Comparing Cumulative Trends (with an application to COVID-19 data)

Many applications involve looking at and comparing trends in data. We will discuss some statistics that could 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 a case study, in which we studied the trend over time of COVID-19 in New Jersey (NJ) 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. Overall, the method performed well and detected insightful differences. Various socio-economic factors could have influenced the spread of COVID-19 within NJ. It was also found that socio-economic factors which could have influenced the spread of COVID-19 within NJ are population, distance to NYC, and percent of low-income households. The dynamic nature of these relationships also needs to be studied, perhaps using extensions of the methodology discussed here.