Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data

Yeqian Liu; James Plott; Yingxiao Huang

doi:doi:10.11648/j.ajtas.20211003.15

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Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data

Yeqian Liu, James Plott, Yingxiao Huang

Published in American Journal of Theoretical and Applied Statistics (Volume 10, Issue 3)

Received: 10 June 2021 Accepted: 23 June 2021 Published: 29 June 2021

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Abstract

In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).

Published in	American Journal of Theoretical and Applied Statistics (Volume 10, Issue 3)
DOI	10.11648/j.ajtas.20211003.15
Page(s)	167-174
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

Interval-censoring, Cure Rate Model, Informative Censoring, Sieve Maximum Likelihood Estimation, EM Algorithm, Bernstein Polynomial

References

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[5]	Hu, T., and L. Xiang. (2016). Partially linear transformation cure models for interval-censored data. Computational Statistics and Data Analysis. 93, 257–69.
[6]	Liu, Y., Hu, T. & Sun, J. (2020). Regression analysis of intervalcensored failure time data with cured subgroup and mismeasured covariates. Communications in Statistics - Theory and Methods. 49(1): 189-202.
[7]	Riester, K., Kappos, L., Selmaj, K., Lindborg, S., Lipkovich, I. & Elkins, J. (2019). Impact of informative censoring on the treatment effect estimate of disability worsening in multiple sclerosis clinical trials. Multiple Sclerosis and Related Disorders. 39, 101865.
[8]	Li, Y., Tiwari, R. & Guha, S. (2007). Mixture cure survival models with dependent censoring. Journal of the Royal Statistical Society: Series B. 69, 285–306.
[9]	Othus, M., Li, Y., Tiwari, R. (2007). A class of semiparametric mixture cure survival models with dependent censoring. Journal of American Statistical Association. 104, 1241–1250.
[10]	Rondeau, V., Schaffner, E., Corbiere, F., Gonzalez, J. & Pelissier, S. (2011). Cure frailty models for survival data: application to recurrences for breast cancer and to hospital readmissions for colorectal cancer. Statistical Methods in Medical Research. 22 (3): 1–18.
[11]	Huang, X., Wolfe, R. A. (2002). A Frailty Model for Informative Censoring. Biometrics. 58 (3): 510–520.
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[16]	Zeng, D., Yin, G., and Ibrahim, J. G. (2006). Semiparametric Transformation Models for Survival Data with a Cure Fraction. Journal of the American Statistical Association. 101, 670–684.

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APA Style

Yeqian Liu, James Plott, Yingxiao Huang. (2021). Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data. American Journal of Theoretical and Applied Statistics, 10(3), 167-174. https://doi.org/10.11648/j.ajtas.20211003.15

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ACS Style

Yeqian Liu; James Plott; Yingxiao Huang. Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data. Am. J. Theor. Appl. Stat. 2021, 10(3), 167-174. doi: 10.11648/j.ajtas.20211003.15

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AMA Style

Yeqian Liu, James Plott, Yingxiao Huang. Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data. Am J Theor Appl Stat. 2021;10(3):167-174. doi: 10.11648/j.ajtas.20211003.15

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@article{10.11648/j.ajtas.20211003.15,
  author = {Yeqian Liu and James Plott and Yingxiao Huang},
  title = {Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {3},
  pages = {167-174},
  doi = {10.11648/j.ajtas.20211003.15},
  url = {https://doi.org/10.11648/j.ajtas.20211003.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211003.15},
  abstract = {In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).},
 year = {2021}
}

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TY  - JOUR
T1  - Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data
AU  - Yeqian Liu
AU  - James Plott
AU  - Yingxiao Huang
Y1  - 2021/06/29
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211003.15
DO  - 10.11648/j.ajtas.20211003.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 167
EP  - 174
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211003.15
AB  - In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).
VL  - 10
IS  - 3
ER  -

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Author Information

Yeqian Liu

Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, USA
James Plott

Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, USA
Yingxiao Huang

Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, USA

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Plain Text BibTeX RIS

APA Style

Yeqian Liu, James Plott, Yingxiao Huang. (2021). Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data. American Journal of Theoretical and Applied Statistics, 10(3), 167-174. https://doi.org/10.11648/j.ajtas.20211003.15

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ACS Style

Yeqian Liu; James Plott; Yingxiao Huang. Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data. Am. J. Theor. Appl. Stat. 2021, 10(3), 167-174. doi: 10.11648/j.ajtas.20211003.15

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AMA Style

Yeqian Liu, James Plott, Yingxiao Huang. Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data. Am J Theor Appl Stat. 2021;10(3):167-174. doi: 10.11648/j.ajtas.20211003.15

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@article{10.11648/j.ajtas.20211003.15,
  author = {Yeqian Liu and James Plott and Yingxiao Huang},
  title = {Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {3},
  pages = {167-174},
  doi = {10.11648/j.ajtas.20211003.15},
  url = {https://doi.org/10.11648/j.ajtas.20211003.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211003.15},
  abstract = {In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Sieve Estimation for Mixture Cure Rate Model with Informatively Interval-Censored Failure Time Data
AU  - Yeqian Liu
AU  - James Plott
AU  - Yingxiao Huang
Y1  - 2021/06/29
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211003.15
DO  - 10.11648/j.ajtas.20211003.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 167
EP  - 174
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211003.15
AB  - In biomedical and public health studies, interval-censored data arise when the failure time of interest is not exactly observed and instead only known to lie within an interval. Furthermore, the failure time and censoring time may be dependent. There may also exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. Many authors have investigated inference procedure for interval-censored data. However, most existing methods either assume no cured subgroup or apply only to limited situations such that the failure time and the observation time have to be independent. To take both cured subgroups and informative censoring into consideration for regression analysis of interval-censored data, we employ a mixture cure model and propose a sieve maximum likelihood estimation approach using Bernstein Polynomials. A novel expectation-maximization algorithm with the use of subject-specific independent log-normal latent variable is developed to obtain the numerical solutions of the model. The robustness and finite-sample performance of the proposed method in terms of estimation accuracy and predictive power is evaluated by an extensive simulation study which suggest that the proposed method works well for practical situations. In addition, we provide an illustrative example using NASA’s hypobaric decompression sickness database (HDSD).
VL  - 10
IS  - 3
ER  -

Copy | Download