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Local linear regression on correlated survival data

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  • Jin, Zhezhen
  • He, Wenqing

Abstract

Correlated survival data arise in many contexts, and the regression analysis of such data is often of interest in practice. In this paper, we study a weighted local linear regression method for the analysis of correlated censored data, which is a natural extension of classical nonparametric regression that models directly the effect of covariates on survival time, using an unknown smooth nonparametric function. The estimation and inference are based on local linear regression and a class of unbiased data transformations. The most important feature of the proposed method is to weight local observations with local variance, which is the key to improve the estimation efficiency. We derive the asymptotic properties of the resulting estimator and show that the asymptotic variance of the nonparametric estimator is minimized with the correct specification of correlation structure. We evaluate the performance of the proposed method using simulation studies, and illustrate the proposed method with an analysis of data from the Busselton Health Study.

Suggested Citation

  • Jin, Zhezhen & He, Wenqing, 2016. "Local linear regression on correlated survival data," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 285-294.
    • Handle: RePEc:eee:jmvana:v:147:y:2016:i:c:p:285-294
    DOI: 10.1016/j.jmva.2016.02.006
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    References listed on IDEAS

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    1. Zhangsheng Yu & Xihong Lin, 2008. "Nonparametric regression using local kernel estimating equations for correlated failure time data," Biometrika, Biometrika Trust, vol. 95(1), pages 123-137.
    2. Z. Jin & D. Y. Lin & Z. Ying, 2006. "Rank Regression Analysis of Multivariate Failure Time Data Based on Marginal Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 1-23, March.
    3. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    4. Lai, T. L. & Ying, Z. L. & Zheng, Z. K., 1995. "Asymptotic Normality of a Class of Adaptive Statistics with Applications to Synthetic Data Methods for Censored Regression," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 259-279, February.
    5. Kani Chen & Zhezhen Jin, 2005. "Local polynomial regression analysis of clustered data," Biometrika, Biometrika Trust, vol. 92(1), pages 59-74, March.
    6. 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.
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