Sample size calculations for randomised trials including both independent and paired data

Area of Science:

• Biostatistics
• Health Research Methodology
• Clinical Trial Design

Background:

• Sample size determination is crucial for the validity and efficiency of health research trials.
• Existing methods for sample size calculations do not adequately address trials with a mix of independent and paired data.
• This gap hinders accurate planning for complex randomized trials.

Purpose of the Study:

• To derive algebraic design effects for sample size calculations in randomized trials containing both independent and paired data.
• To provide a framework for determining appropriate sample sizes in complex health research settings.
• To validate the derived design effects through simulation and practical examples.

Main Methods:

• Algebraic derivation of design effects assuming paired data clustering is handled using generalized estimating equations (GEE).
• Consideration of both continuous and binary outcomes.
• Inclusion of three randomization methods: cluster, individual, and randomization to opposite treatment groups.
• Exploration of independence and exchangeable working correlation structures within GEE.

Main Results:

• The design effect is demonstrated to be dependent on the intracluster correlation coefficient, the proportion of paired data, the chosen working correlation structure, outcome type, and randomization method.
• Simulations confirmed the validity of the derived design effects.
• Example calculations illustrate the practical application of these design effects in sample size planning.

Conclusions:

• The derived design effects provide a robust method for sample size calculations in randomized trials with mixed independent and paired data.
• These methods will facilitate more accurate and appropriate sample size planning for future complex health research.
• This work addresses a significant methodological gap in clinical trial design.