Sample size requirements for detecting treatment effect heterogeneity in cluster randomized trials

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Health Services Research

Background:

• Cluster randomized trials (CRTs) are common in health research, but existing statistical methods primarily focus on overall treatment effects.
• There is a lack of clear guidance on sample size and power for detecting differential treatment effects (heterogeneity) within subpopulations in CRTs.

Purpose of the Study:

• To develop a novel sample size formula for identifying treatment effect heterogeneity in two-level CRTs.
• To investigate the influence of intraclass correlation coefficients (ICCs) on sample size calculations for detecting differential treatment effects.

Main Methods:

• Developed a new sample size formula for two-level CRTs with continuous outcomes and continuous/binary covariates.
• Derived a closed-form design effect formula for practical application.
• Conducted extensive simulations to validate the formula and used linear mixed-effects models with treatment-by-covariate interaction for analysis.
• Extended the method to include multiple covariates.

Main Results:

• The proposed sample size formula accurately predicts empirical power across various parameter settings.
• Simulations confirmed that the formula aligns well with power achieved using linear mixed-effects models.
• The roles of adjusted and marginal ICCs were investigated in the context of detecting heterogeneity.

Conclusions:

• The developed sample size formula provides a valuable tool for researchers planning CRTs with the objective of detecting treatment effect heterogeneity.
• The findings facilitate more precise study planning and resource allocation for studies investigating differential treatment effects in subpopulations.
• The method was illustrated using data from the HF-ACTION study, demonstrating its practical utility.