Muyan (Jimmy) Jiang

A large fraction of total healthcare expenditure occurs due to end-of-life (EOL) care, which means it is important to study the problem of more carefully incentivizing necessary versus unnecessary EOL care because this has the potential to reduce overall healthcare spending. This paper introduces a principal-agent model that integrates a mixed payment system of fee-for-service and pay-for-performance in order to analyze whether it is possible to better align healthcare provider incentives with patient outcomes and cost-efficiency in EOL care. The primary contributions are to derive optimal contracts for EOL care payments using a principal-agent framework under three separate models for the healthcare provider, where each model considers a different level of risk tolerance for the provider. We derive these optimal contracts by converting the underlying principal-agent models from a bilevel optimization problem into a single-level optimization problem that can be analytically solved. Our results are demonstrated using a simulation where an optimal contract is used to price intracranial pressure monitoring for traumatic brain injuries.

We consider tridiagonal matrices (a_ij)_i,j=1^n with constant main diagonal and such that a_i,i+1a_i+1,i=1 for i=1,\ldots,n-1. For these matrices, criteria are established under which their Kippenhahn curves contain elliptical components or even consist completely of such. These criteria are in terms of a system of homogeneous polynomial equations in variables (\absa_j,j+1-\absa_j+1,j)^2, and established via a unified approach across arbitrary dimensions. The results are illustrated, and specific numerical examples are provided for n=7, thus generalizing earlier work in the lower-dimensional setting.

Accurately estimating the effects of continuous treatment variables on binary outcomes is challenging. Tradi- tional logistic regression models assume linearity and struggle with dependencies among treatment effects and patient outcomes. Such limitations hinder optimizing treatments, essential for data-driven decision-making and its various applications (e.g., precision medicine). We introduce a semiparametric regression model that blends the interpretability of parametric models with the adaptability of nonparametric approaches, featuring a dual- score system for assessing patient prognosis and determining an optimal treatment level. We demonstrate the potential of our approach by conducting numerical simulations that suggest convergence occurs, and then we apply our approach to a case study using the International Warfarin Pharmacogenomics Consortium (IWPC) dataset.

Studies on the effects of school openings or closures during the Covid‐19 pandemic seem to reach contrasting conclusions even in similar contexts. We aim at clarifying this controversy. A mathematical analysis of compartmental models with subpopulations has been conducted, starting from the SIR model, and progressively adding features modeling outbreaks or upsurge of variants, lockdowns, and vaccinations. We find that in all cases, the in‐school transmission rates only affect the overall course of the pandemic above a certain context dependent threshold. We provide rigorous proofs and computations of the thresdhold through linearization. We then confirm our theoretical findings through simulations and the review of data‐driven studies that exhibit an often unnoticed phase transition. Specific implications are: awareness about the threshold could inform choice of data collection, analysis and release, such as in‐school transmission rates, and clarify the reason for divergent conclusions in similar studies; schools may remain open at any stage of the Covid‐19 pandemic, including variants upsurge, given suitable containment rules; these rules would be extremely strict and hardly sustainable if only adults are vaccinated, making a compelling argument for vaccinating children whenever possible.

Vascular shunt insertion is a fundamental surgical procedure used to temporarily restore blood flow to tissues. It is often performed in the field after major trauma. We formulate a problem of automated vascular shunt insertion and propose a pipeline to perform Automated Vascular Shunt Insertion (AVSI) using a da Vinci Research Kit. The pipeline uses a learned visual model to estimate the locus of the vessel rim, plans a grasp on the rim, and moves to grasp at that point. The first robot gripper then pulls the rim to stretch open the vessel with a dilation motion. The second robot gripper then proceeds to insert a shunt into the vessel phantom (a model of the blood vessel) with a chamfer tilt followed by a screw motion. Results suggest that AVSI achieves a high success rate even with tight tolerances and varying vessel orientations up to 30°.