Sequential tests for non-proportional hazards data.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Survival Analysis

Background:

• The log-rank test is standard for comparing survival endpoints in clinical trials.
• The proportional hazards assumption is critical for the log-rank test and Cox models.
• Violations of proportional hazards render the hazard ratio ill-defined and affect test power.

Purpose of the Study:

• To introduce and validate sequential test statistics based on the average hazard ratio.
• To provide a robust alternative for survival endpoint comparisons when proportional hazards are violated.
• To enable the use of standard group-sequential methods with the average hazard ratio.

Main Methods:

• Proving asymptotic multivariate normality and independent increments for average hazard ratio test statistics.
• Utilizing established methods for calculating group-sequential boundaries.
• Conducting simulation studies to evaluate finite sample characteristics in proportional and non-proportional hazards settings.

Main Results:

• Average hazard ratio based sequential test statistics are asymptotically multivariate normal with independent increments.
• This property allows for the application of standard group-sequential boundary calculation methods.
• Simulation studies confirm the method's performance in various hazard scenarios.

Conclusions:

• The average hazard ratio provides a statistically sound and interpretable measure for survival endpoints, especially with non-proportional hazards.
• The developed sequential test statistics are compatible with existing group-sequential software and methods.
• This approach enhances the reliability and flexibility of sequential analyses in clinical trials.