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Marc Bevand
2020-06-09 14:17:18 -07:00
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README.md
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# Calculating the age-stratified infection fatality ratio (IFR) of COVID-19
*Updated: 09 June 2020*
Author: Marc Bevand
The [largest serological prevalence survey][sero] of COVID-19 was conducted in
Spain on 60 897 valid samples between 27 April and 11 May. We used its results
to calculate the overall and age-stratified IFR of COVID-19 with the Python
script `calc_ifr.py`:
```
$ ./calc_ifr.py
Ages 0 to 9: 109803 infected, 3 deaths, 0.003% IFR
Ages 10 to 19: 180401 infected, 7 deaths, 0.004% IFR
Ages 20 to 29: 216507 infected, 33 deaths, 0.015% IFR
Ages 30 to 39: 261550 infected, 87 deaths, 0.033% IFR
Ages 40 to 49: 436122 infected, 281 deaths, 0.065% IFR
Ages 50 to 59: 412847 infected, 864 deaths, 0.209% IFR
Ages 60 to 69: 313907 infected, 2363 deaths, 0.753% IFR
Ages 70 to 79: 256631 infected, 6470 deaths, 2.521% IFR
Ages 80 to 89: 123416 infected, 10982 deaths, 8.898% IFR
Ages 90 to 199: 33807 infected, 5654 deaths, 16.724% IFR
Ages 0 to 199: 2344992 infected, 26744 deaths, 1.140% IFR
```
The average IFR for Spain is **1.140%**. However the true IFR may be higher due
to right-censoring and under-reporting of deaths.
The Spanish serological study was conducted between 27 April 2020 and 11 May 2020 and
remains the largest published study available to this day. The age-stratified
IFR was calculated from three sources:
1. Detailed *prevalence data for age brackets*, from the [serosurvey][sero] (page 8)
1. *Deaths per age brackets* from the [Ministry of Health's daily report for 11 May][deaths] (page 1 and table 3)
1. *Population pyramid* for Spain, from [worldpopulationreview.com][wpop]
Important detail to note: there were 26 744 total deaths, however age information
was only available for 18 722 deaths, and was missing for 8 022 deaths.
We assume that these 8 022 deaths were distributed proportionally among age
brackets, which seems to be a reasonable assumption.
# Applying the age-stratified IFR to other countries
The script `calc_ifr.py` is also able to apply the age-stratified IFR to
another population pyramid, thus calculating the expected average IFR for other
countries.
In the second half of the script, edit `pyramid_target` with the demographics data.
As an example, we supply pyramid data for the United States and calculate an IFR of **0.721%**:
```
IFR on target country assuming disease prevalence equal among ages: 0.721%
```
[sero]: https://www.mscbs.gob.es/gabinetePrensa/notaPrensa/pdf/13.05130520204528614.pdf
[deaths]: https://www.mscbs.gob.es/profesionales/saludPublica/ccayes/alertasActual/nCov-China/documentos/Actualizacion_102_COVID-19.pdf
