Incorporating cost in power analysis for three-level cluster-randomized designs.

Area of Science:

• Biostatistics
• Experimental Design
• Health Services Research

Background:

• Cluster-randomized experiments are common in nested structures like schools.
• Determining adequate sample sizes for statistical power is crucial.
• Unit costs at different hierarchical levels must be considered in study design.

Purpose of the Study:

• To provide methods for computing statistical power within an optimal design framework.
• To incorporate costs of units at all three levels for three-level cluster-randomized designs.
• To guide researchers in determining optimal sample sizes under budget constraints.

Main Methods:

• Developed methods for power computation in three-level cluster-randomized balanced designs.
• Incorporated two levels of nesting at the second and third levels.
• Integrated unit costs at all hierarchical levels into the optimal design framework.

Main Results:

• Optimal sample sizes are determined by variances at each level and the cost of each unit.
• Higher statistical power is associated with larger effect sizes.
• Lower intraclass correlations and unit costs at higher levels increase power estimates.

Conclusions:

• The presented methods facilitate cost-effective study design in complex hierarchical settings.
• Researchers can optimize sample sizes by balancing effect size, intraclass correlations, and unit costs.
• This framework aids in achieving adequate statistical power within budgetary limitations.