Testing for Linear Regression Relationships in Randomly Right-Censored Varying-Coefficient Models

Abstract

A test statistic is constructed to test linear relationships in randomly right-censored varying-coefficient models. A residual-based bootstrap procedure is employed to derive the p-value of the test. The performance of the test is examined by extensive simulations. The simulation results show that the bootstrap estimate of the null distribution of the test statistic is approximately valid and the test method with the residual-based bootstrap works satisfactorily for at least moderate censoring rates of the response. Furthermore, the proposed test is applied to the Stanford heart transplant data for exploring a linear regression relationship between the logrithm of the survival time and the age of the patients.

Keywords:

• Bootstrap
• Local linear fitting
• Randomly right-censored varying-coefficient model

Mathematics Subject Classification:

• Primary 62N01
• Secondary 62G10

Acknowledgments

This research was supported by the National Natural Science Foundation of China (No. 10971161). The authors would like to thank the reviewer for the valuable suggestions, which led to significant improvement on the article.