Document Type

Dissertation - Open Access

Award Date

2026

Degree Name

Doctor of Philosophy (PhD)

Department / School

Mathematics and Statistics

First Advisor

Semhar Michael

Abstract

This dissertation contains three chapters on different applications of mixture regression models, broadly in materials science and public health. We begin with a basic application of finite mixture models and regression mixture models. The materials science analysis was performed entirely using data from finite element simulations of the additive manufacturing process via powder bed fusion. Visualization of the clustering solution as applied to the additive manufacturing designs highlighted the intuitive patterns that could be found. These patterns simultaneously yield the regression coefficients and subgroups of the geometric regions, providing a way to predict stresses and strains in a new geometry specific to a cluster. In the public health application, methodology development for regression mixture models was undertaken due to a natural limitation arising from public health data on death rates. Suppression intervals naturally arose because privacy laws prevent the exact number of deaths from being reported when the count is between 1 and 9. Hence, the density functions used were modified to have a uniform distribution over the known suppression region. This adjustment was then carried through for the regression mixture setting, which was verified in simulation. The CDC-WONDER database was used to extract synthetic opioid death data. When applied to the county-level synthetic opioid death rates, we found that 3 clusters were optimal, and many covariates have opposing polarities, suggesting the need to consider heterogeneous populations as was done. Lastly, regression mixtures in the context of survival analysis were considered and applied to patients with end-stage kidney disease. The Cox regression model, a popular semi-parametric approach for survival analysis, does not account for latent subpopulations. This dissertation provides alternative approaches to account for heterogeneous populations and non-linear relationships between the survival response and covariates. The derivation of an extension of Cox regression to mixtures of Cox regression is provided. These were then applied to a dataset from the USRDS comprising over 2 million patients. Significant improvement over the Cox PH model was observed for most alternative approaches, as measured by the C-index, thereby enabling the modeling of patients with heterogeneous survival outcomes. The Cox mixture alternative did not identify meaningfully distinct subpopulations. The dissertation presents various applications and extensions of regression and survival mixture models, with strong results demonstrated in simulation studies and real-data analyses.

Publisher

South Dakota State University

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Rights Statement

In Copyright