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 2020-05-16:

Reported Case Count: 1,430,912

Predicted Case Count: 1,592,169

Percentage Underreporting in Case Count: 10.1%

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 345813 370424 (355100, 404082) 1.1 68781.6 17776.3 26%
NJ 143905 157030 (148569, 172076) 1.1 52123.6 16201.5 31%
IL 90369 99626 (93701, 112219) 1.1 42503.9 7131.5 17%
MA 83421 90083 (85739, 98596) 1.1 63210.6 12103.2 19%
CA 74936 85413 (78486, 99204) 1.1 28697.6 1896.5 7%
PA 60622 70022 (64037, 82471) 1.2 24983.0 4735.4 19%
MI 50079 55983 (52230, 63427) 1.1 35796.6 5014.5 14%
TX 45198 52763 (47923, 61680) 1.2 22278.8 1558.8 7%
FL 43210 49083 (45271, 57522) 1.1 28347.4 2011.9 7%
MD 36986 42102 (38962, 49037) 1.1 30240.8 6117.8 20%
GA 36681 41939 (38636, 48463) 1.1 28431.9 3454.8 12%
CT 36085 39724 (37393, 44006) 1.1 43729.4 10121.2 23%
LA 33837 36760 (34905, 40651) 1.1 54463.4 7278.7 13%
VA 28672 33544 (30542, 38816) 1.2 20855.7 3359.1 16%
OH 26954 31749 (28578, 37721) 1.2 21060.8 2305.9 11%
IN 26655 31057 (28385, 37448) 1.2 24575.6 3959.3 16%
CO 20838 24505 (22260, 29067) 1.2 20495.8 3618.5 18%
NC 17129 20060 (18222, 23879) 1.2 22077.1 1633.2 7%
WA 17773 19928 (18586, 22521) 1.1 35185.1 2334.0 7%
TN 16970 18650 (17584, 20932) 1.1 45357.8 2484.9 5%
MN 14240 16463 (15134, 19480) 1.2 23879.0 2525.0 11%
IA 14049 15974 (14744, 18508) 1.1 29655.8 4452.8 15%
AZ 13169 15534 (14090, 18213) 1.2 19509.1 1809.2 9%
WI 11685 13644 (12402, 15998) 1.2 24103.7 2006.9 8%
RI 12219 12912 (12448, 13830) 1.1 99095.6 11534.3 12%
AL 11216 12731 (11816, 14743) 1.1 29789.4 2287.5 8%
MO 10456 12183 (11145, 14634) 1.2 21907.9 1703.6 8%
MS 10801 12119 (11260, 13866) 1.1 35893.0 3629.2 10%
NE 9416 10679 (9876, 12574) 1.1 29577.5 4867.6 16%
SC 8407 9877 (8947, 11978) 1.2 21290.0 1632.8 8%
KS 7886 9233 (8354, 11035) 1.2 21141.6 2706.9 13%
KY 7225 8293 (7647, 9593) 1.1 27145.7 1617.2 6%
DE 7373 8177 (7684, 9224) 1.1 39309.3 7571.6 19%
NV 6614 7696 (6994, 9331) 1.2 23422.8 2147.3 9%
UT 6913 7545 (7142, 8447) 1.1 50910.8 2156.3 4%
DC 6871 7525 (7114, 8467) 1.1 48656.1 9735.8 20%
NM 5503 5965 (5679, 6543) 1.1 57039.0 2624.4 5%
OK 5086 5778 (5339, 6632) 1.1 29869.3 1285.3 4%
AR 4463 5148 (4724, 5971) 1.2 27016.0 1478.9 5%
SD 3887 4397 (4066, 5095) 1.1 30988.2 4393.8 14%
OR 3541 4159 (3772, 4983) 1.2 21221.3 839.5 4%
NH 3464 3929 (3638, 4433) 1.1 31339.0 2547.6 8%
ID 2351 2799 (2522, 3346) 1.2 19442.5 1315.6 7%
ME 1603 1915 (1716, 2366) 1.2 17627.4 1192.5 7%
ND 1761 1894 (1807, 2057) 1.1 67861.9 2310.8 3%
WV 1441 1605 (1498, 1829) 1.1 39581.6 804.1 2%
VT 933 1039 (973, 1175) 1.1 37188.2 1495.2 4%
WY 715 814 (749, 935) 1.1 27683.4 1235.4 4%
HI 637 729 (671, 848) 1.1 27386.7 449.9 2%
MT 466 540 (495, 646) 1.2 23782.3 436.0 2%
AK 388 428 (402, 472) 1.1 44314.4 530.4 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↩