A PARTIAL LIKELIHOOD APPROACH TO LONGITUDINAL CATEGORICAL DATA USING A CONTINUOUS TIME SEMI-MARKOV CHAIN MODEL

Longitudinal studies have been critical in understanding the characteristics of chronic diseases or interventions. Since many processes have natural multi-categorical responses over time, multi-state stochastic models have been used to estimate the transition rates between stages. Some multi-state models applied in practice assume the Markov property. The Markov property constrains the sojourn distribution to be exponentially distributed. While useful theoretical properties arise by the Markov assumption, we will consider a more flexible framework by allowing arbitrarily distributed waiting times. This describes a semi-Markov process which has already been applied to various fields in Public Health. Similar to Markov model developments, semi-Markov models have been extended to add covariate e↵ects on each transition intensity for better estimation. Statistical inference methods for semi-Markov chains are still being developed for unique problems for ecient estimation and computational feasibility. Particularly, in this dissertation, we have developed a partial likelihood based approach under a semi-Markov framework. First, we will consider estimating parameters for a three to four stage process by a partial likelihood approach and examining the sensitives of the transition intensity estimates with models that have a gamma or Weibull sojourn time. This approach will estimate the hazard rates between discrete stages. Secondly, we will extend the semiMarkov model to include covariate e↵ects on the transition rates and again, analyze its results with models assuming the gamma or Weibull sojourn time. Two applications will be considered to illustrate our method: A caregiver stress-level study from the Baylor’s Alzhemier’s Disease and Memory Disorders Center and a depression severity level study from the Hispanic Established Population for the Epidemiological Study of the Elderly (HEPESE)

Conditional deep generative models as surrogates for spatial field solution reconstruction with quantified uncertainty in Structural Health Monitoring applications

In recent years, increasingly complex computational models are being built to describe physical systems which has led to increased use of surrogate models to reduce computational cost. In problems related to Structural Health Monitoring (SHM), models capable of both handling high-dimensional data and quantifying uncertainty are required. In this work, our goal is to propose a conditional deep generative model as a surrogate aimed at such applications and high-dimensional stochastic structural simulations in general. To that end, a conditional variational autoencoder (CVAE) utilizing convolutional neural networks (CNNs) is employed to obtain reconstructions of spatially ordered structural response quantities for structural elements that are subjected to stochastic loading. Two numerical examples, inspired by potential SHM applications, are utilized to demonstrate the performance of the surrogate. The model is able to achieve high reconstruction accuracy compared to the reference Finite Element (FE) solutions, while at the same time successfully encoding the load uncertainty.Comment: 28 pages, 14 figures. Submitted to Elsevier Journal for publicatio

Computational Approaches For Designing Protein/inhibitor Complexes And Membrane Protein Variants

Drug discovery of small-molecule protein inhibitors is a vast enterprise that involves several scientific disciplines (i.e. genomics, cell biology, x-ray crystallography, chemistry, computer science, statistics), with each discipline focusing on a particular aspect of the process. In this thesis, I use computational and experimental approaches to explore the most fundamental aspect of drug discovery: the molecular interactions of small-molecules inhibitors with proteins. In Part I (Chapters I and II), I describe how computational docking approaches can be used to identify structurally diverse molecules that can inhibit multiple protein targets in the brain. I illustrate this approach using the examples of microtubule-stabilizing agents and inhibitors of cyclooxygenase(COX)-I and 5-lipoxygenase (5-LOX). In Part II (Chapters III and IV), I focus on membrane proteins, which are notoriously difficult to work with due to their low natural abundances, low yields for heterologous over expression, and propensities toward aggregation. I describe a general approach for designing water-soluble variants of membrane proteins, for the purpose of developing cell-free, label-free, detergent-free, solution-phase studies of protein structure and small-molecule binding. I illustrate this approach through the design of a water-soluble variant of the membrane protein Smoothened, wsSMO. This wsSMO stands to serve as a first-step towards developing membrane protein analogs of this important signaling protein and drug target