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 2020-05-18:

Reported Case Count: 1,476,966

Predicted Case Count: 1,772,191

Percentage Underreporting in Case Count: 16.7%

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 350121 409731 (363975, 534468) 1.2 72654.9 17997.8 25%
NJ 146334 174813 (151832, 237487) 1.2 54892.4 16475.0 30%
IL 94191 113764 (98907, 158861) 1.2 45924.3 7433.1 16%
MA 86010 100333 (89125, 134203) 1.2 66859.0 12478.8 19%
CA 78839 95309 (82493, 136444) 1.2 31262.3 1995.3 6%
PA 62234 76506 (65643, 112211) 1.2 26004.1 4861.3 19%
MI 51142 61556 (53552, 82697) 1.2 39748.0 5120.9 13%
TX 47784 58972 (50162, 83425) 1.2 23909.5 1648.0 7%
FL 45588 55897 (47937, 77230) 1.2 30347.3 2122.6 7%
MD 38804 47415 (40644, 67252) 1.2 32242.2 6418.5 20%
GA 37701 45555 (39395, 61333) 1.2 33075.4 3550.9 11%
CT 37419 44877 (39258, 61358) 1.2 47852.2 10495.4 22%
LA 34432 40837 (35704, 58206) 1.2 57040.6 7406.7 13%
VA 30388 37306 (31847, 53377) 1.2 22302.2 3560.2 16%
OH 27923 34198 (29323, 47285) 1.2 22624.7 2388.8 11%
IN 27778 34073 (29236, 47460) 1.2 26327.6 4126.1 16%
CO 21633 26573 (22742, 39799) 1.2 21801.3 3756.6 17%
NC 18512 22647 (19388, 33657) 1.2 23735.9 1765.1 7%
WA 18288 22193 (19186, 30271) 1.2 36900.5 2401.6 7%
TN 17388 20997 (18190, 29566) 1.2 47630.9 2546.1 5%
MN 15668 19169 (16468, 26939) 1.2 26701.2 2778.2 10%
IA 14651 17736 (15223, 25204) 1.2 31771.4 4643.6 15%
AZ 13937 17314 (14747, 25062) 1.2 20850.0 1914.8 9%
WI 12543 15423 (13200, 21473) 1.2 26143.2 2154.3 8%
RI 12674 14862 (13161, 20227) 1.2 106243.3 11963.8 11%
AL 11771 14327 (12370, 20685) 1.2 31887.4 2400.7 8%
MS 11296 13598 (11916, 19050) 1.2 38010.9 3795.5 10%
MO 10789 13121 (11373, 17991) 1.2 25587.9 1757.9 7%
NE 10220 12545 (10700, 18236) 1.2 33932.9 5283.3 16%
SC 8661 10720 (9183, 16021) 1.2 23371.1 1682.2 7%
KS 7886 9760 (8304, 13716) 1.2 21141.6 2706.9 13%
KY 7688 9393 (8054, 13187) 1.2 29027.4 1720.8 6%
DE 7670 9234 (8022, 13003) 1.2 41966.0 7876.7 19%
UT 7238 8622 (7543, 11382) 1.2 53260.8 2257.7 4%
NV 6857 8487 (7221, 12180) 1.2 26179.5 2226.2 9%
DC 7123 8453 (7431, 11313) 1.2 51754.9 10092.8 20%
NM 5857 6935 (6121, 9588) 1.2 61323.1 2793.3 5%
OK 5310 6453 (5598, 8453) 1.2 31203.7 1341.9 4%
AR 4759 5794 (4982, 8298) 1.2 28227.5 1577.0 6%
SD 3987 4836 (4176, 6960) 1.2 32282.5 4506.8 14%
OR 3623 4501 (3829, 6707) 1.2 22371.2 859.0 4%
NH 3556 4354 (3744, 6169) 1.2 32912.9 2615.3 8%
ID 2419 2992 (2542, 4221) 1.2 20520.8 1353.6 7%
ND 1900 2225 (1964, 2829) 1.2 72462.6 2493.2 3%
ME 1687 2097 (1778, 3107) 1.2 17689.9 1255.0 7%
WV 1490 1787 (1566, 2470) 1.2 42122.7 831.4 2%
VT 940 1148 (990, 1631) 1.2 35709.0 1506.4 4%
WY 754 915 (787, 1275) 1.2 29520.1 1302.8 4%
HI 639 778 (675, 1080) 1.2 29433.5 451.3 2%
MT 468 583 (490, 916) 1.2 25154.9 437.9 2%
AK 396 477 (415, 658) 1.2 47366.9 541.3 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↩