The performance of the log rank test for different relationships between the hazards: the case of the triangular test in comparison with some other sequential tests

Abstract

Sequential designs are widely used in medical research for the reason being one of ethics to terminate or alternate a trial as soon as significant evidence are available that saves time, cost and other resources. The most popular and frequently used sequential framework in real life is the Triangular Test with the Christmas tree correction for the important statistical properties that it possesses. Often the log-rank test is used in clinical medicine, and it has been found to be more efficient when the hazards of intervention groups are proportional. Therefore, this study intends to identify the performance of the log-rank test for different relationships between the Hazards departures from proportional hazards in the framework of the sequential design of the Triangular Test as well as some other sequential designs. The results indicate that the log-rank test maintains the desirable significance level when the interim sample size consists of 200 or a greater number of patients for the Triangular design. Moreover, the study findings include that the power of the test is high when proportional hazard is satisfied. The Triangular design performs better with respect to type I error as well as power.

Keywords:

• Christmas tree correction
• Log rank test
• Proportional hazards
• Sequential test
• Simulation
• Whitehead’s triangular test

Acknowledgments

The authors thank Professor John Whitehead for evaluating the results and giving valuable feedback and comments for improvement of this study.