Power considerations for generalized estimating equations analyses of four-level cluster randomized trials

Area of Science:

• Biostatistics
• Health Services Research
• Epidemiology

Background:

• Four-level cluster randomized trials (CRTs) are increasingly used in healthcare research.
• These trials involve complex nested structures, such as evaluations within participants, divisions, and clusters.
• Accurate sample size and power calculations are crucial for the validity of these complex study designs.

Purpose of the Study:

• To develop methods for sample size and power calculations in four-level intervention studies, with a focus on CRTs.
• To derive closed-form sample size formulas applicable to intervention assignment at any level within the four-level structure.
• To account for complex intraclass correlations in multilevel CRTs.

Main Methods:

• Utilized the generalized estimating equations (GEE) approach.
• Derived closed-form sample size formulas using model-based and sandwich variance estimators.
• Considered three types of intraclass correlations to model clustering effects.
• Assumed arbitrary link and variance functions for broad applicability.

Main Results:

• Developed accurate sample size and power calculation formulas for four-level CRTs.
• Demonstrated good correspondence between empirical power and predicted power, even with as few as eight clusters.
• The proposed methods are effective for both balanced and unbalanced designs.

Conclusions:

• The developed methods provide reliable tools for sample size and power calculations in complex four-level CRTs.
• These methods enhance the planning and efficiency of healthcare intervention studies.
• The findings support the use of matrix-adjusted estimating equations with bias-corrected sandwich variance for analyzing such data.