Sample size calculations for evaluating treatment policies in multi-stage designs

Area of Science:

• Clinical Trials Methodology
• Biostatistics
• Adaptive Trial Design

Background:

• Sequential multiple assignment randomized (SMAR) designs evaluate adaptive treatment strategies (ATS).
• Calculating sample sizes for SMAR designs is challenging due to sequential and adaptive elements.
• Multi-stage randomization in ATS evaluation complicates sample size determination.

Purpose of the Study:

• Derive sample size formulas for the nested structure of successive SMAR randomizations.
• Address the impact of overlapping data and between-strategy covariance on sample size.
• Focus on scenarios where covariance significantly improves inferential efficiency and reduces sample size.

Main Methods:

• Utilize two methodologies for SMAR trials: optimal semi-parametric and Bayesian predictive estimators.
• Employ a 'hybrid' approach generalizing t-test power calculations.
• Incorporate effect size and regression quantities familiar to trialists.

Main Results:

• Simulation studies validate underlying assumptions and the approximation of between-strategy covariance.
• Formula sensitivity analysis indicates effect size has the greatest influence on sample size.
• Covariance adjustment significantly reduces sample size for distinguishing distinct strategies with small effects.

Conclusions:

• Methods are generalizable to K-stage SMAR trials.
• Practical guidance is needed for trialists to apply derived sample size methods.
• Defining distinct ATS by clinically relevant effect size aids in sample size determination.