A class of tests of proportional hazards assumption for left-truncated and right-censored data

Abstract

In this paper, we proposed a class of tests of proportional hazards assumption for left-truncated and right-censored data based on a pair of estimators of the hazard ratio constant. Using counting process and martingale theory, the asymptotically normal distribution of the test statistic is derived and a family of consistent estimators of variance are also provided. Extensive simulation studies were conducted to evaluate the performance of the proposed test statistics under finite sample situations. Two real data sets are analyzed to illustrate our method.

Keywords:

• proportional hazards assumption
• two-sample problem
• hazard ratio
• left-truncated and right-censored data
• counting process

Classification codes:

• 62N01
• 62N03

Acknowledgments

The authors are very grateful to the Editor and the two referees for their careful reading and insightful comments, which lead to a substantially improved manuscript. We also thank Prof. Shen Paosheng, Department of Statistics, Tunghai University, Taichung, Taiwan, for beneficial discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.