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

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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.