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Analyzing the general biased data by additive risk model

Science China Mathematics 2017年第4期60卷 685-700页

作者： LI YanFeng MA HuiJuan WANG DeHui ZHOU Yong College of Mathematics Jilin University Department of Biostatistics and Bioinformatics Emory University School of Statistics and Management Shanghai University of Finance and Economics Academy of Mathematics and Systems Science Chinese Academy of Sciences

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.

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

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An embedded estimating equation for the additive risk model with biased-sampling data

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Science China Mathematics 2018年第8期61卷 1495-1518页

作者： Feipeng Zhang Xingqiu Zhao Yong Zhou School of Mathematics and Statistics Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education)Hunan Normal University Department of Applied Mathematics The Hong Kong Polytechnic University School of Statistics East China Normal University Academy of Mathematics and Systems Science Chinese Academy of Sciences

This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weighted estimating equation for the covariate coefficients, by embedding the biased-sampling data into left-truncated and right-censored data. The asymptotic properties(consistency and asymptotic normality) of the proposed estimator are derived via the modern empirical processes theory. Based on the cumulative residual processes, we also propose graphical and numerical methods to assess the adequacy of the additive risk *** good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.

关键词： additive risk model biased-sampling data missing covariates estimating equation model checking

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