Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data
Abstract
:1. Introduction
2. Methodology
3. Technical Details
3.1. Choice of Lag
3.2. Choice of Number of Mass Points
3.3. Clustering and MAP Rule
4. Results
4.1. Robust Rates for All Countries
4.2. Finding Clusters of Countries
4.3. Case Study 1: San Marino Data in 2021
4.4. Case Study 2: Saudi Arabia Data in 2021
5. Discussion
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
BIC | Bayesian Information Criterion |
EM | Expectation-Maximization |
MAP | Maximum a posteriori |
NaN | Not a Number |
NPML | Nonparametric maximum likelihood |
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Study ID | Region | Sample Size | Lag (Days) | Deaths (Count) |
---|---|---|---|---|
Zhou et al. (2020) [17] | China, Wuhan | 191 | 18.5 | 53 |
Ruan et al. (2020) [18] | China, Wuhan | 150 | 18.0 | 68 |
Jin et al. (2020) [19] | China, Wuhan | 1056 | 13.0 | 37 |
Chen et al. (2020) [20] | China, Wuhan | 50 | 13.0 | 50 |
Verity et al.(2020) [1] | China, mainland | 3665 | 17.8 | NA |
Harrison et al. (2020) [21] | UK | 7802 | 7 | 7802 |
Harrison et al. (2021) [22] | UK | 1026 | 21 | 236 |
Faes et al. (2020) [23] | Belgium | 14,618 | 9 | 1534 |
Hawryluk et al. (2020) [24] | Brazil | 1,557,000 | 15.2 | NA |
Marschner (2021) [25] | Australia | 6235 | 18.1 | 816 |
Lefrancq et al. (2021) [26] | France | 198,846 | 19.0 | 33,269 |
Asirvatham et al. (2021) [27] | India | 1761 | 4.0 | 1710 |
Mehta et al. (2021) [28] | India | 346 | 9.0 | 76 |
Location | Population | Cases | Fitted | Raw | Fitted | Deaths | Fitted | Raw | Fitted |
---|---|---|---|---|---|---|---|---|---|
Cases | Case Rate | Case Rate | Deaths | Death Rate | Death Rate | ||||
Afghanistan | 40,099,462 | 83 | 91.839 | 0.0000021 | 0.0000023 | 1 | 0.359 | 0.0120482 | 0.0039064 |
Albania | 2,854,710 | 219 | 229.240 | 0.0000767 | 0.0000803 | 0 | 0.251 | 0.0000000 | 0.0010937 |
Algeria | 44,177,969 | 8 | 2.766 | 0.0000002 | 0.0000001 | 0 | 0.005 | 0.0000000 | 0.0019397 |
Andorra | 79,034 | 0 | 0.013 | 0.0000000 | 0.0000002 | 0 | 0.000 | NaN | 0.0019828 |
Angola | 34,503,774 | 0 | 2.160 | 0.0000000 | 0.0000001 | 0 | 0.004 | NaN | 0.0019489 |
Anguilla | 15,753 | 0 | 0.005 | 0.0000000 | 0.0000003 | 0 | 0.000 | NaN | 0.0019829 |
Antigua/Barbuda | 93,220 | 0 | 0.014 | 0.0000000 | 0.0000002 | 0 | 0.000 | NaN | 0.0019828 |
Argentina | 45,276,780 | 0 | 2.835 | 0.0000000 | 0.0000001 | 0 | 0.005 | NaN | 0.0019386 |
Armenia | 2,790,974 | 0 | 0.183 | 0.0000000 | 0.0000001 | 0 | 0.000 | NaN | 0.0019801 |
Aruba | 106,536 | 0 | 0.016 | 0.0000000 | 0.0000001 | 0 | 0.000 | NaN | 0.0019828 |
Australia | 25,921,089 | 32,895 | 36,211.746 | 0.0012690 | 0.0013970 | 62 | 75.118 | 0.0018848 | 0.0020744 |
Austria | 8,922,082 | 5233 | 5305.067 | 0.0005865 | 0.0005946 | 5 | 4.154 | 0.0009555 | 0.0007830 |
Azerbaijan | 10,312,992 | 21 | 23.619 | 0.0000020 | 0.0000023 | 0 | 0.040 | 0.0000000 | 0.0016807 |
Bahamas | 407,906 | 34 | 33.705 | 0.0000834 | 0.0000826 | 0 | 0.054 | 0.0000000 | 0.0015891 |
Bahrain | 1,463,265 | 2078 | 2044.180 | 0.0014201 | 0.0013970 | 0 | 1.553 | 0.0000000 | 0.0007595 |
Bangladesh | 169,356,251 | 874 | 973.659 | 0.0000052 | 0.0000057 | 2 | 1.425 | 0.0022883 | 0.0014636 |
Barbados | 281,200 | 145 | 146.826 | 0.0005156 | 0.0005221 | 0 | 0.173 | 0.0000000 | 0.0011807 |
Belarus | 9,578,168 | 0 | 0.600 | 0.0000000 | 0.0000001 | 0 | 0.001 | NaN | 0.0019734 |
Belgium | 11,611,420 | 0 | 0.727 | 0.0000000 | 0.0000001 | 0 | 0.001 | NaN | 0.0019714 |
Belize | 400,031 | 277 | 238.169 | 0.0006924 | 0.0005954 | 1 | 0.433 | 0.0036101 | 0.0018169 |
Location | Cases | Fitted Cases | Raw CASE Rate | Fitted Case Rate | Fitted Deaths | Raw Death Rate | Fitted Death Rate |
