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Nonparametric Sieve Maximum Likelihood Estimation of Semi-Competing Risks Data

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  • Xifen Huang

    (School of Mathematics, Yunnan Normal University, Kunming 650092, China)

  • Jinfeng Xu

    (School of Mathematics, Yunnan Normal University, Kunming 650092, China)

Abstract

In biomedical studies involving time-to-event data, a subject may experience distinct types of events. We consider the problem of estimating the transition functions for a semi-competing risks model under illness-death model framework. We propose to estimate the intensity functions by maximizing a B-spline based sieve likelihood. The method yields smooth estimates without parametric assumptions. Our proposed approach facilitates easy computation of the covariance of the model parameters and yields direct interpretation. Compared with existing approaches, our proposed method requires neither the subjective specification of the frailty distribution nor the Markov or semi-Markov assumption which may be unmet in real applications. We establish the consistency, the convergence rate, and the asymptotic normality of the proposed estimators under some regularity conditions. We also provide simulation studies to assess the finite-sample performance of the proposed modeling and estimation strategy. A real data application is further used to illustrate the proposed methodology.

Suggested Citation

  • Xifen Huang & Jinfeng Xu, 2022. "Nonparametric Sieve Maximum Likelihood Estimation of Semi-Competing Risks Data," Mathematics, MDPI, vol. 10(13), pages 1-10, June.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2248-:d:849138
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    References listed on IDEAS

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    1. Weijing Wang, 2003. "Estimating the association parameter for copula models under dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 257-273, February.
    2. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
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