Sample size requirements to detect an intervention by time interaction in longitudinal cluster randomized clinical...

Area of Science:

• Biostatistics
• Clinical Trials
• Longitudinal Data Analysis

Background:

• Longitudinal cluster-randomized clinical trials (cluster-RCTs) involve interventions assigned to clusters, with subjects within clusters receiving the same treatment.
• Repeated assessments over time are common in these designs, necessitating appropriate statistical models.

Purpose of the Study:

• To derive closed-form formulae for statistical power and sample size calculations in three-level longitudinal cluster-RCTs.
• To facilitate accurate planning and resource allocation for such clinical trials.

Main Methods:

• Application of a mixed-effects linear regression model for three-level cluster-RCT data.
• Derivation of formulae for statistical power and sample size using maximum likelihood estimates.
• Validation through a simulation study comparing theoretical and empirical estimates.

Main Results:

• Closed-form formulae for statistical power to detect intervention-by-time interaction were derived.
• Sample size requirements for each level were determined.
• Statistical power is dependent on the product of second- and third-level data units, not correlations within the second level.

Conclusions:

• The derived formulae provide accurate estimates for statistical power and sample size in longitudinal cluster-RCTs.
• These methods simplify the design of complex clinical trials with nested data structures.
• The findings support robust planning for intervention studies with clustered and repeated measures data.