Marc Bevand
99 lines
4.9 KiB
Markdown
99 lines
4.9 KiB
Markdown
# Calculating the age-stratified infection fatality ratio (IFR) of COVID-19
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*Updated: 10 June 2020*
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Author: Marc Bevand
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The largest serological prevalence survey of COVID-19 was conducted by Spain
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during the second round of a study that analyzed 63 564 samples between 18 May
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2020 and 01 June 2020. We used its [provisional results][sero] published on 03
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June to calculate the overall and age-stratified IFR of COVID-19 with the
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Python script `calc_ifr.py`:
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```
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$ ./calc_ifr.py
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Ages 0 to 9: 115013 infected, 4 deaths, 0.003% IFR
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Ages 10 to 19: 177929 infected, 7 deaths, 0.004% IFR
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Ages 20 to 29: 212099 infected, 32 deaths, 0.015% IFR
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Ages 30 to 39: 281290 infected, 86 deaths, 0.030% IFR
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Ages 40 to 49: 447942 infected, 287 deaths, 0.064% IFR
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Ages 50 to 59: 410213 infected, 874 deaths, 0.213% IFR
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Ages 60 to 69: 334709 infected, 2404 deaths, 0.718% IFR
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Ages 70 to 79: 270572 infected, 6451 deaths, 2.384% IFR
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Ages 80 to 89: 131703 infected, 11150 deaths, 8.466% IFR
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Ages 90 to 199: 46631 infected, 5827 deaths, 12.497% IFR
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Ages 0 to 199: 2428102 infected, 27121 deaths, 1.117% IFR
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```
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The average IFR for Spain is **1.117%**. However the true IFR may be higher due
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to right-censoring, under-reporting of deaths, or low specificity of the serological test;
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or the true IFR may be lower due to low sensitivity of the serological test.
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The Spanish serological study remains the largest published study available to
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this day. The age-stratified IFR was calculated from three sources:
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1. Detailed *prevalence data for age brackets*, from the [serosurvey][sero] (table 1)
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1. *Total deaths* and *deaths per age bracket* from the [Ministry of Health's daily report for 29 May][daily] (table 2 and table 3)
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1. *Population pyramid* for Spain, from [worldpopulationreview.com][wpop]
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In order to minimize right-censoring (deaths lagging infections,) the
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parameters *total deaths* and *deaths per age bracket* should be obtained from
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a point in time as close as possible to when the serosurvey was conducted (18
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May to 01 June, preferably closer to the mid-point 25 May.) This is because the
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seroconversion time is roughly the same as the time between infection and
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death. We found only two Ministry of Health reports in this time period that
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document deaths per age bracket: [18 May][dailyalt], [29 May][daily]. However
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the Ministry of Health has made significant corrections to deaths statistics on
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25 May by subtracting approximately 2 000 deaths. Therefore we trusted the
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statistics from 29 May over those of 18 May. Furthermore, 29 May is closer to
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the mid-point.
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Important detail to note: there were 27 121 total deaths, however age information
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was only available for 20 585 deaths, and was missing for 6 536 deaths.
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We assume that these 6 536 deaths were distributed proportionally—not equally—among age
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brackets, which seems to be a reasonable assumption.
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Regarding the specificity of the commercial test used (COVID-19 IgG Rapid Test
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Cassette by Zhejiang Orient Gene Biotech Co Ltd) we found various claims, all
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100% or close, so no significant false positives are expected:
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* 100% claimed by the manufacturer ([serosurvey][sero], page 3)
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* 100% measured by the Ministry of Health ([serosurvey][sero], page 3)
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* 99.2% measured by a [third-party][hoffman]
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However the sensitivity is more uncertain:
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* 97% claimed by the manufacturer ([serosurvey][sero], page 3)
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* 79% measured by the Ministry of Health ([serosurvey][sero], page 3)
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* 93.1% measured by a [third-party][hoffman]
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So a false negative rate anywhere from 3% to 21% could be possible, and we
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think it is premature to adjust IFR calculations given the exact sensitivity is
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not known.
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# Applying the age-stratified IFR to other countries
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The script `calc_ifr.py` is also able to apply the age-stratified IFR to
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another population pyramid, thus calculating the expected average IFR for other
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countries.
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In the second half of the script, edit `pyramid_target` with the demographics data.
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As an example, we supply pyramid data for the United States and calculate an IFR of **0.658%**:
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```
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$ ./calc_ifr.py
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[...]
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IFR on target country assuming disease prevalence equal among ages: 0.658%
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```
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However the average IFR is highly dependent on factors other than age: varying
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prevalence among age brackets, underlying health conditions, access to
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healthcare, socioeconomic status, ethnicity, etc, so this estimate should be
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interpreted with caution.
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[sero]: https://www.mscbs.gob.es/ciudadanos/ene-covid/docs/ESTUDIO_ENE-COVID19_SEGUNDA_RONDA_INFORME_PRELIMINAR.pdf
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[daily]: https://www.mscbs.gob.es/profesionales/saludPublica/ccayes/alertasActual/nCov-China/documentos/Actualizacion_120_COVID-19.pdf
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[dailyalt]: https://www.mscbs.gob.es/profesionales/saludPublica/ccayes/alertasActual/nCov-China/documentos/Actualizacion_109_COVID-19.pdf
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[wpop]: https://worldpopulationreview.com/countries/spain-population/
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[hoffman]: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7178815/
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