Exact log-rank tests for unequal follow-up

Area of Science:

• Biostatistics
• Survival Analysis
• Clinical Trials

Background:

• Standard log-rank and Wilcoxon tests have limitations with unequal sample sizes.
• Existing exact tests require equal follow-up, limiting their applicability.
• Asymptotic tests may not maintain size accuracy when sample sizes differ significantly.

Purpose of the Study:

• To develop novel exact tests for comparing survival data with unequal sample sizes and follow-up.
• To address the limitations of existing asymptotic and exact survival analysis methods.
• To provide robust statistical tools for clinical trial data analysis.

Main Methods:

• Developed two new exact tests: one conditioning on risk sets, another permuting survival times with realized follow-up.
• Compared new tests against asymptotic log-rank, exact complete permutation, and artificial censoring methods.
• Evaluated test performance using an empirical study and a breast cancer dataset.

Main Results:

• The exact procedure conditioning on realized follow-up demonstrated highly satisfactory performance.
• This new method proved particularly advantageous with unequal follow-up times.
• Empirical comparisons confirmed the superiority of the proposed exact test in specific scenarios.

Conclusions:

• The developed exact test conditioning on realized follow-up is a valuable tool for survival data analysis.
• It offers improved accuracy and reliability, especially in complex clinical trial settings with unequal follow-up.
• This method enhances the ability to accurately compare survival experiences across different patient groups.