Designing three-level cluster randomized trials to assess treatment effect heterogeneity.

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Health Services Research

Background:

• Cluster randomized trials (CRTs) commonly feature three-level structures (participants nested in subclusters, nested in clusters).
• While average treatment effects are primary, assessing treatment effect heterogeneity across subpopulations is increasingly important.
• Existing methods for powering heterogeneity analyses in three-level CRTs are limited.

Purpose of the Study:

• To derive novel analytical design formulas for powering confirmatory analyses of treatment effect heterogeneity in three-level CRTs.
• To provide methods applicable to various effect modifiers (cluster, subcluster, participant levels) and randomization designs.
• To offer practical insights for study design and analysis of treatment effect heterogeneity.

Main Methods:

• Derivation of design formulas based on the asymptotic covariance matrix.
• Characterization of a nested exchangeable correlation structure for outcomes and effect modifiers.
• Application of a linear mixed analysis of covariance model.

Main Results:

• Novel analytical formulas for sample size and power calculations for treatment effect heterogeneity in three-level CRTs.
• Demonstration of broad applicability across different effect modifier levels and randomization schemes.
• Validation of methods through a simulation study and illustration with real-world trial examples.

Conclusions:

• The derived formulas provide a robust framework for designing three-level CRTs to effectively evaluate treatment effect heterogeneity.
• These methods enhance the ability to detect variations in treatment effects across patient subpopulations.
• The findings offer valuable guidance for researchers planning and analyzing complex cluster randomized trials.