Sample size requirements for comparing time-to-failure among k treatment groups

Area of Science:

• Biostatistics
• Clinical Trial Design
• Survival Analysis

Background:

• Clinical trials frequently involve comparing efficacy across multiple treatment arms (k ≥ 3).
• Accurate sample size determination is crucial for trial power and reliable results.
• Existing methods often focus on two-group comparisons, which may not suffice for k ≥ 3.

Purpose of the Study:

• To derive and present sample size requirements for k-group comparative clinical trials.
• To utilize time-to-failure data, assuming an exponential distribution, as the primary efficacy measure.
• To offer a simplified sample size formula when the largest difference among groups is specified.

Main Methods:

• Development of sample size formulas for k-group survival data under an exponential distribution.
• Generalization of existing two-group sample size methodologies.
• Analysis of sample size needs considering multiple comparisons inherent in k ≥ 3 groups.

Main Results:

• Formulas for sample size calculation in k-group comparative trials are provided.
• A simplified sample size expression is derived for specific alternative hypotheses.
• The inadequacy of applying two-group sample size methods to multi-group trials is demonstrated.

Conclusions:

• The provided sample size calculations are essential for designing robust multi-group clinical trials.
• Researchers must use k-group specific methods to ensure adequate power and control for multiple comparisons.
• Heuristic application of two-group sample size formulas can lead to underpowered or inefficient trials.