Doctoral Dissertations

Abstract

"This dissertation focuses on two areas of statistics: DNA methylation and survival analysis. The first part of the dissertation pertains to the detection of differentially methylated regions in the human genome. The varying distribution of gaps between succeeding genomic locations, which are represented on the microarray used to quantify methylation, makes it challenging to identify regions that have differential methylation. This emphasizes the need to properly account for the correlation in methylation shared by nearby locations within a specific genomic distance. In this work, a normalized kernel-weighted statistic is proposed to obtain an optimal amount of "information" from neighboring locations to detect those differences. The large sample properties of the proposed statistic are also studied. Simulation studies show that the proposed method captures the true length of differentially methylated regions more accurately than a widely used existing method.

The second focus area of the dissertation pertains to mixture cure models in survival analysis. Mixture cure models are those based on a cured and uncured population. The choice of models for the cured and uncured is crucial in developing statistical models for this type of population. In this work, a flexible mixture cure model is proposed that incorporates a generalized partially linear single-index model for modeling the cure part and an additive hazard model for the uncured. This model proves to be particularly effective when dealing with large data sets where an underlying baseline mechanism is expected. In such cases, limited models like the logistic regression are not suitable. By employing the additive hazard model, the proposed approach offers an alternative for modeling cure survival data, especially when hazard differences are of interest and the proportional hazard assumption is violated"--Abstract, p. iv

Advisor(s)

Adekpedjou, Akim
Olbricht, Gayla R.

Committee Member(s)

Samaranayake, V. A.
Wen, Xuerong Meggie
Thimgan, Matthew S.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics and Statistics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2023

Pagination

xii, 162 pages

Note about bibliography

Includes_bibliographical_references_(pages 149-161)

Rights

© 2023 Daniel Ahmed Alhassan, All Rights Reserved

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 12287

Electronic OCLC #

1426046229

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