[wpop]: https://worldpopulationreview.com/countries/spain-population/
calc_ifr.py
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#!/usr/bin/python3
#
# Calculate the age-stratified IFR based on the Spanish serosurvey of 60897 participants.
# Author: Marc Bevand — @zorinaq
# Prevalence of antibodies by age bracket, in % (serosurvey dates: 27-April-2020 to 11-May-2020)
# Source: https://www.mscbs.gob.es/gabinetePrensa/notaPrensa/pdf/13.05130520204528614.pdf (page 8)
prevalence_by_age = {
(0,0): 1.1,
(1,4): 2.2,
(5,9): 3.0,
(10,14): 3.9,
(15,19): 3.8,
(20,24): 4.5,
(25,29): 4.8,
(30,34): 3.8,
(35,39): 4.6,
(40,44): 5.3,
(45,49): 5.7,
(50,54): 5.8,
(55,59): 6.1,
(60,64): 5.9,
(65,69): 6.2,
(70,74): 6.9,
(75,79): 6.1,
(80,84): 5.1,
(85,89): 5.6,
(90,199): 5.8,
}
# Total deaths, and number of deaths by age bracket (as of 11-May-2020)
# Source: https://www.mscbs.gob.es/profesionales/saludPublica/ccayes/alertasActual/nCov-China/documentos/Actualizacion_102_COVID-19.pdf (page 1 and table 3)
# Total deaths (26744) differs from the total for all age brackets (18722)
# because age information is not available for 8022 deaths, as explained in
# table 3 header: «Distribución de casos hospitalizados, ingresados en UCI y
# fallecidos por grupos de edad y sexo información disponible»
total_deaths = 26744
deaths_by_age = {
(0,9): 2,
(10,19): 5,
(20,29): 23,
(30,39): 61,
(40,49): 197,
(50,59): 605,
(60,69): 1654,
(70,79): 4529,
(80,89): 7688,
(90,199): 3958,
}
deaths_by_age[(0,199)] = total_brackets = sum(deaths_by_age.values()) # 18722
# To properly calculate the IFR, we need to account for the extra 8022 deaths
# for which age information was not available, so we simply assume they are
# distributed proportionally among age brackets
for bracket in deaths_by_age:
deaths_by_age[bracket] *= (total_deaths / total_brackets)
# Population pyramid for Spain (age 0 to 100)
# Source: https://worldpopulationreview.com/countries/spain-population/
# Hack to extract the raw data: https://twitter.com/zorinaq/status/1265380966450622464
# pyramid_spain[N] = number of people of age N
pyramid_spain = [
389071,395760,404555,414953,411842,432086,450617,467032,480928,493573,
506233,510163,501625,485224,469003,450996,438622,436275,440530,443668,
447359,450865,453090,454935,458810,464718,470848,476697,483276,491535,
500604,515444,538403,566972,594959,622001,652353,686993,723042,757510,
792033,815052,820836,814644,807993,799212,788640,777807,766575,752713,
736006,722714,715523,711721,706221,700412,690511,674241,653635,633659,
614107,592701,569064,544537,519985,494201,475071,466281,463940,460575,
457809,451462,438746,421694,405814,390815,372987,351294,327555,303574,
277747,258748,250683,249083,246213,244626,235612,214376,185512,155765,
131040,113392,91852,66359,48324,40084,32862,24229,14184,8251,
12310]
def get_infected(bracket):
'''Returns number of infected people in the given age bracket.'''
i = 0
for age in range(bracket[0], bracket[1] + 1):
for (bracket2, percentage) in prevalence_by_age.items():
if age >= bracket2[0] and age <= bracket2[1] and age < len(pyramid_spain):
i += pyramid_spain[age] * percentage / 100.0
return i
ifrs = {}
for (bracket, deaths) in deaths_by_age.items():
infected = get_infected(bracket)
ifr = 100.0 * deaths / infected
print('Ages {:2} to {:3}: {:7} infected, {:5} deaths, {:6.3f}% IFR'.format(
bracket[0], bracket[1], round(infected), round(deaths), ifr))
if bracket != (0,199):
ifrs[bracket] = ifr
print('True IFR may be higher due to right-censoring and under-reporting of deaths')
# Now we apply the age-stratified IFR to a target country with a different
# population pyramid.
pyramid_usa = [
3931967,3919500,3919461,3930158,3903010,3955644,4008192,4059364,4107872,4156677,
4208742,4241520,4245220,4231306,4220681,4208740,4210781,4236404,4278618,4316059,
4347272,4397310,4474657,4565701,4651027,4737732,4788205,4782769,4739004,4695388,
4645691,4592419,4541165,4490237,4433909,4375200,4315098,4254149,4194587,4137614,
4082405,4040406,4017264,4008404,4003094,4002870,4009404,4022256,4040872,4061465,
4080383,4112964,4165027,4226569,4281521,4332795,4362769,4360922,4333852,4300884,
4260806,4197638,4106208,3993650,3871350,3735929,3602786,3480392,3361570,3234769,
3107225,2956039,2770249,2564001,2361344,2156197,1973453,1827535,1707062,1586129,
1469802,1357365,1245835,1137042,1035221,938832,849231,767290,691462,616131,
563171,502660,421119,320109,246668,212578,178289,135554,84374,52727,
89949]
pyramid_target = pyramid_usa
sim_total = 0
sim_deaths = 0
for (bracket, ifr) in ifrs.items():
for age in range(bracket[0], bracket[1] + 1):
if age < len(pyramid_target):
sim_total += pyramid_target[age]
sim_deaths += pyramid_target[age] * ifr / 100.0
assert sim_total == sum(pyramid_target)
print('IFR on target country assuming disease prevalence equal among ages: {:6.3f}%'.format(100.0 * sim_deaths / sim_total))