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A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data

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  • Lianming Wang
  • Christopher S. McMahan
  • Michael G. Hudgens
  • Zaina P. Qureshi

Abstract

type="main" xml:lang="en"> The proportional hazards model (PH) is currently the most popular regression model for analyzing time-to-event data. Despite its popularity, the analysis of interval-censored data under the PH model can be challenging using many available techniques. This article presents a new method for analyzing interval-censored data under the PH model. The proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function. Formulating the PH model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility. A novel expectation-maximization (EM) algorithm is developed for finding the maximum likelihood estimates of the parameters. The derivation of the EM algorithm relies on a two-stage data augmentation involving latent Poisson random variables. The resulting algorithm is easy to implement, robust to initialization, enjoys quick convergence, and provides closed-form variance estimates. The performance of the proposed regression methodology is evaluated through a simulation study, and is further illustrated using data from a large population-based randomized trial designed and sponsored by the United States National Cancer Institute.

Suggested Citation

  • Lianming Wang & Christopher S. McMahan & Michael G. Hudgens & Zaina P. Qureshi, 2016. "A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data," Biometrics, The International Biometric Society, vol. 72(1), pages 222-231, March.
    • Handle: RePEc:bla:biomet:v:72:y:2016:i:1:p:222-231
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    Cited by:

    1. Qingning Zhou & Jianwen Cai & Haibo Zhou, 2018. "Outcome†dependent sampling with interval†censored failure time data," Biometrics, The International Biometric Society, vol. 74(1), pages 58-67, March.
    2. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    3. Ruiwen Zhou & Huiqiong Li & Jianguo Sun & Niansheng Tang, 2022. "A new approach to estimation of the proportional hazards model based on interval-censored data with missing covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 335-355, July.
    4. Liuquan Sun & Shuwei Li & Lianming Wang & Xinyuan Song & Xuemei Sui, 2022. "Simultaneous variable selection in regression analysis of multivariate interval‐censored data," Biometrics, The International Biometric Society, vol. 78(4), pages 1402-1413, December.
    5. Marra, Giampiero & Farcomeni, Alessio & Radice, Rosalba, 2021. "Link-based survival additive models under mixed censoring to assess risks of hospital-acquired infections," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    6. Yanqing Sun & Qingning Zhou & Peter B. Gilbert, 2023. "Analysis of the Cox Model with Longitudinal Covariates with Measurement Errors and Partly Interval Censored Failure Times, with Application to an AIDS Clinical Trial," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 430-454, July.
    7. Shuwei Li & Limin Peng, 2023. "Instrumental variable estimation of complier causal treatment effect with interval‐censored data," Biometrics, The International Biometric Society, vol. 79(1), pages 253-263, March.
    8. Li‐Pang Chen & Bangxu Qiu, 2023. "Analysis of length‐biased and partly interval‐censored survival data with mismeasured covariates," Biometrics, The International Biometric Society, vol. 79(4), pages 3929-3940, December.
    9. Fan Feng & Guanghui Cheng & Jianguo Sun, 2023. "Variable Selection for Length-Biased and Interval-Censored Failure Time Data," Mathematics, MDPI, vol. 11(22), pages 1-20, November.
    10. Chun Yin Lee & Kin Yau Wong & Kwok Fai Lam & Dipankar Bandyopadhyay, 2023. "A semiparametric joint model for cluster size and subunit‐specific interval‐censored outcomes," Biometrics, The International Biometric Society, vol. 79(3), pages 2010-2022, September.
    11. Fei Gao & Kwun Chuen Gary Chan, 2019. "Semiparametric regression analysis of length‐biased interval‐censored data," Biometrics, The International Biometric Society, vol. 75(1), pages 121-132, March.
    12. Prabhashi W. Withana Gamage & Monica Chaudari & Christopher S. McMahan & Edwin H. Kim & Michael R. Kosorok, 2020. "An extended proportional hazards model for interval-censored data subject to instantaneous failures," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 158-182, January.
    13. Prabhashi W. Withana Gamage & Christopher S. McMahan & Lianming Wang, 2023. "A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 188-212, January.
    14. Liu, Wenting & Li, Huiqiong & Tang, Niansheng & Lyu, Jun, 2024. "Variational Bayesian approach for analyzing interval-censored data under the proportional hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
    15. Du, Mingyue & Li, Huiqiong & Sun, Jianguo, 2021. "Regression analysis of censored data with nonignorable missing covariates and application to Alzheimer Disease," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    16. Xiaoguang Wang & Ziwen Wang, 2021. "EM algorithm for the additive risk mixture cure model with interval-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 91-130, January.
    17. Yi, Fengting & Tang, Niansheng & Sun, Jianguo, 2020. "Regression analysis of interval-censored failure time data with time-dependent covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    18. Li, Shuwei & Hu, Tao & Zhao, Xingqiu & Sun, Jianguo, 2019. "A class of semiparametric transformation cure models for interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 153-165.
    19. Yudong Wang & Zhi‐Sheng Ye & Hongyuan Cao, 2021. "On computation of semiparametric maximum likelihood estimators with shape constraints," Biometrics, The International Biometric Society, vol. 77(1), pages 113-124, March.
    20. Du, Mingyue & Zhao, Xingqiu & Sun, Jianguo, 2022. "Variable selection for case-cohort studies with informatively interval-censored outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    21. Shuwei Li & Jianguo Sun & Tian Tian & Xia Cui, 2020. "Semiparametric regression analysis of doubly censored failure time data from cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 315-338, April.
    22. Gamage, Prabhashi W. Withana & McMahan, Christopher S. & Wang, Lianming & Tu, Wanzhu, 2018. "A Gamma-frailty proportional hazards model for bivariate interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 354-366.
    23. Sisi Chen & Fengkai Yang, 2023. "Expectation-Maximization Algorithm for the Weibull Proportional Hazard Model under Current Status Data," Mathematics, MDPI, vol. 11(23), pages 1-23, November.

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