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

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Abstract

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 coeffcients, 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 model. The good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.

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Acknowledgements

Zhang’s work was supported by National Natural Science Foundation of China (Grant Nos. 11771133 and 11401194) and the Natural Science Foundation of Hunan Province of China (Grant No. 2017JJ3021). Zhao’s work was supported by National Natural Science Foundation of China (Grant No. 11771366). Zhou’s work was supported by the State Key Program of National Natural Science Foundation of China (Grant No. 71331006) and the State Key Program in the Major Research Plan of National Natural Science Foundation of China (Grant No. 91546202).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education), Hunan Normal University, Changsha, 410081, China

    Feipeng Zhang

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    Xingqiu Zhao

  3. School of Statistics, East China Normal University, Shanghai, 200241, China

    Yong Zhou

  4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yong Zhou

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  1. Feipeng Zhang
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  2. Xingqiu Zhao
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Correspondence to Feipeng Zhang.

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Zhang, F., Zhao, X. & Zhou, Y. An embedded estimating equation for the additive risk model with biased-sampling data. Sci. China Math. 61, 1495–1518 (2018). https://doi.org/10.1007/s11425-017-9268-0

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  • DOI: https://doi.org/10.1007/s11425-017-9268-0

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