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

Adane Fekadu Wogu; Shanshan Zhao; Hazel Bogan Nichols; Jianwen Cai

doi:doi:10.11648/j.ajam.20210905.12

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

Adane Fekadu Wogu, Shanshan Zhao, Hazel Bogan Nichols, Jianwen Cai

Published in American Journal of Applied Mathematics (Volume 9, Issue 5)

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), 2024. 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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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

Adane Fekadu Wogu

Department of Biostatistics & Informatics, University of Colorado Anschutz Medical Campus, Aurora, USA
Shanshan Zhao

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

Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, USA
Jianwen Cai

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

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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}
}

Copy | Download

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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