First Advisor

Bruno M. Jedynak

Term of Graduation

Spring 2022

Date of Publication


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences


Mathematics and Statistics





Physical Description

1 online resource (xiv, 105 pages)


In order to understand the entire course of slow progressing diseases like Alzheimer's dementia or multiple sclerosis, it is essential to characterize long term disease dynamics from a healthy stage to a late disease stage. Cohort studies typically recruit subjects at different stages of the disease and then follow them for a relatively short period of time. In this dissertation, we propose a novel Bayesian nonlinear mixed effects model with latent time scale to characterize long term disease dynamics using the observed short term longitudinal data from cohort studies without relying on clinical diagnosis. This model can accommodate noisy longitudinal multi-modal data with missing values. We train the proposed model using Hamiltonian Monte Carlo to estimate the model parameters. To test the novel model for parameter recovery, we first conducted a simulation data experiment. Later we applied the model to two real world datasets: (1) Alzheimer's Disease Neuroimaging Initiative (ADNI) for dementia, and (2) Optical Coherence Tomography (OCT) for multiple sclerosis. The results from simulation experiment indicated that all the ground truth fixed effect parameters are within the estimated 80% credible interval and more than 80% of ground truth random effects are within their estimated 80% credible interval. For the ADNI dataset, we predicted time to Alzheimer's dementia with root mean squared error (RMSE) of 1.85 years and found that the latent scale was significantly correlated with discrete disease staging scale Clinical Dementia Rating Sum of Boxes (CDRSB) with correlation coefficient of 0.66. Finally, for OCT data, the estimated slopes of biomarkers were consistent with the hypothesis in published literature. Moreover, the latent scale was significantly correlated with Expanded Disability Status Scale (EDSS), a commonly used measure to assess MS progression with correlation coefficient of 0.45. In addition to that, we also demonstrated the use of this model for prediction of future biomarker values given the subjects history of measurements. The above results support the broader clinical utility of the model for staging subjects and prediction of future biomarker measurements from limited short term longitudinal data.


©2022 Kruti Pandya

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This work benefitted from the RTG activities under NSF grant DMS-2136228.

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