Sample size calculations for within-patient comparisons with a binary or survival endpoint

Area of Science:

• Biostatistics
• Clinical Trial Design
• Medical Research Methodology

Background:

• Randomized clinical trials (RCTs) are essential for evaluating new treatments.
• Comparing treatments using multiple units within each patient (e.g., repeated measures) is a common design.
• Accurate sample size determination is critical for the validity and efficiency of clinical trials.

Purpose of the Study:

• To derive formulae for calculating the required number of failures in RCTs with binary or survival endpoints when using multiple units per patient.
• To provide methods for calculating the total number of units and patients needed in such trial designs.
• To highlight potential underestimation of sample size by conventional methods in specific scenarios.

Main Methods:

• Derivation of statistical formulae for sample size estimation.
• Application of formulae to randomized clinical trials with binary endpoints.
• Application of formulae to randomized clinical trials with survival endpoints.
• Illustrative examples demonstrating the calculation of required units and patients.

Main Results:

• Formulae were developed for determining the necessary number of failures for trials with binary or survival endpoints.
• Calculations for the total number of units and patients were demonstrated with examples.
• Results indicate that conventional sample size calculations may underestimate requirements when multiple units are used per patient, particularly with a small number of units per patient.

Conclusions:

• The derived formulae provide a more accurate method for sample size calculation in complex clinical trial designs.
• Researchers must consider the number of units per patient when determining sample size to avoid underestimation.
• Adoption of these methods ensures adequate statistical power and efficient resource allocation in clinical trials.