Lifetime Data Analysis

, Volume 25, Issue 1, pp 128–149 | Cite as

Additive hazards model with auxiliary subgroup survival information

  • Jie He
  • Hui Li
  • Shumei Zhang
  • Xiaogang DuanEmail author


The semiparametric additive hazards model is an important way for studying the effect of potential risk factors for right-censored time-to-event data. In this paper, we study the additive hazards model in the presence of auxiliary subgroup \(t^*\)-year survival information. We formulate the known auxiliary information in the form of estimating equations, and combine them with the conventional score-type estimating equations for the estimation of the regression parameters based on the maximum empirical likelihood method. We prove that the new estimator of the regression coefficients follows asymptotically a multivariate normal distribution with a sandwich-type covariance matrix that can be consistently estimated, and is strictly more efficient, in an asymptotic sense, than the conventional one without incorporation of the available auxiliary information. Simulation studies show that the new proposal has substantial advantages over the conventional one in terms of standard errors, and with the accommodation of more informative information, the proposed estimator becomes more competing. An AIDS data example is used for illustration.


Additive hazards model Auxiliary information Empirical likelihood Estimation efficiency 



We thank the two referees, the associate editor and the editor for their constructive and insightful comments that led to significant improvements in the article. This research was supported by the National Natural Science Foundation of China Grant 11771049.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsBeijing Normal UniversityBeijingPeople’s Republic of China
  2. 2.Department of StatisticsBeijing Normal UniversityBeijingPeople’s Republic of China

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