Date of Graduation

Summer 2010

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

George Mathew

Keywords

survival analysis, hazard functions, Kaplan-Meier product limit formula, Cox proportional hazards model, log-rank test

Subject Categories

Mathematics

Abstract

Survival analysis is a branch of statistics and biostatistics that studies and compares the survival times and probabilities of survival for patients with certain diseases in clinical trials. The patients involved in the study may be grouped by the treatments they undergo or by multiple covariates present in the study. Each group or covariate can be analyzed to determine their affect on the probability on survival. In order to explore the various methods of survival analysis, a simulated data set and data set available from a clinical trial were analyzed. In the case of the simulated data set, the probability of survival was estimated for each survival time employing the Kaplan-Meier product limit formula. The results from the analysis were in agreement with the available results from theory. The patients involved in the clinical study were separated into two groups, the standard treatment group and the test treatment group. The survival probabilities were estimated assuming that the survival times follow a certain probability distribution. The survival probabilities were also estimated employing non-parametric methods such as the Kaplan-Meier product limit formula and Cox proportional hazards model. It was found that though there was less difference in the estimated probability of survival at the beginning of the trial, patients belonging to the test treatment group had higher probability of survival at the end of the trial than those belonging to the standard treatment group.

Copyright

© Kimberly Justine White

Campus Only

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