Statistical power and sample size requirements to detect an intervention by time interaction in four-level...

Area of Science:

• Biostatistics
• Health Sciences Research Methodology
• Longitudinal Study Design

Background:

• Cluster/group randomized controlled trials (CRTs) are vital in health sciences when individual randomization is impractical.
• CRTs mitigate contamination bias, administrative burdens, and ethical concerns.
• Hierarchical data structures in CRTs necessitate specialized analytical approaches.

Purpose of the Study:

• To design and analyze four-level longitudinal cluster randomized trials.
• To investigate differences between treatment groups over time within a complex hierarchical structure.
• To develop methods for power and sample size calculations in such trials.

Main Methods:

• Utilized a random intercept mixed effects linear regression model.
• Incorporated a time by intervention interaction term for analysis.
• Derived closed-form expressions for the power function.

Main Results:

• Sample size equations were determined, independent of correlations among lower-level units (classes/students).
• The power function's dependency on the product of units across different levels was established.
• Optimal unit allocation strategies were identified to minimize variance under fixed costs.

Conclusions:

• The developed formulae provide accurate theoretical power estimates, closely matching empirical results from simulations.
• The methodology is applicable to complex, multi-level longitudinal CRTs, such as education-based HIV prevention studies.
• This work offers a robust framework for designing and analyzing advanced CRT designs.