Volume 5, Issue 5, September 2016, Page: 290-296
Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties
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
Received: Jul. 21, 2016;       Accepted: Aug. 1, 2016;       Published: Aug. 21, 2016
DOI: 10.11648/j.ajtas.20160505.17      View  3749      Downloads  99
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.
Keywords
Survival Analysis, Censored Data, Product Limit Estimator, Modified Kaplan-Meier
To cite this article
Job Isaac Mukangai, Leo Odiwuor Odongo, Estimating Survivor Function Using Adjusted Product Limit Estimator in the Presence of Ties, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 5, 2016, pp. 290-296. doi: 10.11648/j.ajtas.20160505.17
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Collett, D. (1994). Modeling Survival Data in Medical Research (1st edn.). London: Chapman & Hall/CRC.
[2]
Klein, J. P. and Goel, P. K. (2013). Survival Analysis: State of the art. Springer-science+Business media
[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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