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A semiparametric accelerated failure time partial linear model and its application to breast cancer

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  • Zou, Yubo
  • Zhang, Jiajia
  • Qin, Guoyou
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    Abstract

    Breast cancer is the most common non-skin cancer in women and the second most common cause of cancer-related death in US women. It is well known that the breast cancer survival rate varies with age at diagnosis. For most cancers, the relative survival rate decreases with age, but breast cancer may show an unusual age pattern. In order to reveal the stage risk and age effects pattern, we propose a semiparametric accelerated failure time partial linear model and develop its estimation method based on the penalized spline (P-spline) and the rank estimation approach. The simulation studies demonstrate that the proposed method is comparable to the parametric approach when data is not contaminated, and more stable than parametric methods when data is contaminated. By applying the proposed model and method to the breast cancer data set of Atlantic County, New Jersey, from the SEER program, we successfully reveal the significant effects of stage, and show that women diagnosed at age around 38 years have consistently higher survival rates than either younger or older women.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 3 (March)
    Pages: 1479-1487

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1479-1487

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Accelerated failure time model Partial linear model Penalized spline Rank estimation Robustness;

    References

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    1. Jianhua Z. Huang & Liangyue Zhang & Lan Zhou, 2007. "Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 451-477.
    2. Brent A. Johnson, 2008. "Variable selection in semiparametric linear regression with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 351-370.
    3. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    4. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
    5. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    6. Cai, Jianwen & Fan, Jianqing & Jiang, Jiancheng & Zhou, Haibo, 2007. "Partially Linear Hazard Regression for Multivariate Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 538-551, June.
    7. Zhezhen Jin & D. Y. Lin & Zhiliang Ying, 2006. "On least-squares regression with censored data," Biometrika, Biometrika Trust, vol. 93(1), pages 147-161, March.
    8. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    9. 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.
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