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Versatile estimation in censored single-index hazards regression

Author

Listed:
  • Chin-Tsang Chiang

    (National Taiwan University)

  • Shao-Hsuan Wang

    (National Taiwan University)

  • Ming-Yueh Huang

    (National Taiwan University)

Abstract

One attractive advantage of the presented single-index hazards regression is that it can take into account possibly time-dependent covariates. In such a model formulation, the main theme of this research is to develop a theoretically valid and practically feasible estimation procedure for the index coefficients and the induced survival function. In particular, compared with the existing pseudo-likelihood approaches, our one proposes an automatic bandwidth selection and suppresses an influence of outliers. By making an effective use of the considered versatile survival process, we further reduce a substantial finite-sample bias in the Chambless-Diao type estimator of the most popular time-dependent accuracy summary. The asymptotic properties of estimators and data-driven bandwidths are also established under some suitable conditions. It is found in simulations that the proposed estimators and inference procedures exhibit quite satisfactory performances. Moreover, the general applicability of our methodology is illustrated by two empirical data.

Suggested Citation

  • Chin-Tsang Chiang & Shao-Hsuan Wang & Ming-Yueh Huang, 2018. "Versatile estimation in censored single-index hazards regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 523-551, June.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0600-6
    DOI: 10.1007/s10463-017-0600-6
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    References listed on IDEAS

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    1. Chin-Tsang Chiang & Shr-Yan Huang, 2009. "Estimation for the Optimal Combination of Markers without Modeling the Censoring Distribution," Biometrics, The International Biometric Society, vol. 65(1), pages 152-158, March.
    2. Chiang, Chin-Tsang & Huang, Ming-Yueh, 2012. "New estimation and inference procedures for a single-index conditional distribution model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 271-285.
    3. Khan, Shakeeb & Tamer, Elie, 2007. "Partial rank estimation of duration models with general forms of censoring," Journal of Econometrics, Elsevier, vol. 136(1), pages 251-280, January.
    4. Martin W. McIntosh & Margaret Sullivan Pepe, 2002. "Combining Several Screening Tests: Optimality of the Risk Score," Biometrics, The International Biometric Society, vol. 58(3), pages 657-664, September.
    5. Patrick J. Heagerty & Thomas Lumley & Margaret S. Pepe, 2000. "Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker," Biometrics, The International Biometric Society, vol. 56(2), pages 337-344, June.
    6. Zeng, Donglin & Lin, D.Y., 2007. "Efficient Estimation for the Accelerated Failure Time Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1387-1396, December.
    7. Lopez, Olivier & Patilea, Valentin & Van Keilegom, Ingrid, 2013. "Single index regression models in the presence of censoring depending on the covariates," LIDAM Reprints ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Gørgens, Tue, 2004. "Average Derivatives For Hazard Functions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 437-463, June.
    9. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
    10. Ewa Strzalkowska-Kominiak & Ricardo Cao, 2014. "Beran-based approach for single-index models under censoring," Computational Statistics, Springer, vol. 29(5), pages 1243-1261, October.
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