Item request has been placed! ×
Item request cannot be made. ×
loading  Processing Request

Exact sensitivity analysis of Markov reward processes via algebraic geometry

Item request has been placed! ×
Item request cannot be made. ×
loading   Processing Request
  • معلومة اضافية
    • الموضوع:
      2024
    • Collection:
      Computer Science
      Mathematics
    • نبذة مختصرة :
      We introduce a new approach for deterministic sensitivity analysis of Markov reward processes, commonly used in cost-effectiveness analyses, via reformulation into a polynomial system. Our approach leverages cylindrical algebraic decomposition (CAD), a technique arising from algebraic geometry that provides an exact description of all solutions to a polynomial system. While it is typically intractable to build a CAD for systems with more than a few variables, we show that a special class of polynomial systems, which includes the polynomials arising from Markov reward processes, can be analyzed much more tractably. We establish several theoretical results about such systems and develop a specialized algorithm to construct their CAD, which allows us to perform exact, multi-way sensitivity analysis for common health economic analyses. We develop an open-source software package that implements our algorithm. Finally, we apply it to two case studies, one with synthetic data and one that re-analyzes a previous cost-effectiveness analysis from the literature, demonstrating advantages of our approach over standard techniques. Our software and code are available at: \url{https://github.com/mmaaz-git/markovag}.
      Comment: 46 pages
    • الرقم المعرف:
      edsarx.2410.05471