# How many cases of COVID-19 does each U.S. state really have?

Reported U.S. case counts are based on the number of administered tests. Since not everyone is tested, this number is biased. We use Bayesian techniques to estimate the true number of cases.

**Warning:**This analysis contains the results of a predictive model. There are a number of assumptions made which include some speculation. Furthermore, this analysis was not prepared or reviewed by an Epidimiologist. Therefore, the assumptions and methods presented should be scrutinized carefully before arriving at any conclusions.

## COVID-19 Case Estimates, by State

### Definition Of Fields:

**Reported Cases**: The number of cases reported by each state, which is a function of how many tests are positive.**Est Cases**: The predicted number of cases, accounting for the fact that not everyone is tested.**Est Range**: The 95% confidence interval of the predicted number of cases.**Ratio**:`Estimated Cases`

divided by`Reported Cases`

.**Tests per Million**: The number of tests administered per one million people. The less tests administered per capita, the larger the difference between reported and estimated number of cases, generally.**Cases per Million**: The number of**reported**cases per on million people.**Positive Test Rate**: The**reported**percentage of positive tests.

## Appendix: Model Diagnostics

### Derived relationship between Test Capacity and Case Under-reporting

Plotted is the estimated relationship between test capacity (in terms of people per test -- larger = less testing) and the likelihood a COVID-19 case is reported (lower = more under-reporting of cases).

The lines represent the posterior samples from our MCMC run (note the x-axis is plotted on a log scale). The rug plot shows the current test capacity for each state (black '|') and the capacity one week ago (cyan '+'). For comparison, South Korea's testing capacity is currently at the very left of the graph (200 people per test).

## About this Analysis

This analysis was done by Joseph Richards.

This project^{1} uses the testing rates per state from https://covidtracking.com/, which reports case counts and mortality by state. This is used to **estimate the number of unreported (untested) COVID-19 cases in each U.S. state.**

The analysis makes a few assumptions:

- The probability that a case is reported by a state is a function of the number of tests run per person in that state. Hence the degree of under-reported cases is a function of tests run per capita.
- The underlying mortality rate is the same across every state.
- Patients take time to succumb to COVID-19, so the mortality counts
*today*reflect the case counts*7 days ago*. E.g., mortality rate = (cumulative deaths today) / (cumulative cases 7 days ago).

The model attempts to find the most likely relationship between state-wise test volume (per capita) and under-reporting, such that the true underlying mortality rates between the individual states are as similar as possible. The model simultaneously finds the most likely posterior distribution of mortality rates, the most likely *true* case count per state, and the test volume vs. case underreporting relationship.

Full details about the model are available at: https://github.com/jwrichar/COVID19-mortality↩