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Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error

Author

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  • Li-Pang Chen

    (University of Western Ontario)

  • Grace Y. Yi

    (University of Western Ontario
    University of Western Ontario)

Abstract

Many methods have been developed for analyzing survival data which are commonly right-censored. These methods, however, are challenged by complex features pertinent to the data collection as well as the nature of data themselves. Typically, biased samples caused by left-truncation (or length-biased sampling) and measurement error often accompany survival analysis. While such data frequently arise in practice, little work has been available to simultaneously address these features. In this paper, we explore valid inference methods for handling left-truncated and right-censored survival data with measurement error under the widely used Cox model. We first exploit a flexible estimator for the survival model parameters which does not require specification of the baseline hazard function. To improve the efficiency, we further develop an augmented nonparametric maximum likelihood estimator. We establish asymptotic results and examine the efficiency and robustness issues for the proposed estimators. The proposed methods enjoy appealing features that the distributions of the covariates and of the truncation times are left unspecified. Numerical studies are reported to assess the finite sample performance of the proposed methods.

Suggested Citation

  • Li-Pang Chen & Grace Y. Yi, 2021. "Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 481-517, June.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:3:d:10.1007_s10463-020-00755-2
    DOI: 10.1007/s10463-020-00755-2
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    References listed on IDEAS

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    1. Sharon X. Xie & C. Y. Wang & Ross L. Prentice, 2001. "A risk set calibration method for failure time regression by using a covariate reliability sample," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 855-870.
    2. Xiao Song & Yijian Huang, 2005. "On Corrected Score Approach for Proportional Hazards Model with Covariate Measurement Error," Biometrics, The International Biometric Society, vol. 61(3), pages 702-714, September.
    3. Jing Qin & Yu Shen, 2010. "Statistical Methods for Analyzing Right-Censored Length-Biased Data under Cox Model," Biometrics, The International Biometric Society, vol. 66(2), pages 382-392, June.
    4. Thomas Augustin, 2004. "An Exact Corrected Log‐Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 43-50, March.
    5. Yang Ning & Grace Yi & Nancy Reid, 2018. "A Class of Weighted Estimating Equations for Semiparametric Transformation Models with Missing Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(1), pages 87-109, March.
    6. Wang, C. Y., 1999. "Robust sandwich covariance estimation for regression calibration estimator in Cox regression with measurement error," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 371-378, December.
    7. Chengcheng Hu & D. Y. Lin, 2002. "Cox Regression with Covariate Measurement Error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 637-655, December.
    8. Ying Yan & Grace Y. Yi, 2016. "A Class of Functional Methods for Error-Contaminated Survival Data Under Additive Hazards Models with Replicate Measurements," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 684-695, April.
    9. Yi Li & Louise Ryan, 2006. "Inference on Survival Data with Covariate Measurement Error – An Imputation‐based Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 169-190, June.
    10. Shanshan Zhao & Ross L. Prentice, 2014. "Covariate measurement error correction methods in mediation analysis with failure time data," Biometrics, The International Biometric Society, vol. 70(4), pages 835-844, December.
    11. Chiung-Yu Huang & Jing Qin & Dean A. Follmann, 2012. "A maximum pseudo-profile likelihood estimator for the Cox model under length-biased sampling," Biometrika, Biometrika Trust, vol. 99(1), pages 199-210.
    12. Fan Wu & Sehee Kim & Jing Qin & Rajiv Saran & Yi Li, 2018. "A pairwise likelihood augmented Cox estimator for left†truncated data," Biometrics, The International Biometric Society, vol. 74(1), pages 100-108, March.
    13. Grace Y. Yi & Yanyuan Ma & Donna Spiegelman & Raymond J. Carroll, 2015. "Functional and Structural Methods With Mixed Measurement Error and Misclassification in Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 681-696, June.
    14. Wendy F. Greene & Jianwen Cai, 2004. "Measurement Error in Covariates in the Marginal Hazards Model for Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 60(4), pages 987-996, December.
    15. Masayuki Henmi & Shinto Eguchi, 2004. "A paradox concerning nuisance parameters and projected estimating functions," Biometrika, Biometrika Trust, vol. 91(4), pages 929-941, December.
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