Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties

Job Isaac Mukangai; Leo Odiwuor Odongo

doi:doi:10.11648/j.ajtas.20160505.17

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Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties

Job Isaac Mukangai, Leo Odiwuor Odongo

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)

Received: 21 July 2016 Accepted: 1 August 2016 Published: 21 August 2016

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Abstract

We develop an adjusted Product Limit estimator for estimating survival probabilities in the presence of ties that incorporates censored individuals using the proportion of failing for uncensored individuals. We also develop a variance estimator of the adjusted Product Limit estimator for calculating confidence intervals. Simulation studies are carried out to assess the performance of the developed estimator in comparison to the performance of Kaplan-Meier and modified Kaplan-Meier estimators. Some simulation results are presented and one real data is used for illustration. The results indicate that the proposed estimator out performs the other estimators in estimating survival probabilities in presence of ties.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI	10.11648/j.ajtas.20160505.17
Page(s)	290-296
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), 2016. Published by Science Publishing Group

Keywords

Survival Analysis, Censored Data, Product Limit Estimator, Modified Kaplan-Meier

References

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[3]	John P. K., Hans C. V. H., Joseph G. I. and Thomas H. S. (2014). Handbook of Survival Analysis. London: Chapman & Hall/CRC.
[4]	Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations, Journal of the Amer. Statist. Assoc. 53, 457-481.
[5]	Zaman, Q., Atif, M., Iqbal, M., Pfeiffer, K. P. and Rafiq, M. (2014). Estimation of Survival Probabilities in the Presence of Ties. Short Title: Survival Probabilities in the Presence of Ties. Life Science Journal; 11(10s), 155-164.
[6]	Lacny S., Todd W., Fiona C., Dereck J. R., Peter D. F., William A. G. and Deborah A. M. (2015). Kaplan-Meier Survival Analysis Overestimates the Risk of Revision Arthroplasty. A Meta-analysis. Clin Orthop Relat Res; 473, 3431–3442.
[7]	Biau D. J., Latouche A., and Porcher R. (2007). Competing events influence estimated survival probability—when is Kaplan-Meier analysis appropriate? Clin Orthop Relat Res. 462, 229–233.
[8]	Pintilie M. (2006). Competing Risks: A Practical Perspective. West Sussex: John Wiley & Sons.
[9]	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
[10]	Maller, R. and Zhou, X. (1996). Survival Analysis with Long-term survivors. John Wiley & Sons: Chichester
[11]	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.
[12]	Greenwood, M. (1926). The natural duration of cancer, Reports on public Health and Medical Subjects, His Majesty’s Stationery Office, London. 33, 18-26.

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APA Style

Job Isaac Mukangai, Leo Odiwuor Odongo. (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. https://doi.org/10.11648/j.ajtas.20160505.17

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ACS Style

Job Isaac Mukangai; Leo Odiwuor Odongo. Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties. Am. J. Theor. Appl. Stat. 2016, 5(5), 290-296. doi: 10.11648/j.ajtas.20160505.17

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AMA Style

Job Isaac Mukangai, Leo Odiwuor Odongo. Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties. Am J Theor Appl Stat. 2016;5(5):290-296. doi: 10.11648/j.ajtas.20160505.17

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@article{10.11648/j.ajtas.20160505.17,
  author = {Job Isaac Mukangai and Leo Odiwuor Odongo},
  title = {Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {290-296},
  doi = {10.11648/j.ajtas.20160505.17},
  url = {https://doi.org/10.11648/j.ajtas.20160505.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.17},
  abstract = {We develop an adjusted Product Limit estimator for estimating survival probabilities in the presence of ties that incorporates censored individuals using the proportion of failing for uncensored individuals. We also develop a variance estimator of the adjusted Product Limit estimator for calculating confidence intervals. Simulation studies are carried out to assess the performance of the developed estimator in comparison to the performance of Kaplan-Meier and modified Kaplan-Meier estimators. Some simulation results are presented and one real data is used for illustration. The results indicate that the proposed estimator out performs the other estimators in estimating survival probabilities in presence of ties.},
 year = {2016}
}

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TY  - JOUR
T1  - Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties
AU  - Job Isaac Mukangai
AU  - Leo Odiwuor Odongo
Y1  - 2016/08/21
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.17
DO  - 10.11648/j.ajtas.20160505.17
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  - 290
EP  - 296
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.17
AB  - We develop an adjusted Product Limit estimator for estimating survival probabilities in the presence of ties that incorporates censored individuals using the proportion of failing for uncensored individuals. We also develop a variance estimator of the adjusted Product Limit estimator for calculating confidence intervals. Simulation studies are carried out to assess the performance of the developed estimator in comparison to the performance of Kaplan-Meier and modified Kaplan-Meier estimators. Some simulation results are presented and one real data is used for illustration. The results indicate that the proposed estimator out performs the other estimators in estimating survival probabilities in presence of ties.
VL  - 5
IS  - 5
ER  -

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Author Information

Job Isaac Mukangai

Department of Statistics and Actuarial Science, Kenyatta University, Nairobi, Kenya
Leo Odiwuor Odongo

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

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APA Style

Job Isaac Mukangai, Leo Odiwuor Odongo. (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. https://doi.org/10.11648/j.ajtas.20160505.17

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ACS Style

Job Isaac Mukangai; Leo Odiwuor Odongo. Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties. Am. J. Theor. Appl. Stat. 2016, 5(5), 290-296. doi: 10.11648/j.ajtas.20160505.17

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AMA Style

Job Isaac Mukangai, Leo Odiwuor Odongo. Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties. Am J Theor Appl Stat. 2016;5(5):290-296. doi: 10.11648/j.ajtas.20160505.17

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@article{10.11648/j.ajtas.20160505.17,
  author = {Job Isaac Mukangai and Leo Odiwuor Odongo},
  title = {Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {290-296},
  doi = {10.11648/j.ajtas.20160505.17},
  url = {https://doi.org/10.11648/j.ajtas.20160505.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.17},
  abstract = {We develop an adjusted Product Limit estimator for estimating survival probabilities in the presence of ties that incorporates censored individuals using the proportion of failing for uncensored individuals. We also develop a variance estimator of the adjusted Product Limit estimator for calculating confidence intervals. Simulation studies are carried out to assess the performance of the developed estimator in comparison to the performance of Kaplan-Meier and modified Kaplan-Meier estimators. Some simulation results are presented and one real data is used for illustration. The results indicate that the proposed estimator out performs the other estimators in estimating survival probabilities in presence of ties.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties
AU  - Job Isaac Mukangai
AU  - Leo Odiwuor Odongo
Y1  - 2016/08/21
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.17
DO  - 10.11648/j.ajtas.20160505.17
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  - 290
EP  - 296
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.17
AB  - We develop an adjusted Product Limit estimator for estimating survival probabilities in the presence of ties that incorporates censored individuals using the proportion of failing for uncensored individuals. We also develop a variance estimator of the adjusted Product Limit estimator for calculating confidence intervals. Simulation studies are carried out to assess the performance of the developed estimator in comparison to the performance of Kaplan-Meier and modified Kaplan-Meier estimators. Some simulation results are presented and one real data is used for illustration. The results indicate that the proposed estimator out performs the other estimators in estimating survival probabilities in presence of ties.
VL  - 5
IS  - 5
ER  -

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