Novel optimization methods for cancer screening and treatment

鉴于基于证据和个性化决策的最新趋势，需要强大的数据驱动建模方法来获得针对实际工程问题的个性化最优干预计划。我们建议开发基于随机动态规划和整数规划的新的工程工具来解决实际决策问题。虽然拟议的研究将应用于癌症筛查和治疗，但主要重点是开发工程方法。我们将研究大规模随机动态规划和整数规划方法在癌症筛查和治疗中的应用。这些应用领域充满了操作问题，这些问题可能会对拟议方法的局限性提供有价值的反馈，从而在这些方法领域开辟了新的途径。具体地说，序列决策问题将被描述为随机动态规划模型(例如，部分可观测的马尔可夫决策过程模型)，并将探索导出最优解的结构属性，并利用这些属性为这些模型找到有效的解方法。此外，对于这些应用问题中遇到的大规模整数规划公式，将提出各种分解方案。该计划的主题1将集中于开发能够克服随机动态规划中的建模和算法挑战的新方法。我们将调查个性化的癌症筛查和治疗问题，并测试所提出的解决方法的可行性。使用来自文献和我们的合作者的临床数据，我们将应用这些方法来确定癌症筛查和治疗的最佳策略。拟议的方法可能有助于发展洞察力，以改进癌症筛查和治疗实践并使其个人化，产生重大贡献，因为癌症是加拿大的主要死亡原因。该方法还将提高随机动态规划的工程知识，为其他工程应用提供参考。该计划的主题2将探索在放射治疗治疗计划中出现的大规模离散优化模型。具体地说，我们将研究调强放射治疗中的通量图优化和分解以及放射外科中缺乏有效求解方法的放射外科扇区持续时间优化。我们将为这些问题开发新的优化模型，并探索决策图等新解决方法的有效性。研究结果将为决策者提供有价值的规划、调度和操作工具。拟议的研究将扩展到考虑更一般的情况。

Given the recent trends in evidence-based and personalized decision making, powerful data-driven modeling approaches are needed to obtain personalized optimal intervention plans for practical engineering problems. We propose developing novel engineering tools based on stochastic dynamic programming and integer programming to address practical decision making problems. While proposed research will be applied to cancer screening and treatment, the main focus is on developing engineering methodology. We will investigate the applications of large-scale stochastic dynamic programming and integer programming methods in cancer screening and treatment. These application areas are rich with operational problems that potentially provide valuable feedback on limitations of the proposed methodologies, thus opening new avenues in these methodological domains. In particular, sequential decision making problems will be formulated as stochastic dynamic programming models (e.g., partially observable Markov decision process models), and deriving structural properties of the optimal solutions, and exploiting those properties to find efficient solution methods for these models will be explored. Moreover, various decomposition schemes will be proposed for the large-scale integer programming formulations encountered in these application problems. Theme 1 of the program will focus on developing novel methods that can overcome modeling and algorithmic challenges in stochastic dynamic programming. We will investigate personalized cancer screening and treatment problems, and test the viability of the proposed solution methods. Using clinical data from the literature and our collaborators, we will apply these methods to determine optimal policies for cancer screening and treatment. The proposed methodology may help develop insights to improve and personalize cancer screening and treatment practices, yielding a significant contribution as cancer is a leading cause of death in Canada. The proposed approach will also improve the engineering knowledge on stochastic dynamic programming for other engineering applications. Theme 2 of the program will explore large-scale discrete optimization models that arise in radiation therapy treatment planning. Specifically, we will investigate fluence map optimization and decomposition in intensity modulated radiation therapy and sector duration optimization in radiosurgery, which lack efficient solution methods for practical instances. We will develop novel optimization models for these problems and explore the effectiveness of new solution methodologies such as decision diagrams. The results will provide valuable planning, scheduling and operational tools for decision makers. The proposed research will be extended to consider more general settings.