Improving small-sample inference in group randomized trials with binary outcomes

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Epidemiology

Background:

• Group Randomized Trials (GRTs) involve randomizing groups, not individuals, which can lead to over-dispersed binomial data.
• Intra-cluster correlation (ICC) quantifies this relatedness within clusters, often treated as a nuisance parameter in standard analyses.
• Traditional inference methods like the Wald statistic may yield inaccurate test sizes, especially with small sample sizes or high ICC.

Purpose of the Study:

• To address the issue of non-nominal test sizes in Group Randomized Trials (GRTs) arising from intra-cluster correlation (ICC).
• To develop and validate methods for adjusting statistical tests to ensure accurate inference for treatment effects in GRTs.
• To provide practical solutions for handling ICC in the analysis of binary outcomes from GRTs.

Main Methods:

• Utilized quasi-likelihood methods with a logistic link for inference on treatment effects.
• Developed an adjustment method for the estimated standard error when the ICC is known.
• Proposed approaches for managing non-nominal test sizes when the ICC is estimated from data.

Main Results:

• Identified that the Wald statistic can have a variance less than 1, leading to test sizes smaller than nominal, particularly when marginal probabilities are extreme and ICC is present.
• Demonstrated that the proposed standard error adjustment method ensures the Wald statistic approximates a standard normal distribution when ICC is known.
• Simulation results confirmed the utility of the methods across various realistic GRT settings.

Conclusions:

• Standard Wald statistics in GRTs may be unreliable due to ICC, necessitating adjustments for accurate treatment effect estimation.
• The developed methods effectively correct for non-nominal test sizes, improving the validity of statistical inference in GRTs.
• These findings offer practical solutions for researchers conducting GRTs with binary outcomes and correlated data.