Statistical Power in Two-Level Hierarchical Linear Models with Arbitrary Number of Factor Levels

Area of Science:

• Health Services Research
• Biostatistics
• Clinical Trials

Background:

• The US healthcare system requires robust studies to understand patient outcomes in hierarchical settings.
• Two-level models with nested units (e.g., patients within practices) are common in health research.
• Accurate statistical power is crucial for detecting treatment effects in these complex designs.

Purpose of the Study:

• To develop a statistical power function for two-level hierarchical models with two factors.
• To compare power across cluster, multisite, and split-plot randomized designs.
• To simplify sample size and cost-efficiency calculations for health researchers.

Main Methods:

• Developed a power function based on sample sizes (n, J), factor levels (a, b), intraclass correlation (ρ), and effect sizes (δ).
• Expressed power for cluster (C), multisite (M), and split-plot (S) designs.
• Compared design impacts on power to optimize sample size and minimize cost.

Main Results:

• The power function accurately and conservatively computes statistical power.
• It simplifies calculations, requiring knowledge of only three effect size differences.
• The approach facilitates selection of optimal designs and sample sizes under budget constraints.

Conclusions:

• This method provides a simplified approach to power computation for complex hierarchical study designs.
• It aids researchers in determining adequate sample sizes and selecting cost-effective designs.
• Enhances the efficiency and accuracy of health services and clinical research.