluster trials.

Conclusions:

• Variance ratio methods are recommended for confidence intervals of intraclass correlation coefficient in cluster randomized trials.
• Searle's method shows good performance under normality assumptions.
• Sample size calculations for cluster trials may require greater precision, potentially necessitating larger study datasets for reliable rho estimation.
• Further research with larger cluster-based studies is needed to improve the precision of rho estimates.