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A Spline‐Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval‐Censored Data

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  • YING ZHANG
  • LEI HUA
  • JIAN HUANG

Abstract

. We propose a spline‐based semiparametric maximum likelihood approach to analysing the Cox model with interval‐censored data. With this approach, the baseline cumulative hazard function is approximated by a monotone B‐spline function. We extend the generalized Rosen algorithm to compute the maximum likelihood estimate. We show that the estimator of the regression parameter is asymptotically normal and semiparametrically efficient, although the estimator of the baseline cumulative hazard function converges at a rate slower than root‐n. We also develop an easy‐to‐implement method for consistently estimating the standard error of the estimated regression parameter, which facilitates the proposed inference procedure for the Cox model with interval‐censored data. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated using data from a breast cosmesis study.

Suggested Citation

  • Ying Zhang & Lei Hua & Jian Huang, 2010. "A Spline‐Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 338-354, June.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:2:p:338-354
    DOI: 10.1111/j.1467-9469.2009.00680.x
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    References listed on IDEAS

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    1. Jamshidian, Mortaza, 2004. "On algorithms for restricted maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 137-157, March.
    2. Tianxi Cai & Rebecca A. Betensky, 2003. "Hazard Regression for Interval-Censored Data with Penalized Spline," Biometrics, The International Biometric Society, vol. 59(3), pages 570-579, September.
    3. William B. Goggins & Dianne M. Finkelstein, 2000. "A Proportional Hazards Model for Multivariate Interval-Censored Failure Time Data," Biometrics, The International Biometric Society, vol. 56(3), pages 940-943, September.
    4. Torben Martinussen, 2002. "Efficient estimation in additive hazards regression with current status data," Biometrika, Biometrika Trust, vol. 89(3), pages 649-658, August.
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