---|---|---|---|---|---|---|---|
Afghanistan | 53 | 65.833 | 0.0000013 | 0.0000016 | 0.439 | 0.0120482 | 0.0066713 |
Albania | 53 | 54.046 | 0.0000186 | 0.0000189 | 0.070 | 0.0000000 | 0.0012918 |
Algeria | 4 | 3.914 | 0.0000001 | 0.0000001 | 0.007 | 0.0000000 | 0.0018068 |
Andorra | 0 | 0.017 | 0.0000000 | 0.0000002 | 0.000 | NaN | 0.0018613 |
Angola | 0 | 3.056 | 0.0000000 | 0.0000001 | 0.006 | NaN | 0.0018185 |
Anguilla | 0 | 0.007 | 0.0000000 | 0.0000004 | 0.000 | NaN | 0.0018614 |
Antigua and Barbuda | 0 | 0.019 | 0.0000000 | 0.0000002 | 0.000 | NaN | 0.0018612 |
Argentina | 0 | 4.010 | 0.0000000 | 0.0000001 | 0.007 | NaN | 0.0018054 |
Armenia | 0 | 0.273 | 0.0000000 | 0.0000001 | 0.001 | NaN | 0.0018576 |
Aruba | 0 | 0.021 | 0.0000000 | 0.0000002 | 0.000 | NaN | 0.0018612 |
Australia | 33,223 | 33,031.390 | 0.0012817 | 0.0012743 | 48.139 | 0.0018848 | 0.0014574 |
Austria | 2183 | 2284.134 | 0.0002447 | 0.0002560 | 3.953 | 0.0009555 | 0.0017305 |
Azerbaijan | 0 | 0.925 | 0.0000000 | 0.0000001 | 0.002 | 0.0000000 | 0.0018483 |
Bahamas | 20 | 19.675 | 0.0000490 | 0.0000482 | 0.032 | 0.0000000 | 0.0016104 |
Bahrain | 997 | 1054.167 | 0.0006814 | 0.0007204 | 0.340 | 0.0000000 | 0.0003224 |
Bangladesh | 54 | 60.609 | 0.0000003 | 0.0000004 | 0.722 | 0.0022883 | 0.0119116 |
Barbados | 104 | 93.738 | 0.0003698 | 0.0003334 | 0.099 | 0.0000000 | 0.0010537 |
Belarus | 0 | 0.861 | 0.0000000 | 0.0000001 | 0.002 | NaN | 0.0018492 |
Belgium | 5944 | 6189.447 | 0.0005119 | 0.0005330 | 1.182 | NaN | 0.0001910 |
Belize | 224 | 212.846 | 0.0005600 | 0.0005321 | 0.638 | 0.0036101 | 0.0029986 |
ℓ | 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|
Afghanistan | 0.020 | 0.174 | 0.230 | 0.577 | 4 |
Albania | 0.313 | 0.369 | 0.172 | 0.145 | 2 |
Algeria | 0.259 | 0.324 | 0.174 | 0.243 | 2 |
Andorra | 0.254 | 0.320 | 0.174 | 0.252 | 2 |
Angola | 0.258 | 0.323 | 0.174 | 0.245 | 2 |
Anguilla | 0.254 | 0.320 | 0.174 | 0.252 | 2 |
Antigua and Barbuda | 0.254 | 0.320 | 0.174 | 0.252 | 2 |
Argentina | 0.259 | 0.324 | 0.174 | 0.243 | 2 |
Armenia | 0.254 | 0.320 | 0.174 | 0.251 | 2 |
Aruba | 0.254 | 0.320 | 0.174 | 0.252 | 2 |
Australia | 0.000 | 1.000 | 0.000 | 0.000 | 2 |
Austria | 0.000 | 0.839 | 0.161 | 0.000 | 2 |
Azerbaijan | 0.255 | 0.321 | 0.174 | 0.250 | 2 |
Bahamas | 0.277 | 0.340 | 0.175 | 0.208 | 2 |
Bahrain | 0.746 | 0.247 | 0.007 | 0.000 | 1 |
Bangladesh | 0.000 | 0.025 | 0.099 | 0.875 | 4 |
Barbados | 0.351 | 0.392 | 0.164 | 0.093 | 2 |
Belarus | 0.255 | 0.321 | 0.174 | 0.250 | 2 |
Belgium | 1.000 | 0.000 | 0.000 | 0.000 | 1 |
Belize | 0.054 | 0.397 | 0.348 | 0.201 | 2 |
−8.564 | −6.531 | −5.458 | −4.251 | ||
0.254 | 0.320 | 0.174 | 0.252 |
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Almohaimeed, A.; Einbeck, J.; Qarmalah, N.; Alkhidhr, H. Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data. Int. J. Environ. Res. Public Health 2022, 19, 14960. https://doi.org/10.3390/ijerph192214960
Almohaimeed A, Einbeck J, Qarmalah N, Alkhidhr H. Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data. International Journal of Environmental Research and Public Health. 2022; 19(22):14960. https://doi.org/10.3390/ijerph192214960
Chicago/Turabian StyleAlmohaimeed, Amani, Jochen Einbeck, Najla Qarmalah, and Hanan Alkhidhr. 2022. "Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data" International Journal of Environmental Research and Public Health 19, no. 22: 14960. https://doi.org/10.3390/ijerph192214960
APA StyleAlmohaimeed, A., Einbeck, J., Qarmalah, N., & Alkhidhr, H. (2022). Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data. International Journal of Environmental Research and Public Health, 19(22), 14960. https://doi.org/10.3390/ijerph192214960