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

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Longitudinal Data Analysis

Background:

• Longitudinal cluster randomized clinical trials (cluster-RCTs) involve subjects nested within higher-level units (e.g., clinics), creating three-level hierarchical data.
• Testing intervention effects on the rate of change over time requires modeling subject-specific slopes, often as random coefficients in mixed-effects models.
• Substantial between-subject variation in slopes necessitates accurate sample size calculations to avoid underpowered studies.

Purpose of the Study:

• To propose and evaluate ordinary least squares (OLS) based approaches for determining sample sizes at each level of a three-level hierarchical cluster-RCT design.
• To detect differences in mean slopes between two intervention groups when subject-specific slopes are modeled as random.
• To compare sample size requirements for random versus fixed slope models.

Main Methods:

• Development of OLS-based methods for sample size determination in three-level hierarchical cluster-RCTs with random slopes.
• Simulation studies to compare OLS-based estimates with empirical maximum likelihood estimates.
• Analysis of the impact of random slope variance on sample size requirements.

Main Results:

• Proposed OLS-based sample size calculations are accurate, yielding results virtually identical to empirical maximum likelihood estimates, even with varying cluster sizes.
• Sample size is dependent on the product of the number of second and third-level units, not individual variances of random intercepts.
• The variance of the random slope significantly impacts sample size determination; fixed slope models can lead to underpowered studies when substantial between-subject slope variation exists.

Conclusions:

• OLS-based methods provide a reliable approach for sample size determination in longitudinal cluster-RCTs with random slopes.
• Accurate estimation of between-subject slope variation is critical for appropriate sample size calculation.
• Failure to account for random slopes in sample size calculations can lead to seriously underpowered studies, compromising the ability to detect true intervention effects.