The estimation for the general additive–multiplicative hazard model using the length-biased survival data

  • Chengbo LiEmail author
  • Yong Zhou
Regular Article


We use the general additive–multiplicative hazard model to analyze the length biased data with right censorship and use the estimating equation method that incorporates the information about length-biased sampling scheme to do the inference. In addition, some graphical and numerical methods are developed for assessing the adequacy of the general additive–multiplicative hazard model. The procedures are derived from cumulative sums of martingale-based residuals over follow-up time and covariate values. The simulations are conducted to insure the good performance of this method. An application to the Oscar data is also illustrated.


Composite estimator General additive–multiplicative hazard model Length biased sampling Martingale Model checking 



The authors thank the Editor, an Associate Editor and the anonymous reviewers for their constructive suggestions, which have helped greatly improve our paper. Zhou’s work is supported by the State Key Program in the Major Research Plan of National Natural Science Foundation of China (91546202), the State Key Program of National Natural Science Foundation of China (71331006). Li’s research is partly supported by the National Natural Science Foundation of China Grants (NO. 11601307).

Supplementary material

362_2018_1079_MOESM1_ESM.pdf (194 kb)
Supplementary material 1 (pdf 193 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of StatisticsDongbei University of Finance and EconomicsDalianChina
  2. 2.Key Laboratory of Advanced Theory and Application in Statistics and Data ScienceMinistry of EducationShanghaiChina
  3. 3.Institute of Statistics and Interdisciplinary Sciences and School of StatisticsEast China Normal UniversityShanghaiChina

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