RAO'S SCORE TESTS IN SURVIVAL ANALYSIS: EXAMPLES AND BARTLETT TYPE ADJUSTMENTS

Abstract

Score method in hypothesis testing is one of Professor C. R. Rao's great contributions to statistics. It provides a simple and unified way to test some simple and composite hypotheses in many statistical problems. Some popular tests in statistical practice derived with the help of intuitions can be shown as score tests under some statistical models. The subject-years test and log-rank test in survival analysis are two of the examples. In this paper, we first introduce these two examples. After formulating these two tests as score tests, we then review some recent results on the Bartlett type adjustments for these tests.

Keywords:

• Asymptotic expansion
• Bartlett adjustment log-rank test
• Proportional hazard model
• Score test
• Subject-years test

ACKNOWLEDGMENTS

This paper is based on a presentation in the meeting “Statistics: Reflection on the Past and Visions for the Future” and dedicated to the 80th birthday of Professor C. R. Rao. The author would like to thank Professor Rao for introducing him the score test when he was working as a Research Associate in the Center for Multivariate Analysis of the Pennsylvania State University and starting research in survival analysis. The author would also like to thank Professor Rao for his continuous encouragements and guidance after he left the Penn State.