Date of Graduation

Fall 2017

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Yingcia Su

Keywords

survival analysis, Kaplan-Meir estimator, modified Kaplan-Meir estimator, censored data, hazard plotting, life table

Subject Categories

Survival Analysis

Abstract

The popular Kaplan-Meir estimator has traditionally been used to great effect as a survival function estimator. However, the Kaplan-Meir estimator is dependent upon a maximum likelihood parameter estimator which may not be the best estimator in all cases. We modify the Kaplan-Meir estimator, based on a Bayes parameter estimation, in hopes of providing a more accurate survival estimator for small sample sizes. Core elements of survival analysis are presented, acting as a foundation from which to construct and compare our modified Kaplan-Meir estimator. It is hypothesized that our modified Kaplan-Meir estimator is generally more accurate than the standard Kaplan-Meir estimator for smaller sample sizes, while the standard Kaplan-Meir estimator remains appropriate for larger sample sizes. Both Kaplan-Meir estimators are compared to theoretical distributions, with the traditional expectation that theoretical distributions will model data best if data can be fitted to a theoretical distribution. In order to show validity for our hypothesis one smaller data set and one larger data set were analyzed. The results of the analysis appeared to agree with our hypothesis.

Copyright

© Justin A. Bancroft

Open Access

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