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Expectation-Maximization Algorithm for the Weibull Proportional Hazard Model under Current Status Data

Author

Listed:
  • Sisi Chen

    (School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

  • Fengkai Yang

    (School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

Abstract

Due to the flexibility of the Weibull distribution and the proportional hazard (PH) model, Weibull PH is widely used in survival analysis under right censored data and interval censored data but it is seldom investigated under current status data, partially because there is less information in current status data than in right censored data and interval censored data. This paper considers the Weibull PH model under the current status data and introduces the Poisson latent variables to augment the data, then uses the expectation-maximization (EM) algorithm to obtain the maximum likelihood estimators of the model parameters. The EM algorithm is compared with the Newton–Raphson (NR) algorithm from several perspectives in the simulation studies, and the results show that the proposed method has several highlights, such as computational simplicity, improved convergence stability, and overall estimator results that are either comparable or slightly better in terms of bias. Furthermore, the performance of the Weibull PH model and the semi-parametric PH model is compared under two simulation scenarios, and two standard model selection criteria are used for model selection. The results indicate that the Weibull PH model has significant advantages when failure time follows a Weibull distribution. Lastly, the Weibull PH model along with EM algorithm is applied to lung tumor data and intraocular lens (IOL) calcification data with the aim of assessing the impact of covariates, including environmental factors and gender, on event timing and risk.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4826-:d:1290900
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    References listed on IDEAS

    as
    1. Balakrishnan, N. & Mitra, Debanjan, 2012. "Left truncated and right censored Weibull data and likelihood inference with an illustration," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4011-4025.
    2. 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.
    3. 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.
    4. 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.
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