Graduation Semester and Year
Summer 2026
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Jianzhong Su
Second Advisor
Hristo Kojouharov
Third Advisor
Wei Jiang
Fourth Advisor
Li Wang
Abstract
Glucose transporter type 1 deficiency syndrome (GLUT1-DS) is a rare neurometabolic disorder with heterogeneous neurological and developmental severity. Because patient-level severity is not observed as a single validated outcome, this dissertation develops a Bayesian late-fusion supportability framework for constructing and predicting an ordered latent severity phenotype from clinical, genetic, and EEG-derived evidence. The primary target was constructed in a larger clinical cohort using age-5 symptom burden and learning cognition, then assigned to an aligned multimodal prediction cohort. Target-defining variables were excluded from supervised predictors, and models were evaluated using patient-exclusive cross-validation with training-fold preprocessing and fold-wise EEG PCA.
The primary binary target produced clinically ordered lower- and higher-severity groups. In the aligned cohort, the strongest overall model was a Bayesian Gaussian diagonal classifier using clinical, genetic, and EEG-derived features, achieving balanced accuracy 0.814, macro-F1 0.771, MCC 0.564, and permutation p-value 0.0010. The selected operational prototype was L2-regularized logistic regression using early clinical variables and reduced genetic annotations, achieving balanced accuracy 0.736, macro-F1 0.696, MCC 0.416, and permutation p-value 0.0090. Sensitivity analyses showed that the reduced TY+PH genetics branch was more stable than including exon annotation, and that three-class staging was less supportable because of small or inconsistently represented classes.
A secondary trajectory prototype using 70 patients with complete age-5, age-10, and LC data showed strong internal performance for binary longitudinal severity grouping, with balanced accuracy 0.873, macro-F1 0.874, MCC 0.796, and kappa 0.796. Overall, the framework identifies binary lower-versus-higher severity prediction as the most defensible target resolution in the current cohort, supports selective clinical-genetic evidence as an operational direction, and provides a leakage-controlled structure for evaluating severity targets, modalities, and models in small rare-disease data.
Keywords
GLUT1 deficiency syndrome, Bayesian late fusion, rare-disease severity prediction, multimodal data fusion, latent severity phenotype, clinical-genetic-EEG integration, machine learning, electroencephalography, patient-exclusive cross-validation, leakage-controlled validation
Disciplines
Data Science | Medical Biomathematics and Biometrics | Numerical Analysis and Computation | Other Applied Mathematics
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Rodriguez, Jordan M., "A Bayesian Late-Fusion Supportability Framework for Rare-Disease Severity Prediction in GLUT1 Deficiency Syndrome" (2026). Mathematics Dissertations. 4.
https://mavmatrix.uta.edu/math_dissertations2/4
Included in
Data Science Commons, Medical Biomathematics and Biometrics Commons, Numerical Analysis and Computation Commons, Other Applied Mathematics Commons
Comments
This work would not have been possible without the guidance, support, and patience of many individuals who contributed to my academic and personal growth over the course of this program.
First and foremost, I would like to thank my advisor, Dr.~Su, for his mentorship, insight, and steady encouragement throughout this research. His guidance shaped not only the direction of this thesis but also my development as a researcher. I would also like to thank Dr.~Pascual and the members of my committee for their time, thoughtful feedback, and willingness to engage critically with this work. Their perspectives strengthened both the mathematical rigor and the clarity of the final manuscript.
I am thankful to the faculty, staff, and students within the department who fostered a collaborative and supportive environment. In particular, I acknowledge the SURGE program and related research initiatives that provided early opportunities to explore interdisciplinary research and develop the foundations that led to this work.
I am grateful to the patients and families whose data made this research possible. While privacy constraints limit direct acknowledgment, their contributions are the foundation of this study, and I hope this work honors their trust.
Finally, I would like to thank my friends and family for their unwavering support throughout this journey. Their patience, encouragement, and belief in me made it possible to persist through the challenges of graduate study.