Confidence interval estimation for the win probability in cluster randomized trials with hierarchical composite...

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Statistical Inference

Background:

• Cluster randomized trials (CRTs) often involve multiple, hierarchically ordered endpoints, posing challenges for treatment effect estimation.
• Existing methods struggle to account for complex correlation structures and differing clinical importance across endpoints.

Purpose of the Study:

• To develop and validate a robust statistical method for estimating treatment effects in CRTs with hierarchical composite endpoints.
• To provide accurate confidence intervals and hypothesis tests for the nonparametric treatment effect, termed the "win probability."

Main Methods:

• A pairwise comparison approach is employed, evaluating endpoints hierarchically to determine treatment arm wins.
• A novel "win fraction" method utilizes a working linear mixed model on transformed univariate responses for variance estimation.
• Large-sample inference is based on the central limit theorem, with simulation and a case study for validation.

Main Results:

• Simulation studies demonstrate that the proposed win fraction method maintains nominal 95% coverage probability and controls type I error.
• The method shows good performance across various cluster trial designs, outperforming the empirical bootstrap estimator in terms of coverage.
• Confidence intervals may be conservative with fewer than 30 clusters due to the large-sample nature of the method.

Conclusions:

• The win fraction method offers a reliable and efficient approach for analyzing CRTs with hierarchical composite endpoints.
• It effectively handles multiple endpoints on different scales, bypasses complex correlation matrix specification, and allows for adjustments.
• The method is computationally faster than bootstrap alternatives and implementable in standard statistical software.