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Hazard rate estimation for left truncated and right censored data

Author

Listed:
  • Sam Efromovich

    (The University of Texas at Dallas)

  • Jufen Chu

    (Novartis Oncology)

Abstract

Left truncation and right censoring (LTRC) presents a unique challenge for nonparametric estimation of the hazard rate of a continuous lifetime because consistent estimation over the support of the lifetime is impossible. To understand the problem and make practical recommendations, the paper explores how the LTRC affects a minimal (called sharp) constant of a minimax MISE convergence over a fixed interval. The corresponding theory of sharp minimax estimation of the hazard rate is presented, and it shows how right censoring, left truncation and interval of estimation affect the MISE. Obtained results are also new for classical cases of censoring or truncation and some even for the case of direct observations of the lifetime of interest. The theory allows us to propose a relatively simple data-driven estimator for small samples as well as the methodology of choosing an interval of estimation. The estimation methodology is tested numerically and on real data.

Suggested Citation

  • Sam Efromovich & Jufen Chu, 2018. "Hazard rate estimation for left truncated and right censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 889-917, August.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:4:d:10.1007_s10463-017-0617-x
    DOI: 10.1007/s10463-017-0617-x
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    References listed on IDEAS

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    1. A. Antoniadis & G. Grégoire & G. Nason, 1999. "Density and hazard rate estimation for right‐censored data by using wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 63-84.
    2. Chiung-Yu Huang & Jing Qin, 2013. "Semiparametric estimation for the additive hazards model with left-truncated and right-censored data," Biometrika, Biometrika Trust, vol. 100(4), pages 877-888.
    3. Bremhorst, Vincent & Lambert, Philippe, 2016. "Flexible estimation in cure survival models using Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 270-284.
    4. XiaoFei, Lu & Min, Liu, 2014. "Hazard rate function in dynamic environment," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 50-60.
    5. Talamakrouni, Majda & Van Keilegom, Ingrid & El Ghouch, Anouar, 2016. "Parametrically guided nonparametric density and hazard estimation with censored data," LIDAM Reprints ISBA 2016001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Qian, Jing & Betensky, Rebecca A., 2014. "Assumptions regarding right censoring in the presence of left truncation," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 12-17.
    7. Sam Efromovich, 2016. "Minimax theory of nonparametric hazard rate estimation: efficiency and adaptation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 25-75, February.
    8. Efromovich S., 2001. "Density Estimation Under Random Censorship and Order Restrictions: From Asymptotic to Small Samples," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 667-684, June.
    9. Shi, Jianhua & Chen, Xiaoping & Zhou, Yong, 2015. "The strong representation for the nonparametric estimator of length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 49-57.
    10. Yuanjia Wang & Baosheng Liang & Xingwei Tong & Karen Marder & Susan Bressman & Avi Orr-Urtreger & Nir Giladi & Donglin Zeng, 2015. "Efficient estimation of nonparametric genetic risk function with censored data," Biometrika, Biometrika Trust, vol. 102(3), pages 515-532.
    11. Ricardo Cao & Paul Janssen & Noël Veraverbeke, 2005. "Relative hazard rate estimation for right censored and left truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 257-280, June.
    12. Talamakrouni, Majda & Van Keilegom, Ingrid & El Ghouch, Anouar, 2016. "Parametrically guided nonparametric density and hazard estimation with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 308-323.
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