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}.

翻译：本文提出了一种通过多项式系统重构进行马尔可夫奖励过程确定性敏感性分析的新方法，该方法常用于成本效益分析。我们的方法利用圆柱代数分解（CAD）这一源于代数几何的技术，该技术能够精确描述多项式系统的所有解。尽管构建超过少数变量的系统CAD通常难以处理，但我们证明包含马尔可夫奖励过程所产生多项式的一类特殊多项式系统可以进行更高效的分析。我们建立了关于此类系统的若干理论结果，并开发了构建其CAD的专用算法，使得我们能够对常见的卫生经济分析执行精确的多维度敏感性分析。我们开发了实现该算法的开源软件包。最后，我们将其应用于两个案例研究：一个使用合成数据，另一个重新分析了文献中已有的成本效益分析，从而证明了本方法相对于标准技术的优势。我们的软件与代码公开于：\url{https://github.com/mmaaz-git/markovag}。