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Hybrid models composing mechanistic ODE-based dynamics with flexible and expressive neural network components have grown rapidly in popularity, especially in scientific domains where such ODE-based modeling offers important interpretability…
Typically, the current dose prediction models are limited to small amounts of data and require re-training for a specific site, often leading to suboptimal performance. We propose a site-agnostic, 3D dose distribution prediction model using…
This paper presents a dynamic linear model for modeling hourly ozone concentrations over the eastern United States. That model, which is developed within an Bayesian hierarchical framework, inherits the important feature of such models that…
We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor and is ruled by the interplay of hyperelastic energy…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
The recently published ICH E9 addendum on estimands in clinical trials provides a framework for precisely defining the treatment effect that is to be estimated, but says little about estimation methods. Here we report analyses of a clinical…
The Glycemic Index (GI) is a tool for classifying carbohydrates based on their impact on postprandial glycemia, useful for diabetes prevention and management. This study applies a mathematical model for a data driven simulation of the…
Determining the optimal initial dose for warfarin is a critically important task. Several factors have an impact on the therapeutic dose for individual patients, such as patients' physical attributes (Age, Height, etc.), medication profile,…
This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger…
The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into…
Benchmark dose analysis aims to estimate the level of exposure to a toxin that results in a clinically-significant adverse outcome and quantifies uncertainty using the lower limit of a confidence interval for this level. We develop a novel…
Women with polycystic ovary syndrome (PCOS) face substantially elevated risks of body image distress, disordered eating, and metabolic challenges, yet existing natural language processing approaches for detecting these conditions lack…
In this work, we devise a model adaptation strategy for a class of model hierarchies consisting of two levels of model complexity. In particular, the fine model consists of a system of hyperbolic balance laws with stiff reaction terms and…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
With continuous glucose monitoring (CGM), data-driven models on blood glucose prediction have been shown to be effective in related work. However, such (CGM) systems are not always available, e.g., for a patient at home. In this work, we…
Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in…
Reinforcement learning (RL) applications in Clinical Decision Support Systems (CDSS) frequently encounter skepticism because models may recommend inoperable dosing decisions. We propose an end-to-end offline RL framework for dual…
Abnormal hemoglobins can have major consequences for tissue delivery of oxygen. Correct diagnosis of hemoglobinopathies with altered oxygen affinity requires a determination of hemoglobin oxygen dissociation curve (ODC), which relates the…
Panel count data arise in clinical trials when patients are asked to report their occurrences of events of interest periodically but the exact event times are unknown, only the count of events between two successive examinations are…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…