Background Overuse and misuse of prescription opioids have become significant public health burdens in the United States. About 11.5 million people are estimated to have misused prescription opioids for nonmedical purposes in 2016. This has led to a significant number of drug overdose deaths in the United States. Previous studies have examined spatiotemporal clusters of opioid misuse, but they have been restricted to circular shaped regions. Objective The goal of this study was to identify spatiotemporal hot spots of opioid users and opioid prescription claims using Medicare data. Methods We examined spatiotemporal clusters with significantly higher number of beneficiaries and rate of prescriptions for opioids using Medicare payment data from the Centers for Medicare & Medicaid Services. We used network scan statistics to detect significant clusters with arbitrary shapes, the Kulldorff scan statistic to examine the significant clusters for each year (2013, 2014, and 2015) and an expectation-based version to examine the significant clusters relative to past years. Regression analysis was used to characterize the demographics of the counties that are a part of any significant cluster, and data mining techniques were used to discover the specialties of the anomalous providers. Results We examined anomalous spatial clusters with respect to opioid prescription claims and beneficiary counts and found some common patterns across states: the counties in the most anomalous clusters were fairly stable in 2014 and 2015, but they have shrunk from 2013. In Virginia, a higher percentage of African Americans in a county lower the odds of the county being anomalous in terms of opioid beneficiary counts to about 0.96 in 2015. For opioid prescription claim counts, the odds were 0.92. This pattern was consistent across the 3 states and across the 3 years. A higher number of people in the county with access to Medicaid increased the odds of the county being in the anomalous cluster to 1.16 in both types of counts in Virginia. A higher number of people with access to direct purchase of insurance plans decreased the odds of a county being in an anomalous cluster to 0.85. The expectation-based scan statistic, which captures change over time, revealed different clusters than the Kulldorff statistic. Providers with an unusually high number of opioid beneficiaries and opioid claims include specialties such as physician’s assistant, nurse practitioner, and family practice. Conclusions Our analysis of the Medicare claims data provides characteristics of the counties and provider specialties that have higher odds of being anomalous. The empirical analysis identifies highly refined spatial hot spots that are likely to encounter prescription opioid misuse and overdose. The methodology is generic and can be applied to monitor providers and their prescription behaviors in regions that are at a high risk of abuse.

As incorporating software testing into programming assignments becomes routine, educators have begun to assess not only the correctness of students' software, but also the adequacy of their tests. In practice, educators rely on code coverage measures, though its shortcomings are widely known. Mutation analysis is a stronger measure of test adequacy, but it is too costly to be applied beyond the small programs developed in introductory programming courses. We demonstrate how to adapt mutation analysis to provide rapid automated feedback on software tests for complex projects in large programming courses. We study a dataset of 1389 student software projects ranging from trivial to complex. We begin by showing that although the state-of-the-art in mutation analysis is practical for providing rapid feedback on projects in introductory courses, it is prohibitively expensive for the more complex projects in subsequent courses. To reduce this cost, we use a statistical procedure to select a subset of mutation operators that maintains accuracy while minimizing cost. We show that with only 2 operators, costs can be reduced by a factor of 2-3 with negligible loss in accuracy. Finally, we evaluate our approach on open-source software and report that our findings may generalize beyond our educational context.

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Scan statistics is one of the most popular approaches for anomaly detection in spatial and network data. In practice, there are numerous sources of uncertainty in the observed data. However, most prior works have overlooked such uncertainty, which can affect the accuracy and inferences of such methods. In this paper, we develop the first systematic approach to incorporating uncertainty in scan statistics. We study two formulations for robust scan statistics, one based on the sample average approximation and the other using a max-min objective. We show that uncertainty significantly increases the computational complexity of these problems. Rigorous algorithms and efficient heuristics for both formulations are developed with justification of theoretical bounds. We evaluate our proposed methods on synthetic and real datasets, and we observe that our methods give significant improvement in the detection power as well as optimization objective, relative to a baseline.

and a B.Sc. in Electrical and Electronic Engineering from the University of Technology, Jamaica. Her research interests are exploring students' disciplinary identity through engagement with knowledge, curriculum design, assessment and evaluation and teaching for conceptual understanding.