CAREER: Algorithms and Decision Models for Learning in Health Care Systems

这项学院早期职业发展(Career)补助金旨在建立新的算法和数学模型，以优化医疗保健系统的决策。越来越多的数字健康记录为医院等医疗保健提供设施的转型创造了许多机会，潜在地提高了它们的质量和运营效率。例如，最近的研究表明，通过统计预测指导医院决策的好处。然而，当预测不能与组织的工作流程集成时，预测就毫无价值。在这方面，需要将预测与运筹学模型相结合的新方法。这项研究解决了运筹学和统计建模相结合的数学障碍。这种集成的一个例子是构建能够适应手头数据中不确定模式的新的优化算法。这项研究的结果可能会提高医疗保健的质量，降低医疗保健成本。此外，由于这项研究位于机器学习、医学、运筹学和统计学的交叉点，它可以帮助培训这一多学科领域的下一代学术学者(重点是未被充分代表的群体)。大数据时代统计模型的一个共同主题是通过参数或非参数模型来表征“高维”空间中的不确定性。高维空间是指可用预测变量的空间，这些变量可能包含有关决策任务中不确定结果的信息。基于高维数据的模型在医疗保健中特别有用，因为医疗保健系统很复杂，在其患者群体和实践模式中具有许多系统特定的功能。这种潜在的应用已经导致了大量最近的文献(以高维统计为已知)来处理这种建模框架的算法和统计挑战。相比之下，在运筹学文献中，不确定性通常限于少数已知的概率分布，以使数学分析更容易处理。本研究旨在通过将高维统计学的思想与运筹学的数学相结合来放宽上述限制，并将所得到的模型应用于两个应用领域--急诊科等待时间预测和新治疗的个性化管理。例如，在可以被建模为多臂强盗问题的环境中，除了过去决策的数据之外，通过利用许多预测变量的可用性来帮助减少决策中的不确定性的新理论可能是有用的。当预报器的数量增长快于时间周期或样本数量时，缩小这种知识差距需要开发一类新的算法和渐近理论。另一个需要解决的挑战是，在统计设置中，样本通常被假设为独立的，然而，在具有反馈的决策系统中，这一假设失败，因为当前的决策可能会影响未来的样本。

This Faculty Early Career Development (CAREER) grant aims to build new algorithms and mathematical models for optimizing decisions in healthcare systems. Growing availability of digital health records has created many opportunities for transforming health care delivery facilities such as hospitals, potentially improving their quality and operational efficiency. For example, recent research shows the benefits of guiding decisions in a hospital via statistical predictions. However, predictions are worthless when they cannot be integrated with the organization's workflow. In this regard, new ways of combining predictions with operations research models are needed. This research tackles mathematical barriers to the integration of operations research and statistical modeling. An example of this integration would be building new optimization algorithms that can adapt to patterns of uncertainty in the data at hand. The findings of this research can potentially improve quality of medical care and reduce health care costs. In addition, because this research lies at the intersection of machine learning, medicine, operations research, and statistics, it can help train the next generation of academic scholars (with emphasis on underrepresented groups) on this multidisciplinary area.A common theme of statistical models in the age of big data is to characterize uncertainty via parametric or non-parametric models in a "high dimensional" space. High dimensional space refers to the space of available predictor variables that could contain information about uncertain outcomes in a decision task. Models based on high-dimensional data are particularly useful in healthcare because healthcare systems are complex, with many system-specific features in their patient populations and practice patterns. Such potential applications have led to a large body of recent literature (known by high-dimensional statistics) to deal with algorithmic and statistical challenges of such modeling framework. In contrast, in the operations research literature, the uncertainty is typically restricted to few known probability distributions to make mathematical analysis more tractable. This research aims to relax the aforementioned restrictions by combining ideas from the high-dimensional statistics with the mathematics of operations research, and applying the resulting models to two application areas -- wait time prediction in emergency departments, and personalized administration of new treatments. For example, in settings that can be modeled as multi-armed bandit problems, new theory that can help reduce the uncertainty in decisions by utilizing availability of many predictor variables in addition to the data on past decisions can be useful. Reducing this knowledge gap requires developing a new class of algorithms and asymptotic theory when the number of predictors grows faster than time periods or the number of samples. Another challenge that needs to be addressed is that in statistical setting the samples are usually assumed to be independent, however this assumption fails in decision systems with feedback where current decisions may impact future samples.