Degree Level

B.S.

Program

Mathematics

First Advisor

Hill, Kaitlin

Second Advisor

Boies, Lori

Medium

pdf

LCSH subject

Distribution (Probability theory); Stochastic orders; Probabilities

Abstract

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a survival curve based on real-world data, this anticipated behavior may not always be seen. Therefore, it becomes crucial to estimate these curves to provide a more accurate representation of the true survival times for patients under different conditions. To address this challenge, we harness the insights of various statisticians and adapt their methodologies from one-sample and two-sample cases to the more complex scenario of a three-sample case. In this case, we work with data obtained from three distinct populations for several kinds of cancer. Given the inherent complexity of such data, it is highly likely that the empirical survival functions derived from it will not conform to stochastic ordering constraints, necessitating the estimation process. This study investigates four different estimators applied to data representing the relative survival rates of various racial groups affected by eight different types of cancer. Ultimately, our goal is to determine which, if any, of these estimators perform the best in terms of Bias and Mean Square Error.

Publication Date

Spring 2024

Document Type

Thesis

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

Download

Share

COinS