Addressing Cluster-Level Treatment Effect Heterogeneity in Sample Size Determination for Hierarchical 2 × 2 Factorial...

Area of Science:

• Biostatistics
• Clinical Trial Design
• Public Health Interventions

Background:

• Hierarchical $2\times 2$ factorial designs involve cluster-level and individual-level randomization.
• Standard sample size calculations assume uniform treatment effects, which may not hold in cluster randomized trials.
• Heterogeneous treatment effects across clusters introduce additional variability.

Purpose of the Study:

• To extend sample size calculation methods for hierarchical $2\times 2$ factorial trials.
• To address the challenge of heterogeneous treatment effects across clusters.
• To provide formulas for testing controlled, marginal, and interaction effects.

Main Methods:

• Utilized a generalized least squares framework.
• Developed sample size formulas for models with and without intervention interactions.
• Employed simulation studies to validate the derived formulas.

Main Results:

• Derived novel sample size formulas for hierarchical $2\times 2$ factorial trials.
• Formulas account for potential heterogeneity in treatment effects at the cluster level.
• Simulation studies confirmed the accuracy of the proposed sample size calculations.

Conclusions:

• The proposed methods offer a robust approach to sample size determination for complex factorial trials.
• Accurate sample size calculations are crucial for detecting treatment effects in the presence of cluster heterogeneity.
• The methods are illustrated using a suicide prevention trial example.