Statistics and Its Interface

Volume 12 (2019)

Number 1

Proportional mean residual life model with censored survival data under case-cohort design

Pages: 21 – 33



Huijuan Ma (Institute of Statistics and Interdisciplinary Sciences, Faculty of Economics and Managementm East China Normal University, Shanghai, China)

Jianhua Shi (School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, China)

Yong Zhou (Institute of Statistics and Interdisciplinary Sciences and School of Statistics, Faculty of Economics and Management, East China Normal University, Shanghai, China)


Proportional mean residual life model is studied for analysing survival data from the case-cohort design. To simultaneously estimate the regression parameters and the baseline mean residual life function, weighted estimating equations based on an inverse selection probability are proposed. The resulting regression coefficients estimates are shown to be consistent and asymptotically normal with easily estimated variance-covariance. Simulation studies show that the proposed estimators perform very well. An application to a real dataset from the South Welsh nickel refiners study is also given to illustrate the methodology.


case-cohort design, censored survival data, estimating equation, mean residual life

The authors wish to thank the Editor Yuedong Wang, the Associate Editor and two anonymous referees for their valuable and helpful comments. The authors also wish to express their appreciation to Professor Ying Qing Chen and Cindy Zhang for their invaluable assistance of the original version.

Ma’s work is partially supported by National Institutes of Health grant R01 HL113548. Shi’s work is supported by Natural Science Foundation of Fujian Province, China (2016J01026), the Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics, China. Zhou’s work is supported by the State Key Program of National Natural Science Foundation of China (71331006), the State Key Program in the Major Research Plan of National Natural Science Foundation of China (91546202).

Received 30 July 2017

Published 26 October 2018