Visualizing hypothesis tests in survival analysis under anticipated delayed effects

Area of Science:

• Biostatistics
• Clinical Trials
• Survival Analysis

Background:

• Standard statistical methods like the log-rank test and Cox models may be inadequate for randomized clinical trials (RCTs) with time-to-event endpoints when non-proportional hazards are anticipated due to delayed treatment effects.
• Recent statistical literature has explored alternative methods, including weighted log-rank tests and tests based on Restricted Mean Survival Time (RMST).

Purpose of the Study:

• To address the debate on appropriate statistical methods for RCTs with time-to-event data and delayed effects.
• To introduce a novel graphical approach for comparing different statistical methods.
• To facilitate a more informed selection of analysis methods beyond traditional power and type I error considerations.

Main Methods:

• Comparison of weighted log-rank tests and tests based on Restricted Mean Survival Time (RMST).
• Introduction of a graphical method for direct comparison of these statistical approaches.
• Evaluation of power and type I error characteristics of different methods under various conditions.

Main Results:

• Weighted log-rank tests can offer high power but may inflate type I error rates and lack a clear summary measure.
• RMST-based tests provide a mathematically unambiguous summary measure but may not fully capture long-term treatment benefits.
• The proposed graphical approach enables a more nuanced comparison of these methods.

Conclusions:

• The choice of statistical method for RCTs with delayed effects requires careful consideration beyond standard approaches.
• The graphical comparison tool aids in selecting the most appropriate method based on specific trial characteristics.
• This work contributes to improving the statistical rigor and interpretation of time-to-event analyses in clinical trials.