Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship

Job Isaac Mukangai

doi:doi:10.11648/j.bsi.20160101.11

| Peer-Reviewed

Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship

Job Isaac Mukangai

Published in Biomedical Statistics and Informatics (Volume 1, Issue 1)

Received: 8 October 2016 Accepted: 5 November 2016 Published: 5 December 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Censoring is inevitable in survival analysis. The motivating factor for this article concerns the way censored subjects are incorporated in estimation of survival function for grouped data. In practice, the Actuarial estimator of a survival function may be biased due to unevenly distribution of censored subjects within intervals. This article presents a nonparametric estimation of a survival function using the adjusted Product Limit estimator based on grouped observations that are under random censorship. Simulation studies are carried out to assess the performance of the adjusted Product Limit estimator in comparison to the performance of Actuarial (life table) estimator to ascertain the one that is better and real data is used to show applicability of the method in real life. The results strongly indicate that adjusted Product Limit estimator of the survival function outperforms the Actuarial estimator.

Published in	Biomedical Statistics and Informatics (Volume 1, Issue 1)
DOI	10.11648/j.bsi.20160101.11
Page(s)	1-12
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

Life Table, Interval Censoring, Product Limit Estimates, Survival Analysis, Actuarial Estimator

References

[1]	Job I. M. and Leo O. O. (2016). Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties. American Journal of Theoretical and Applied Statistics; 5(5), 290-296.
[2]	Kaplan, E. L. and Meier, P. (1958). Non-parametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457-481.
[3]	Berkson, J. and Gage, R. R. (1950). Calculation of Survival Rates for Cancer. Proceedings of Staff Meetings, Mayo Clinic, 25, 250
[4]	Cutler, S. J. and Ederer, F. (1958). Maximum Utilization of the Life Table Method in Analyzing Survival. Journal of Chronic Diseases, 8, 699—712.
[5]	Breslow, N. and Crowley, J. (1974). A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship, The Annals of Statistics; 2 (3), 437-453.
[6]	Elveback, L. (1958). Estimation of survivorship in chronic disease: the "actuarial" method. J. Amer. Statist. Assoc. 53, 420-440.
[7]	Chiang, C. L. (1968). Introduction to Stochastic Processes in Biostatistics. Wiley, New York.
[8]	Peto, R. (1973). Experimental Survival Curves for Interval Censored Data, Applied Statistics, 22, 86-91.
[9]	Klein, J. P. and Moeschberger, M. L. (1977). Survival Analysis. Springer-Verlag, New York.
[10]	Sun, J. (1996). A non-parametric test for interval-censored failure time data with application to AIDS studies. Statist. Medicine, 15, 1387-1395.
[11]	Gordon, A. C. (2016). Analysis of Mortality: The Life Table and Survival. Springer.
[12]	Michael, J. S. (2015). Survival Analysis. John Wily & Sons Inc.
[13]	Little, A. S. (1952). Estimation of the T-year survival rate from follow-up studies over a limited period of time. Human Biol. 24, 87-116.
[14]	Gilbert, J. P. (1962). Random censorship Ph.D. thesis, University of Chicago.
[15]	R Core Team (version 3.3.0). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org.
[16]	Freireich, E. J., Gehan, E., Schroeder, L. R., Wolman, I. J., Burgert, E. O., Mills, S. D., and Lee, S. (1963). The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukaemia: a model for evaluation of other potentially useful therapy. Blood; 21, 699-716.
[17]	Parker, R. L., Dry, T. J., Willius, F. A., and Gage, R. P. (1946). Life Expectancy in Angina Pectoris. Journal of the American Medical Association, 131, 9 5—100.
[18]	Lee E. T. and John W. W. (2003). Statistical Methods for Survival Data Analysis (3rd Edn.). John Wiley & Sons, Inc., Hoboken, New Jersey.

Cite This Article

Plain Text BibTeX RIS

APA Style

Job Isaac Mukangai. (2016). Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship. Biomedical Statistics and Informatics, 1(1), 1-12. https://doi.org/10.11648/j.bsi.20160101.11

Copy | Download

ACS Style

Job Isaac Mukangai. Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship. Biomed. Stat. Inform. 2016, 1(1), 1-12. doi: 10.11648/j.bsi.20160101.11

Copy | Download

AMA Style

Job Isaac Mukangai. Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship. Biomed Stat Inform. 2016;1(1):1-12. doi: 10.11648/j.bsi.20160101.11

