Statistical inference methods for two crossing survival curves: a comparison of methods

Area of Science:

• Biostatistics
• Survival Analysis

Background:

• Crossing survival curves violate proportional hazards assumption, yet log-rank tests are frequently misused.
• Existing statistical methods for non-proportional hazards are difficult to select without prior knowledge of survival differences.
• Log-rank test is inappropriately used in 70% of studies with crossing survival distributions.

Purpose of the Study:

• To evaluate the performance of various statistical tests under different crossing survival curve scenarios.
• To assess test power and type I error rates across varying censoring rates and distribution parameters.
• To recommend robust statistical methods for survival analysis with crossing curves.

Main Methods:

• Extensive Monte Carlo simulations were conducted.
• Investigated power and type I error rates of multiple statistical procedures.
• Simulations included diverse crossing survival curve patterns, censoring rates, and distribution parameters.

Main Results:

• Adaptive Neyman's smooth tests and the two-stage procedure demonstrated superior power and stability for crossing survival curves.
• These methods maintained acceptable power even under proportional hazards compared to the log-rank test.
• Renyi and Cramér-von Mises tests were conservative; Lin-Xu test showed inflated type I error with increased censoring.

Conclusions:

• Adaptive Neyman's smooth tests and the two-stage procedure are the most stable and feasible methods for survival analysis.
• These recommended tests perform well across various situations and censoring rates.
• They offer broader applicability compared to other tested methods for crossing survival distributions.