gms | German Medical Science

Kongress Medizin und Gesellschaft 2007

17. bis 21.09.2007, Augsburg

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Estimation of survival probabilities in the presence of ties

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  • Qamruz Zaman - Department of Medical Statistics, Informatics & Health Economics, Innsbruck
  • Alexander M Strasak - Department of Medical Statistics, Informatics & Health Economics, Innsbruck
  • Muhammad Azam - Department of Medical Statistics, Informatics & Health Economics, Innsbruck
  • Hanno Ulmer - Department of Medical Statistics, Informatics & Health Economics, Innsbruck
  • Karl-Peter Pfeiffer - Department of Medical Statistics, Informatics & Health Economics, Innsbruck

Kongress Medizin und Gesellschaft 2007. Augsburg, 17.-21.09.2007. Düsseldorf: German Medical Science GMS Publishing House; 2007. Doc07gmds754

The electronic version of this article is the complete one and can be found online at: http://www.egms.de/en/meetings/gmds2007/07gmds754.shtml

Published: September 6, 2007

© 2007 Zaman et al.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en). You are free: to Share – to copy, distribute and transmit the work, provided the original author and source are credited.

Outline

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In the real world we usually face the problem of discrete survival times, typically associated with the presence of ties between events and censored observations. However, the conventional Kaplan-Meier approaches, as well as Greenwood's variance estimator, do not adequately consider this fact, which leads to underestimation of true survival probabilities and variance estimates. We therefore present a modified Kaplan-Meier approach, by explicitly considering the presence of ties called the Tie survival function. A variance estimator based on tie survival function approach is developed. In absence of ties the new variance estimator equals to Greenwood variance estimator, while in uncensored data, it reduces to the binomial variance estimator. A simulation study was conducted in order to compare the performance of the conventional Kaplan-Meier estimator and the tie survivor estimator for different censoring rates. Our simulation results suggest a significant improvement, in terms of bias of the tie survivor approach compared to the conventional Kaplan-Meier estimator. Similarly, the results of variance simulation favor the proposed, tie variance estimator. Our new approaches are illustrated on a leukaemia data set.