Sample size determination for hierarchical longitudinal designs with differential attrition rates

Area of Science:

• Biostatistics
• Clinical Trial Design
• Longitudinal Data Analysis

Background:

• Three-level mixed-effects linear regression models are essential for analyzing clustered longitudinal data, particularly in multicenter randomized clinical trials.
• These designs involve hierarchical structures: measurement occasions (level 1), subjects (level 2), and centers (level 3).
• Models often incorporate random effects for time trends at both subject and center levels.

Purpose of the Study:

• To develop a methodology for sample size determination in three-level mixed-effects linear regression models.
• To provide power characteristics for testing treatment-by-time interactions in such designs.
• To introduce a cost model for selecting optimal study designs.

Main Methods:

• The study derives sample size requirements based on power characteristics for testing treatment-by-time interactions.
• The methodology is general, accommodating varying sampling proportions, group numbers, and attrition rates.
• A cost model is developed to aid in selecting the most parsimonious study design.

Main Results:

• The presented approach offers a general framework for sample size determination in complex longitudinal studies.
• It provides power calculations for both subject-level and cluster-level randomization designs.
• The methodology is illustrated with practical examples relevant to health research.

Conclusions:

• This research provides a robust statistical framework for sample size determination in three-level longitudinal studies.
• The findings are applicable to the design of multicenter clinical trials, optimizing resource allocation.
• The developed methods enhance the rigor and efficiency of planning complex health research studies.