Sample size determination for three-level randomized clinical trials with randomization at the first or second level.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Health Services Research

Background:

• Comparative effectiveness research (CER) trials often use three-level hierarchical designs in real-world healthcare settings.
• Patients are frequently nested within physicians, who are nested within healthcare centers (e.g., hospitals).
• Randomization typically occurs at the third level (centers), but lower-level randomization is also employed.

Purpose of the Study:

• To present and verify explicit closed-form sample size and power formulas for three-level hierarchical designs.
• To evaluate the statistical efficiency of randomization at the first (patient) or second (physician) level compared to the third (center) level.

Main Methods:

• Formulas derived using maximum likelihood estimates from mixed-effect linear models.
• Verification of formulas through simulation studies.
• Comparison of theoretical power with known variances to empirically estimated power with unknown variances.

Main Results:

• Theoretical power closely matches empirical power even with smaller sample sizes when variances are unknown.
• Randomization at the second or first level offers greater statistical efficiency than third-level randomization.
• Second-level randomization power approaches patient-level randomization power under specific conditions (few patients per cluster, low correlation from second-level variation).

Conclusions:

• The developed formulas provide accurate sample size and power calculations for lower-level randomization in three-level designs.
• Randomization at lower hierarchical levels (physician or patient) is a statistically efficient alternative to center-level randomization in CER.
• These findings support optimized clinical trial designs for comparative effectiveness research.