Comparing Trends in Data (with Applications to COVID and Image Data)

Abstract

Many applications involve looking at and comparing trends in data. We will discuss some statistics that can be used to assess the similarity or dissimilarity between pairs of cumulative trends. These statistics can then be used to study sets of trends – for example, to cluster them or to compare them across different groups We will describe one possible approach and illustrate its use in two case studies. In the first case study, we studied the trend over time of COVID-19 in New Jersey in the USA– it was found that areas close to New York City had significantly different (more rapidly increasing) cumulative trends compared to areas further from New York City during the early days of the pandemic, but this difference dissipated as the pandemic progressed and spread within New Jersey itself. In the second case study, we compared two sets of CT scan images of lungs – a significant difference could be detected between COPD-diseased lungs and normal lungs. Overall, the method performed well and detected insightful differences.