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A Cox-Aalen Model for Interval-censored Data

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  • Audrey Boruvka
  • Richard J. Cook

Abstract

type="main" xml:id="sjos12113-abs-0001"> The Cox-Aalen model, obtained by replacing the baseline hazard function in the well-known Cox model with a covariate-dependent Aalen model, allows for both fixed and dynamic covariate effects. In this paper, we examine maximum likelihood estimation for a Cox-Aalen model based on interval-censored failure times with fixed covariates. The resulting estimator globally converges to the truth slower than the parametric rate, but its finite-dimensional component is asymptotically efficient. Numerical studies show that estimation via a constrained Newton method performs well in terms of both finite sample properties and processing time for moderate-to-large samples with few covariates. We conclude with an application of the proposed methods to assess risk factors for disease progression in psoriatic arthritis.

Suggested Citation

  • Audrey Boruvka & Richard J. Cook, 2015. "A Cox-Aalen Model for Interval-censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 414-426, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:414-426
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    File URL: http://hdl.handle.net/10.1111/sjos.12113
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    References listed on IDEAS

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    1. Thomas H. Scheike & Mei‐Jie Zhang, 2002. "An Additive–Multiplicative Cox–Aalen Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 75-88, March.
    2. 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.
    3. Thomas H. Scheike & Mei-Jie Zhang, 2003. "Extensions and Applications of the Cox-Aalen Survival Model," Biometrics, The International Biometric Society, vol. 59(4), pages 1036-1045, December.
    4. 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.
    5. Jong S. Kim, 2003. "Maximum likelihood estimation for the proportional hazards model with partly interval‐censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 489-502, May.
    6. Fay, Michael P. & Shaw, Pamela A., 2010. "Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i02).
    7. Wong, George Y. C. & Yu, Qiqing, 1999. "Generalized MLE of a Joint Distribution Function with Multivariate Interval-Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 155-166, May.
    8. Gang Cheng & Ying Zhang & Liqiang Lu, 2011. "Efficient algorithms for computing the non and semi-parametric maximum likelihood estimates with panel count data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 567-579.
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