Sample size requirements to detect a two- or three-way interaction in longitudinal cluster randomized clinical trials...

Area of Science:

• Biostatistics
• Clinical Trial Design
• Longitudinal Data Analysis

Background:

• Existing sample size formulas for longitudinal cluster randomized trials (CRTs) are established for cluster-level randomization with continuous outcomes.
• These formulas specifically address detecting two-way interaction effects between time and intervention.

Purpose of the Study:

• To demonstrate the applicability of existing sample size formulas to longitudinal trials with subject-level randomization within clusters.
• To extend these formulas to 2-by-2 factorial longitudinal-CRTs, accommodating different randomization levels for testing three-way interactions.

Main Methods:

• Utilizing mixed-effects models to show uncorrelated slope estimates across treatment arms, irrespective of randomization level (subject or cluster) or slope type (fixed or random).
• Extending sample size formulas to accommodate unbalanced study designs.
• Employing simulation studies to validate the derived theoretical findings.

Main Results:

• Sample size formulas for two-way and three-way interactions in longitudinal-CRTs are consistent across second-level (subject) and third-level (cluster) randomization.
• The sample size for testing a three-way interaction is four times larger than for a two-way interaction, applicable to both fixed- and random-slope models and all randomization levels.

Conclusions:

• The developed sample size formulas are validated by simulation studies.
• These findings enhance the flexibility in designing longitudinal clinical trials concerning the randomization and allocation of clusters and subjects.
• The applicability of these findings is limited to longitudinal-CRTs with normally distributed continuous outcomes.