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Semiparametric methods for survival data with measurement error under additive hazards cure rate models

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  • Sandip Barui

    (University of Waterloo)

  • Grace Y. Yi

    (University of Waterloo)

Abstract

It is well established that measurement error has drastically negative impact on data analysis. It can not only bias parameter estimates but may also cause loss of power for testing relationship between variables. Although survival analysis of error-contaminated data has attracted extensive interest, relatively little attention has been paid to dealing with survival data with error-contaminated covariates when the underlying population is characterized by a cured fraction. In this paper, we consider this problem for which lifetimes of the non-cured individuals are featured by the additive hazards model and the measurement error process is described by an additive model. Unlike estimating the relative risk in the proportional hazards model, the additive hazards model allows us to estimate the absolute risk difference associated with the covariates. To allow the model flexibility, we incorporate time-dependent covariates in the model. We develop estimation methods for the two scenarios, without or with measurement error. The proposed methods are evaluated from both the theoretical view point and the numerical perspectives. Furthermore, a real-life data application is presented to illustrate the utility of the methodology.

Suggested Citation

  • Sandip Barui & Grace Y. Yi, 2020. "Semiparametric methods for survival data with measurement error under additive hazards cure rate models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 421-450, July.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:3:d:10.1007_s10985-019-09482-0
    DOI: 10.1007/s10985-019-09482-0
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    References listed on IDEAS

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    1. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    2. Yi Li & Louise Ryan, 2004. "Survival Analysis With Heterogeneous Covariate Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 724-735, January.
    3. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    4. Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    5. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    6. Sun, Liuquan & Zhou, Xian, 2008. "Inference in the additive risk model with time-varying covariates subject to measurement errors," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2559-2566, November.
    7. Mengling Liu & Wenbin Lu & Yongzhao Shao, 2006. "Interval Mapping of Quantitative Trait Loci for Time-to-Event Data with the Proportional Hazards Mixture Cure Model," Biometrics, The International Biometric Society, vol. 62(4), pages 1053-1061, 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. Laurence S. Freedman & Vitaly Fainberg & Victor Kipnis & Douglas Midthune & Raymond J. Carroll, 2004. "A New Method for Dealing with Measurement Error in Explanatory Variables of Regression Models," Biometrics, The International Biometric Society, vol. 60(1), pages 172-181, March.
    10. Liuquan Sun & Zhigang Zhang & Jianguo Sun, 2006. "Additive hazards regression of failure time data with covariate measurement errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 60(4), pages 497-509, November.
    11. Li Y. & Lin X., 2003. "Functional Inference in Frailty Measurement Error Models for Clustered Survival Data Using the SIMEX Approach," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 191-203, January.
    12. Hong‐Bin Fang & Gang Li & Jianguo Sun, 2005. "Maximum Likelihood Estimation in a Semiparametric Logistic/Proportional‐Hazards Mixture Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 59-75, March.
    13. Ma, Yanyuan & Yin, Guosheng, 2008. "Cure Rate Model With Mismeasured Covariates Under Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 743-756, June.
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    1. Suvra Pal & Yingwei Peng & Wisdom Aselisewine, 2024. "A new approach to modeling the cure rate in the presence of interval censored data," Computational Statistics, Springer, vol. 39(5), pages 2743-2769, July.

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