Visualizing Local Maxima of the Ohio overdose epidemic with Vineyards

Abstract

Understanding how spatial patterns evolve over time is a complex task that often arises in the analysis of public health data. In this work, we investigate the use of vineyards from topological data analysis (TDA) in this setting by applying them to time series data related to the overdose epidemic in the state of Ohio. We begin by proposing statistical tests that can be used in order to evaluate whether vineyards are a reasonable technique to study a spatiotemporal dataset. We then apply these tests to the data of drug overdose deaths in Ohio and, finding the data suitable, perform a subsequent analysis using vineyards to visualize the evolution of local maxima of death rates throughout the Ohio overdose epidemic. We conclude by developing statistical methods to quantify the significance and uncertainty of vineyard features and by exploring how vineyard-derived summaries can be used for forecasting.

11 pages, 9 figures