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 2020-05-25:

Reported Case Count: 1,631,475

Predicted Case Count: 1,917,389

Percentage Underreporting in Case Count: 14.9%

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 361515 415702 (377091, 506177) 1.1 87378.7 18583.5 21%
NJ 154154 178209 (161341, 222884) 1.2 67979.5 17355.4 26%
IL 110304 128865 (115891, 162083) 1.2 59022.4 8704.7 15%
CA 92710 110212 (97908, 141646) 1.2 40057.1 2346.4 6%
MA 92675 106801 (96950, 130325) 1.2 77239.4 13445.8 17%
PA 67713 81424 (71974, 105812) 1.2 30940.1 5289.3 17%
TX 54509 66349 (57507, 84022) 1.2 26340.5 1879.9 7%
MI 54679 64766 (57638, 80856) 1.2 45182.6 5475.1 12%
FL 50867 60458 (53489, 79378) 1.2 40564.6 2368.4 6%
MD 46313 55571 (48861, 71047) 1.2 39757.6 7660.5 19%
GA 42838 50503 (44828, 64882) 1.2 45392.7 4034.7 9%
CT 40468 47307 (42281, 59719) 1.2 60061.4 11350.6 19%
VA 36244 43445 (38324, 54921) 1.2 28596.4 4246.3 15%
LA 37169 42843 (38716, 53393) 1.2 67982.4 7995.4 12%
OH 31911 38969 (34097, 51225) 1.2 27765.4 2730.0 10%
IN 31376 37308 (33069, 46690) 1.2 32797.7 4660.6 14%
CO 23964 29254 (25575, 39645) 1.2 26056.2 4161.3 16%
NC 23222 28090 (24385, 36813) 1.2 32098.9 2214.1 7%
MN 20573 24777 (21739, 32261) 1.2 35102.3 3647.9 10%
TN 20145 23520 (21110, 29421) 1.2 56167.3 2949.8 5%
WA 19585 23175 (20625, 28949) 1.2 41533.9 2571.9 6%
IA 17252 20431 (18021, 26048) 1.2 40492.3 5468.0 14%
AZ 16339 19946 (17421, 25766) 1.2 25229.9 2244.8 9%
WI 15277 18454 (16234, 23339) 1.2 34604.6 2623.8 8%
AL 14327 17057 (15040, 21680) 1.2 37893.5 2922.0 8%
RI 14065 15964 (14576, 19718) 1.1 125265.1 13276.9 11%
MS 13252 15500 (13910, 18998) 1.2 46335.7 4452.7 10%
MO 11988 14740 (12755, 19836) 1.2 24704.0 1953.3 8%
NE 11989 14159 (12647, 18227) 1.2 43013.2 6197.8 14%
SC 10096 12116 (10665, 15890) 1.2 31842.3 1960.9 6%
KS 8958 10905 (9512, 14697) 1.2 26236.1 3074.8 12%
DE 8809 10366 (9267, 13909) 1.2 53267.5 9046.3 17%
KY 8571 10207 (9039, 13241) 1.2 38018.9 1918.4 5%
UT 8392 9791 (8787, 12597) 1.2 60647.4 2617.6 4%
NV 7770 9337 (8192, 12171) 1.2 35803.7 2522.6 7%
DC 7966 9241 (8309, 11230) 1.2 73667.8 11287.3 15%
NM 6795 7785 (7090, 9723) 1.1 80654.6 3240.6 4%
OK 6037 7164 (6338, 9417) 1.2 40682.6 1525.7 4%
AR 5922 7047 (6235, 8838) 1.2 35980.1 1962.4 5%
SD 4563 5413 (4822, 6894) 1.2 39455.9 5157.9 13%
NH 4089 4845 (4305, 6177) 1.2 43788.0 3007.3 7%
OR 3927 4829 (4208, 6672) 1.2 26600.8 931.1 4%
ID 2626 3237 (2790, 4309) 1.2 23169.8 1469.4 6%
ND 2418 2780 (2527, 3410) 1.1 85935.3 3173.0 4%
ME 2055 2496 (2187, 3242) 1.2 27901.1 1528.8 5%
WV 1759 2099 (1859, 2722) 1.2 47816.4 981.5 2%
VT 956 1126 (1006, 1416) 1.2 45818.1 1532.1 3%
WY 813 980 (856, 1302) 1.2 34615.4 1404.7 4%
HI 643 775 (680, 1029) 1.2 35011.6 454.1 1%
MT 479 578 (509, 759) 1.2 31232.9 448.2 1%
AK 408 473 (426, 593) 1.2 59472.8 557.7 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