Statistics and Its Interface

Volume 14 (2021)

Number 3

Inference in a mixture additive hazards cure model

Pages: 323 – 338



Dongxiao Han (School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin, China)

Haijin He (Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen, China)

Liuquan Sun (Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Xinyuan Song (Department of Statistics, Chinese University of Hong Kong)

Wei Xu (Department of Biostatistics, Princess Margaret Cancer Centre, and Dalla Lana School of Public Health, University of Toronto, Ontario, Canada)


We propose a mixture additive hazards (AH) cure model for survival data with a cure fraction. The proposed model integrates a logistic regression model for the proportion of patients cured of disease and an AH model for the uncured patients. Generalized estimating equations are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. In addition, model-checking methods are presented to assess the adequacy of the model. The finite-sample performance of the proposed method is evaluated through simulation studies. An application to a human papillomavirus positive oropharyngeal cancer study is conducted to illustrate the proposed method.


additive hazards model, cure model, estimating equation, logistic regression, mixture, model checking

2010 Mathematics Subject Classification

62G08, 62N01

The research of H. He was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11701387), and the Natural Science Foundation of Shenzhen (Grant Nos. JCYJ20190808173603590 and JCYJ20170817100950436). The research of L. Sun was supported in part by NSFC (Grant Nos. 11771431 and 11690015), and Key Laboratory of RCSDS, CAS (No. 2008DP173182). The research of X. Song was supported in part by the Research Grant Council of the HKSAR (GRF Grant Nos. 14301918 and 14303017), and the direct grants of Chinese University of Hong Kong. The research of W. Xu was supported in part by the Canadian Institute of Health Research (Grant No. 145546), and Natural Science and Engineering Research Council of Canada (Grant No. RGPIN- 2017-06672).

Received 9 October 2019

Accepted 7 October 2020

Published 9 February 2021