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Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies

Received: 15 June 2021     Accepted: 6 July 2021     Published: 9 September 2021
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Abstract

Competing risks refer to the situation where there are multiple causes of failure and the occurrence of one type of event prohibits the occurrence of the other types of event or alters the chance to observe them. In large cohort studies with long-term follow-up, there are often competing risks. When the failure events are rare, or the information on certain risk factors is difficult or costly to measure for the full cohort, a case-cohort study design can be a desirable approach. In this paper, we consider a semiparametric proportional subdistribution hazards model in the presence of competing risks in case-cohort studies. The subdistribution hazards function, unlike the cause-specific hazards function, gives the advantage of outlining the marginal probability of a particular type of event. We propose estimating equations based on inverse probability weighting techniques for the estimation of the model parameters. In the estimation methods, we considered a weighted availability indicator to properly account for the case-cohort sampling scheme. We also proposed a Breslow-type estimator for the cumulative baseline subdistribution hazard function. The resulting estimators are shown, using empirical processes and martingale properties, to be consistent and asymptotically normally distributed. The performance of the proposed methods in finite samples are examined through simulation studies by considering different levels of censoring and event of interest percentages. The simulation results from the different scenarios suggest that the parameter estimates are reasonably close to the true values of the respective parameters in the model. Finally, the proposed estimation methods are applied to a case-cohort sample from the Sister Study, in which we illustrated the proposed methods by studying the association between selected CpGs and invasive breast cancer in the presence of ductal carcinoma in situ as competing risk.

Published in American Journal of Applied Mathematics (Volume 9, Issue 5)
DOI 10.11648/j.ajam.20210905.12
Page(s) 165-185
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Case-cohort Study, Competing Risks, Inverse Probability of Censoring Weight, Subdistribution Hazard, Weighted Estimating Equation

References
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Cite This Article
  • APA Style

    Adane Fekadu Wogu, Shanshan Zhao, Hazel Bogan Nichols, Jianwen Cai. (2021). Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies. American Journal of Applied Mathematics, 9(5), 165-185. https://doi.org/10.11648/j.ajam.20210905.12

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    ACS Style

    Adane Fekadu Wogu; Shanshan Zhao; Hazel Bogan Nichols; Jianwen Cai. Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies. Am. J. Appl. Math. 2021, 9(5), 165-185. doi: 10.11648/j.ajam.20210905.12

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    AMA Style

    Adane Fekadu Wogu, Shanshan Zhao, Hazel Bogan Nichols, Jianwen Cai. Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies. Am J Appl Math. 2021;9(5):165-185. doi: 10.11648/j.ajam.20210905.12

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  • @article{10.11648/j.ajam.20210905.12,
      author = {Adane Fekadu Wogu and Shanshan Zhao and Hazel Bogan Nichols and Jianwen Cai},
      title = {Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies},
      journal = {American Journal of Applied Mathematics},
      volume = {9},
      number = {5},
      pages = {165-185},
      doi = {10.11648/j.ajam.20210905.12},
      url = {https://doi.org/10.11648/j.ajam.20210905.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210905.12},
      abstract = {Competing risks refer to the situation where there are multiple causes of failure and the occurrence of one type of event prohibits the occurrence of the other types of event or alters the chance to observe them. In large cohort studies with long-term follow-up, there are often competing risks. When the failure events are rare, or the information on certain risk factors is difficult or costly to measure for the full cohort, a case-cohort study design can be a desirable approach. In this paper, we consider a semiparametric proportional subdistribution hazards model in the presence of competing risks in case-cohort studies. The subdistribution hazards function, unlike the cause-specific hazards function, gives the advantage of outlining the marginal probability of a particular type of event. We propose estimating equations based on inverse probability weighting techniques for the estimation of the model parameters. In the estimation methods, we considered a weighted availability indicator to properly account for the case-cohort sampling scheme. We also proposed a Breslow-type estimator for the cumulative baseline subdistribution hazard function. The resulting estimators are shown, using empirical processes and martingale properties, to be consistent and asymptotically normally distributed. The performance of the proposed methods in finite samples are examined through simulation studies by considering different levels of censoring and event of interest percentages. The simulation results from the different scenarios suggest that the parameter estimates are reasonably close to the true values of the respective parameters in the model. Finally, the proposed estimation methods are applied to a case-cohort sample from the Sister Study, in which we illustrated the proposed methods by studying the association between selected CpGs and invasive breast cancer in the presence of ductal carcinoma in situ as competing risk.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Proportional Subdistribution Hazards Model for Competing Risks in Case-Cohort Studies
    AU  - Adane Fekadu Wogu
    AU  - Shanshan Zhao
    AU  - Hazel Bogan Nichols
    AU  - Jianwen Cai
    Y1  - 2021/09/09
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ajam.20210905.12
    DO  - 10.11648/j.ajam.20210905.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 165
    EP  - 185
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20210905.12
    AB  - Competing risks refer to the situation where there are multiple causes of failure and the occurrence of one type of event prohibits the occurrence of the other types of event or alters the chance to observe them. In large cohort studies with long-term follow-up, there are often competing risks. When the failure events are rare, or the information on certain risk factors is difficult or costly to measure for the full cohort, a case-cohort study design can be a desirable approach. In this paper, we consider a semiparametric proportional subdistribution hazards model in the presence of competing risks in case-cohort studies. The subdistribution hazards function, unlike the cause-specific hazards function, gives the advantage of outlining the marginal probability of a particular type of event. We propose estimating equations based on inverse probability weighting techniques for the estimation of the model parameters. In the estimation methods, we considered a weighted availability indicator to properly account for the case-cohort sampling scheme. We also proposed a Breslow-type estimator for the cumulative baseline subdistribution hazard function. The resulting estimators are shown, using empirical processes and martingale properties, to be consistent and asymptotically normally distributed. The performance of the proposed methods in finite samples are examined through simulation studies by considering different levels of censoring and event of interest percentages. The simulation results from the different scenarios suggest that the parameter estimates are reasonably close to the true values of the respective parameters in the model. Finally, the proposed estimation methods are applied to a case-cohort sample from the Sister Study, in which we illustrated the proposed methods by studying the association between selected CpGs and invasive breast cancer in the presence of ductal carcinoma in situ as competing risk.
    VL  - 9
    IS  - 5
    ER  - 

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Author Information
  • Department of Biostatistics & Informatics, University of Colorado Anschutz Medical Campus, Aurora, USA

  • Biostatistics and Computational Biology Branch, National Institute of Environmental Health Sciences, Research Triangle Park, USA

  • Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, USA

  • Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, USA

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