Confidence interval estimation for treatment effects in cluster randomization trials based on ranks.

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Health Services Research

Background:

• Cluster randomization trials are standard for evaluating health and educational interventions.
• Interpreting treatment effects can be challenging with outcomes lacking meaningful units.
• The Mann-Whitney probability offers a solution by comparing typical responses between treatment arms.

Purpose of the Study:

• To propose novel procedures for estimating the Mann-Whitney probability in cluster randomization trials.
• To develop confidence interval estimation methods, particularly for trials with a small number of large clusters.
• To provide methods applicable to various outcome types (binary, ordinal, continuous) without parametric assumptions.

Main Methods:

• Utilized placement values from overall and arm-specific ranks.
• Applied ratio estimator, cluster-size-weighted means, and mixed models to adjust for clustering.
• Developed nine confidence intervals using three interval methods and three variance estimators.
• Investigated logit and inverse hyperbolic sine transformations for confidence interval procedures.

Main Results:

• Proposed methods are applicable to binary, ordinal, or continuous outcomes.
• Simulation results showed three variance estimators performed comparably.
• Confidence intervals using logit and inverse hyperbolic sine transformations demonstrated superior coverage and narrower width.
• Effective even with as few as 3-5 clusters per arm.

Conclusions:

• The developed procedures effectively estimate the Mann-Whitney probability in cluster randomization trials.
• Confidence intervals based on logit and inverse hyperbolic sine transformations are recommended for their performance.
• These methods enhance the interpretation of treatment effects in cluster randomized studies, especially with limited cluster numbers.