Science China Mathematics

, Volume 60, Issue 4, pp 685–700

# Analyzing the general biased data by additive risk model

• YanFeng Li
• HuiJuan Ma
• DeHui Wang
• Yong Zhou
Articles

## Abstract

This paper proposes a unified semiparametric method for the additive risk model under general biased sampling. By using the estimating equation approach, we propose both estimators of the regression parameters and nonparametric function. An advantage is that our approach is still suitable for the lengthbiased data even without the information of the truncation variable. Meanwhile, large sample properties of the proposed estimators are established, including consistency and asymptotic normality. In addition, the finite sample behavior of the proposed methods and the analysis of three groups of real data are given.

## Keywords

additive risk model unified method length-biased data case-cohort design

62N02 46N60

## Notes

### Acknowledgements

This work was supported by National Institutes of Health of USA (Grant No. R01 HL113548), National Natural Science Foundation of China (Grant Nos. 11271155, 11371168, J1310022, 11571138, 11501241 and 71271128), Science and Technology Research Program of Education Department in Jilin Province for the 12th Five-Year Plan (Grant No. 440020031139), Jilin Province Natural Science Foundation (Grant Nos. 20130101066JC, 20130522102JH and 20150520053JH), the State Key Program of National Natural Science Foundation of China (Grant No. 71331006), National Center for Mathematics and Interdisciplinary Sciences and Shanghai University of Finance and Economics through Project 211 Phase IV and Shanghai Leading Academic Discipline Project A.

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© Science China Press and Springer-Verlag Berlin Heidelberg 2016

## Authors and Affiliations

• YanFeng Li
• 1
• HuiJuan Ma
• 2
• DeHui Wang
• 1
• Yong Zhou
• 3
• 4
1. 1.College of MathematicsJilin UniversityChangchunChina
2. 2.Department of Biostatistics and BioinformaticsEmory UniversityAtlantaUSA
3. 3.School of Statistics and ManagementShanghai University of Finance and EconomicsShanghaiChina