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An extended proportional hazards model for interval-censored data subject to instantaneous failures

Author

Listed:
  • Prabhashi W. Withana Gamage

    (James Madison University)

  • Monica Chaudari

    (University of North Carolina at Chapel Hill)

  • Christopher S. McMahan

    (Clemson University)

  • Edwin H. Kim

    (University of North Carolina at Chapel Hill)

  • Michael R. Kosorok

    (University of North Carolina at Chapel Hill)

Abstract

The proportional hazards (PH) model is arguably one of the most popular models used to analyze time to event data arising from clinical trials and longitudinal studies. In many such studies, the event time is not directly observed but is known relative to periodic examination times; i.e., practitioners observe either current status or interval-censored data. The analysis of data of this structure is often fraught with many difficulties since the event time of interest is unobserved. Further exacerbating this issue, in some such studies the observed data also consists of instantaneous failures; i.e., the event times for several study units coincide exactly with the time at which the study begins. In light of these difficulties, this work focuses on developing a mixture model, under the PH assumptions, which can be used to analyze interval-censored data subject to instantaneous failures. To allow for modeling flexibility, two methods of estimating the unknown cumulative baseline hazard function are proposed; a fully parametric and a monotone spline representation are considered. Through a novel data augmentation procedure involving latent Poisson random variables, an expectation–maximization (EM) algorithm is developed to complete model fitting. The resulting EM algorithm is easy to implement and is computationally efficient. Moreover, through extensive simulation studies the proposed approach is shown to provide both reliable estimation and inference. The motivation for this work arises from a randomized clinical trial aimed at assessing the effectiveness of a new peanut allergen treatment in attaining sustained unresponsiveness in children.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:1:d:10.1007_s10985-019-09467-z
    DOI: 10.1007/s10985-019-09467-z
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    References listed on IDEAS

    as
    1. Minggen Lu & Christopher S. McMahan, 2018. "A partially linear proportional hazards model for current status data," Biometrics, The International Biometric Society, vol. 74(4), pages 1240-1249, December.
    2. Tianxi Cai & Rebecca A. Betensky, 2003. "Hazard Regression for Interval-Censored Data with Penalized Spline," Biometrics, The International Biometric Society, vol. 59(3), pages 570-579, September.
    3. Liu, Hao & Shen, Yu, 2009. "A Semiparametric Regression Cure Model for Interval-Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1168-1178.
    4. Wang, Naichen & Wang, Lianming & McMahan, Christopher S., 2015. "Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 140-150.
    5. K. Muralidharan & P. Lathika, 2006. "Analysis of Instantaneous and Early Failures in Weibull Distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(3), pages 305-316, December.
    6. Cai, Bo & Lin, Xiaoyan & Wang, Lianming, 2011. "Bayesian proportional hazards model for current status data with monotone splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2644-2651, September.
    7. Lianming Wang & David B. Dunson, 2011. "Semiparametric Bayes' Proportional Odds Models for Current Status Data with Underreporting," Biometrics, The International Biometric Society, vol. 67(3), pages 1111-1118, September.
    8. Els Goetghebeur & Louise Ryan, 2000. "Semiparametric Regression Analysis of Interval-Censored Data," Biometrics, The International Biometric Society, vol. 56(4), pages 1139-1144, December.
    9. Ying Zhang & Lei Hua & Jian Huang, 2010. "A Spline‐Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 338-354, June.
    10. Wei Pan, 2000. "A Multiple Imputation Approach to Cox Regression with Interval-Censored Data," Biometrics, The International Biometric Society, vol. 56(1), pages 199-203, March.
    11. 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.
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