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Parametric and semiparametric estimation methods for survival data under a flexible class of models

Author

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  • Wenqing He

    (University of Western Ontario)

  • Grace Y. Yi

    (University of Waterloo)

Abstract

In survival analysis, accelerated failure time models are useful in modeling the relationship between failure times and the associated covariates, where covariate effects are assumed to appear in a linear form in the model. Such an assumption of covariate effects is, however, quite restrictive for many practical problems. To incorporate flexible nonlinear relationship between covariates and transformed failure times, we propose partially linear single index models to facilitate complex relationship between transformed failure times and covariates. We develop two inference methods which handle the unknown nonlinear function in the model from different perspectives. The first approach is weakly parametric which approximates the nonlinear function globally, whereas the second method is a semiparametric quasi-likelihood approach which focuses on picking up local features. We establish the asymptotic properties for the proposed methods. A real example is used to illustrate the usage of the proposed methods, and simulation studies are conducted to assess the performance of the proposed methods for a broad variety of situations.

Suggested Citation

  • Wenqing He & Grace Y. Yi, 2020. "Parametric and semiparametric estimation methods for survival data under a flexible class of models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 369-388, April.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:2:d:10.1007_s10985-019-09480-2
    DOI: 10.1007/s10985-019-09480-2
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    References listed on IDEAS

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    1. Wenqing He & Jerald F. Lawless, 2003. "Flexible Maximum Likelihood Methods for Bivariate Proportional Hazards Models," Biometrics, The International Biometric Society, vol. 59(4), pages 837-848, December.
    2. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    3. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    4. Lu, Xuewen & Cheng, Tsung-Lin, 2007. "Randomly censored partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1895-1922, November.
    5. Grace Yi & Wenqing He & Hua Liang, 2011. "Semiparametric marginal and association regression methods for clustered binary data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 511-533, June.
    6. Wenqing He & Jerald F. Lawless, 2005. "Bivariate location–scale models for regression analysis, with applications to lifetime data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 63-78, February.
    7. 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.
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