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.

Summary for the United States on 2020-05-15:

Reported Case Count: 1,404,839

Predicted Case Count: 1,626,906

Percentage Underreporting in Case Count: 13.6%

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.
Reported Cases Est Cases Est Range Ratio Tests per Million Cases per Million Positive Test Rate
state
NY 343051 383689 (356849, 443834) 1.1 66761.9 17634.4 26%
NJ 142704 162569 (149740, 189085) 1.1 50854.1 16066.3 32%
IL 87937 101675 (92149, 121131) 1.2 40407.5 6939.6 17%
MA 80497 90451 (83511, 106784) 1.1 59489.6 11678.9 20%
CA 73164 86759 (77600, 106776) 1.2 27957.2 1851.7 7%
PA 59636 70942 (63707, 86847) 1.2 24308.3 4658.3 19%
MI 49582 57778 (52665, 70068) 1.2 33632.5 4964.7 15%
TX 43851 53189 (47092, 65496) 1.2 21495.6 1512.3 7%
FL 43210 51168 (45888, 64672) 1.2 28347.4 2011.9 7%
GA 35858 42556 (38315, 53745) 1.2 26925.6 3377.3 13%
MD 35903 42379 (38045, 52818) 1.2 29517.6 5938.6 20%
CT 35464 40721 (37210, 48916) 1.1 41949.5 9947.0 24%
LA 33489 38007 (35030, 44504) 1.1 53258.5 7203.8 14%
VA 27813 33864 (29797, 42721) 1.2 19545.4 3258.5 17%
OH 26357 31858 (28232, 38893) 1.2 19963.2 2254.8 11%
IN 26053 31221 (27806, 38761) 1.2 23801.8 3869.9 16%
CO 20475 25063 (21995, 32004) 1.2 19886.1 3555.5 18%
WA 17512 20369 (18513, 24362) 1.2 34285.4 2299.7 7%
NC 16507 19953 (17702, 25042) 1.2 20906.4 1573.9 8%
TN 16699 19111 (17462, 22881) 1.1 44268.5 2445.2 6%
MN 13435 16213 (14292, 20197) 1.2 22829.9 2382.2 10%
IA 13675 16161 (14543, 19592) 1.2 28301.7 4334.3 15%
AZ 12674 15563 (13663, 20679) 1.2 18456.3 1741.2 9%
WI 11275 13506 (12072, 16966) 1.2 22992.6 1936.5 8%
RI 12016 13151 (12373, 14496) 1.1 95907.8 11342.7 12%
AL 10968 12997 (11657, 15699) 1.2 28957.7 2236.9 8%
MO 10317 12505 (11020, 15399) 1.2 20710.6 1681.0 8%
MS 10483 12176 (11093, 14489) 1.2 35390.0 3522.3 10%
NE 9075 10710 (9657, 13236) 1.2 27574.8 4691.4 17%
SC 8189 9977 (8824, 12881) 1.2 19914.7 1590.5 8%
KS 7468 9116 (8035, 11686) 1.2 19780.9 2563.4 13%
KY 7080 8409 (7494, 10131) 1.2 26276.5 1584.7 6%
DE 7223 8378 (7600, 9861) 1.2 37850.0 7417.6 20%
NV 6499 7787 (6931, 9681) 1.2 22558.6 2110.0 9%
UT 6749 7696 (7065, 9063) 1.1 49944.2 2105.1 4%
DC 6736 7695 (7072, 9217) 1.1 46757.4 9544.5 20%
NM 5364 6066 (5597, 7253) 1.1 54850.0 2558.1 5%
OK 4962 5876 (5268, 7500) 1.2 28350.7 1254.0 4%
AR 4236 5066 (4508, 6353) 1.2 25123.6 1403.7 6%
SD 3792 4470 (4028, 5519) 1.2 29924.5 4286.4 14%
OR 3479 4217 (3748, 5189) 1.2 19927.7 824.8 4%
NH 3299 3867 (3508, 4533) 1.2 28811.3 2426.3 8%
ID 2324 2857 (2500, 3677) 1.2 18888.0 1300.5 7%
ME 1565 1944 (1702, 2506) 1.2 17599.2 1164.3 7%
ND 1647 1845 (1713, 2129) 1.1 65934.3 2161.2 3%
WV 1427 1655 (1506, 1991) 1.2 38341.2 796.3 2%
VT 932 1086 (980, 1322) 1.2 36066.3 1493.6 4%
WY 701 841 (747, 1039) 1.2 26660.5 1211.2 5%
HI 638 755 (681, 932) 1.2 27460.8 450.6 2%
MT 462 555 (493, 717) 1.2 22969.2 432.3 2%
AK 387 444 (407, 524) 1.1 43417.7 529.0 1%

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 project1 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:

  1. 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.
  2. The underlying mortality rate is the same across every state.
  3. 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.

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