4 Presentations

• 
  08:30 AM - 08:52 AM

  An Optimization-based Framework to Minimize the Spread of Diseases in Social Networks with Heterogeneous Nodes

  • Su Li, presenter, University of Toronto
  • Hrayer Aprahamian, Texas A&M University

  We provide an optimization-based framework that identifies social separation policies to mitigate the spread of diseases in social networks. The study considers subject-specific risk information, social structure, and the negative economic impact of imposing restrictions. We first analyze a simplified variation of the problem consisting of a single period and a specific social structure to establish key structural properties and construct a tailored globally-convergent solution scheme. We extend this solution scheme to heuristically solve the more general model with multiple time periods and any social structure. We use real COVID-19 data to illustrate the benefits of proposed framework. Our results reveal that the optimized policies substantially reduce the spread of the disease when compared with existing benchmark algorithms and policies that are based on a single risk factor. In addition, we utilize the considered framework to identify important subject attributes when distributing Personal Protective Equipment. Moreover, results reveal that the optimized policies continue to outperform under a more realistic setting. Our results underscore the importance of considering subject-specific information when designing policies and provide high-level data-driven observations to policy-makers that are tailored to the specific risk profile of the population that is being served.

• 
  08:52 AM - 09:14 AM

  Formal verification of Markov models with learned parameters

  • Muhammad Maaz, presenter, University of Toronto
  • Timothy Chan, University of Toronto

  We present a novel framework for subgroup analysis in Markov microsimulation models where the model parameters are functions of patient characteristics, common in health economic analyses. Current approaches to subgroup analysis rely primarily on sampling representative cohorts. Using ideas from formal verification in computer science, we show that when the functions mapping patient covariates to Markov chain parameters are mixed-integer linear programming (MILP) representable – which encompasses many common cases like if-then rules, decision trees, linear regression, and ReLU neural networks – we can formulate subgroup analysis as a mixed-integer bilinear program. This allows us to determine, without sampling, optimal and pessimal outcomes across patient subgroups and identify which subgroups achieve or miss prespecified outcomes. We develop a decomposition and bound propagation scheme to improve computational efficiency. Lastly, we demonstrate our approach on a case study.

• 
  09:14 AM - 09:36 AM

  Minimizing Nurse Anesthetist Intraoperative Handovers

  • Abhishrut Sinha, presenter, State University of New York, Binghamton
  • Ankit Bansal, State University of New York, Binghamton
  • Osman Ozaltin, North Carolina State University
  • Michael Russell, West Virginia University School of Medicine

  Intraoperative handovers between Certified Registered Nurse Anesthetists (CRNAs) during surgeries pose a significant risk of medical errors, potentially leading to adverse health consequences. To address this, we introduce a two-stage stochastic optimization model that assigns CRNAs to operating rooms. The model aims to minimize intraoperative handovers while accounting for system operational constraints and uncertainties in surgery durations. We present valid inequalities for the second-stage and demonstrate their strength by proving that they define the convex hull of a relaxation of the second-stage integer set. These valid inequalities are important for obtaining good lower bounds for the two-stage stochastic program. We present computational results using data from a hospital system to showcase the effectiveness of our proposed approach.

• 
  09:36 AM - 09:58 AM

  A Geometrical Approach to Beam Angle Optimization

  • Danielle Ripsman, presenter, University of Waterloo
  • Houra Mahmoudzadeh, University of Waterloo

  Beam angle optimization (BAO) is a difficult but essential step for planning radiation therapy treatments. Despite the wealth of proposed methodologies for optimal beam-angle selection in the literature, in practice, clinicians often choose a fixed number of equidistant beams, or rely on manual, iterative planning. This is due, in part, to the requirement for a secondary fluence map optimization (FMO) to validate any BAO selections and the resource-intense calculations needed to calculate the parameters for such a model at each iteration.
  In this talk, the BAO problem is modeled using a geometrical abstraction, allowing it to be considered in a single-stage column generation-driven set-covering framework. This abstraction allows for a reduction in the reliance of BAO modeling on sophisticated dose calculators as well as eliminating the need for time-consuming
  BAO-FMO iteration. The effectiveness of our model, and necessary future steps are demonstrated using clinical patients from a local cancer centre.