Copy | Download

@article{10.11648/j.bsi.20160101.11,
  author = {Job Isaac Mukangai},
  title = {Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship},
  journal = {Biomedical Statistics and Informatics},
  volume = {1},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.bsi.20160101.11},
  url = {https://doi.org/10.11648/j.bsi.20160101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20160101.11},
  abstract = {Censoring is inevitable in survival analysis. The motivating factor for this article concerns the way censored subjects are incorporated in estimation of survival function for grouped data. In practice, the Actuarial estimator of a survival function may be biased due to unevenly distribution of censored subjects within intervals. This article presents a nonparametric estimation of a survival function using the adjusted Product Limit estimator based on grouped observations that are under random censorship. Simulation studies are carried out to assess the performance of the adjusted Product Limit estimator in comparison to the performance of Actuarial (life table) estimator to ascertain the one that is better and real data is used to show applicability of the method in real life. The results strongly indicate that adjusted Product Limit estimator of the survival function outperforms the Actuarial estimator.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship
AU  - Job Isaac Mukangai
Y1  - 2016/12/05
PY  - 2016
N1  - https://doi.org/10.11648/j.bsi.20160101.11
DO  - 10.11648/j.bsi.20160101.11
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20160101.11
AB  - Censoring is inevitable in survival analysis. The motivating factor for this article concerns the way censored subjects are incorporated in estimation of survival function for grouped data. In practice, the Actuarial estimator of a survival function may be biased due to unevenly distribution of censored subjects within intervals. This article presents a nonparametric estimation of a survival function using the adjusted Product Limit estimator based on grouped observations that are under random censorship. Simulation studies are carried out to assess the performance of the adjusted Product Limit estimator in comparison to the performance of Actuarial (life table) estimator to ascertain the one that is better and real data is used to show applicability of the method in real life. The results strongly indicate that adjusted Product Limit estimator of the survival function outperforms the Actuarial estimator.
VL  - 1
IS  - 1
ER  -

Copy | Download

Author Information

Job Isaac Mukangai

Department of Statistics and Actuarial Science, Kenyatta University, Nairobi, Kenya

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Job Isaac Mukangai. (2016). Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship. Biomedical Statistics and Informatics, 1(1), 1-12. https://doi.org/10.11648/j.bsi.20160101.11

Copy | Download

ACS Style

Job Isaac Mukangai. Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship. Biomed. Stat. Inform. 2016, 1(1), 1-12. doi: 10.11648/j.bsi.20160101.11

Copy | Download

AMA Style

Job Isaac Mukangai. Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship. Biomed Stat Inform. 2016;1(1):1-12. doi: 10.11648/j.bsi.20160101.11

Copy | Download

@article{10.11648/j.bsi.20160101.11,
  author = {Job Isaac Mukangai},
  title = {Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship},
  journal = {Biomedical Statistics and Informatics},
  volume = {1},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.bsi.20160101.11},
  url = {https://doi.org/10.11648/j.bsi.20160101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20160101.11},
  abstract = {Censoring is inevitable in survival analysis. The motivating factor for this article concerns the way censored subjects are incorporated in estimation of survival function for grouped data. In practice, the Actuarial estimator of a survival function may be biased due to unevenly distribution of censored subjects within intervals. This article presents a nonparametric estimation of a survival function using the adjusted Product Limit estimator based on grouped observations that are under random censorship. Simulation studies are carried out to assess the performance of the adjusted Product Limit estimator in comparison to the performance of Actuarial (life table) estimator to ascertain the one that is better and real data is used to show applicability of the method in real life. The results strongly indicate that adjusted Product Limit estimator of the survival function outperforms the Actuarial estimator.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Non-parametric Estimation of Survival Function from Grouped Observations Under Random Censorship
AU  - Job Isaac Mukangai
Y1  - 2016/12/05
PY  - 2016
N1  - https://doi.org/10.11648/j.bsi.20160101.11
DO  - 10.11648/j.bsi.20160101.11
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20160101.11
AB  - Censoring is inevitable in survival analysis. The motivating factor for this article concerns the way censored subjects are incorporated in estimation of survival function for grouped data. In practice, the Actuarial estimator of a survival function may be biased due to unevenly distribution of censored subjects within intervals. This article presents a nonparametric estimation of a survival function using the adjusted Product Limit estimator based on grouped observations that are under random censorship. Simulation studies are carried out to assess the performance of the adjusted Product Limit estimator in comparison to the performance of Actuarial (life table) estimator to ascertain the one that is better and real data is used to show applicability of the method in real life. The results strongly indicate that adjusted Product Limit estimator of the survival function outperforms the Actuarial estimator.
VL  - 1
IS  - 1
ER  -

Copy | Download