Sample size determination for comparing several survival curves with unequal allocations

Area of Science:

• Biostatistics
• Clinical Trial Design
• Survival Analysis

Background:

• Existing sample size formulas by Ahnn and Anderson assumed equal subject allocation across treatment groups.
• Generalizing these formulas is crucial for optimizing resource allocation and statistical power in complex trial designs.

Purpose of the Study:

• To generalize existing sample size formulas for unstratified and stratified clinical trial designs to accommodate unequal allocation of subjects.
• To investigate the impact of censoring mechanisms and allocation strategies on sample size determination and statistical power.
• To provide accurate power approximations for the log-rank test.

Main Methods:

• Generalized sample size formulas for unequal allocation in unstratified and stratified designs under proportional hazards.
• Considered three failure/censoring scenarios: exponential failures with exponential/uniform censoring, and Weibull failures with uniform censoring.
• Developed approximate power formulas based on the first two and four moments of the asymptotic distribution.

Main Results:

• The simulated power of the log-rank test was found to be independent of the censoring mechanism.
• For a significance level of 0.05 and power of 0.80, the required sample size was independent of the censoring pattern.
• Simulations indicated empirical powers consistently exceeded the target 0.80 when 50% of patients were allocated to the group with the smallest hazard.

Conclusions:

• The generalized formulas provide a robust framework for sample size calculations in trials with unequal group sizes.
• Censoring patterns do not significantly impact the power of the log-rank test or the required sample size under standard conditions.
• Unequal allocation strategies, particularly favoring groups with smaller hazards, can enhance empirical power beyond target levels.