Median tests for censored survival data; a contingency table approach

Area of Science:

• Biostatistics
• Survival Analysis
• Clinical Trials

Background:

• Median failure time is a practical metric for survival data interpretation.
• Existing methods for comparing medians with censored data are complex, requiring density estimation or intricate variance calculations.

Purpose of the Study:

• To develop a simplified statistical method for comparing median failure times in the presence of censored survival data.
• To address limitations of existing methods by avoiding probability density function estimation and complex variance formulas.

Main Methods:

• Modification of the K-sample median test using a contingency table approach for censored data.
• Construction of a weighted asymptotic test statistic aggregating dependent chi-squared statistics for noninteger cell counts.
• Development of a Fisher's exact test-based statistic for small sample sizes.

Main Results:

• The proposed weighted asymptotic test statistic approximates a chi-squared distribution with k-1 degrees of freedom.
• The small sample test statistic follows a chi-squared distribution with 2 degrees of freedom.
• Simulation studies indicate the method achieves appropriate type I error rates and statistical power.

Conclusions:

• The novel contingency table approach offers a more straightforward and computationally feasible method for comparing median failure times with censored data.
• The proposed methods are validated through simulations and demonstrated on real-world clinical trial data, particularly in breast cancer research.