# Effect of Positivity Rates on Deaths in the United States during the COVID Pandemic

# Introduction

During the past year, the world has been beset by a pandemic going by many names: Coronavirus, COVID-19, SARS-COV-2, et al. This pandemic has been the most virulent disease since the Spanish Flu of the early 1900s.

It is said that to defeat one's opponent, one must know the enemy. A good approach is to understand the trend analysis and correlation of the pandemic’s metrics. The goal of this research is to evaluate the trajectory of deaths due to COVID based on positive test cases. By observing a fall in the rate of positive cases, we can infer that deaths will decline after a lag.

In order to understand the trends, I built an application that visualizes the daily trends of the disease on a state-by-state basis and on the United States as a whole.

# Data Sources

Data about the disease was obtained from covidtracking.com, which is curated by the Atlantic Monthly Group. Each state reports on a daily basis its positive and negative test cases as well as deaths due to COVID. It should be noted that the original data set came from healthdata.gov; however, covidtracking.com was found to have better data on testing as well as cleaner, better “scrubbed” data since the Atlantic Monthly Group manually monitors the data collection process and checks for any anomalies.

Estimated population data for 2020 was taken from Wikipedia.

# Data Calculations

Figures for the United States were calculated as the sum of the 50 states’ figures. Other territories’ data were ignored for this study.

Population data was merged with the COVID data set to arrive at per capita figures. For example, New Cases per Capita was calculated by taking the daily change in total positive cases and dividing by the estimated 2020 population. The importance is to normalize the figures across states with different populations to achieve better comparability. Furthermore, 7-day rolling averages were calculated to remove noise in the data.

Positivity rates were calculated as the number of positive cases on a given day divided by the number of tests given on that day.

# Analysis of Positivity Rates vs. Deaths

By inspecting the graph of positivity rates and deaths over time, one immediately notices that there were a number of cycles where the rates rise and subsequently fall.

Likewise, the number of new deaths per day also exhibits peaks and troughs over time.

We can superimpose these two graphs on each other. There is a noticeable simularity between the ebbs and flows.

In order to establish the presence of a correlated behavior of two time series, I made use of the cross-correlation function defined as:

where X̄ and Ȳ are the means and SD_{X} and SD_{Y} are the standard deviations of the respective time series.

When the statistic is greater than the 5% confidence level, we can accept the Alternative Hypothesis that there is a lagged relationship between the two time series.

Looking at the graph of the cross-correlation function for the positivity rates and deaths, we notice that there is a significant probability for a lag between zero and approximately 45 days.

In order to estimate the strongest lag, we leverage the partial cross-correlation function as coded below in R.

pacf(ts(cbind(dx, dy)), lag.max=45)

where dx = positivity rate and dy = number of deaths. For greater insight into the partial autocorrelation function (which is used here in the code), please see https://en.wikipedia.org/wiki/Partial_autocorrelation_function. Usually, the pacf is run against the same time series; however, in this case, we use two different time series to create the partial cross-correlation function.

The result of the function is graphed below.

From this graph, we notice a significant positive lag at 29 days. Graphing the Positivity Rate with a 29-day lag against the number of deaths, we see a very close correlation in the rising and falling of both curves.

# Conclusion

The death rate lags the positivity rate. Since the positivity rate has started to decline, we should see a decline in the number of new deaths within approximately 29 days later.

This is expected since there is a natural delay between the time a person tests positive and a possible adverse outcome.

This decline will occur in the absence of any other factors such as vaccinations and seasonal changes.

# About This Research

Analysis for this research was performed using R and can be seen online at https://dpwasserman.shinyapps.io/covid_analysis.

The code for the application is housed at https://www.github.com/DPWasserman/covid_analysis.

Graphs were produced through R Studio and Microsoft Excel.