add covid_vs_flu analysis
This commit is contained in:
Marc Bevand
@@ -1,16 +1,73 @@
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*Updated: 27 Sep 2020*
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*Updated: 30 Sep 2020*
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Author: Marc Bevand
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This repository contains code to:
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* apply estimates of the age-stratified infection fatality ratio (IFR) of
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COVID-19 to countries' population pyramids, to find their expected overall IFR
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* calculate the age-stratified IFR from the Spanish ENE-COVID serosurvey
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This project studies the age-stratified infection fatality ratio (IFR) of COVID-19:
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* compare COVID-19 to seasonal influenza (flu)
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* calculate the expected overall IFR based on countries' population pyramids
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* calculate the age-stratified IFR of COVID-19 from the Spanish ENE-COVID serosurvey
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# Comparing COVID-19 to seasonal influenza
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![Infection Fatality Ratio of COVID-19 vs. Seasonal Influenza][covid_vs_flu.png]
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The above chart compares the IFR of COVID-19 to the IFR of seasonal influenza. We
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find that COVID-19 is definitely significantly more fatal than seasonal influenza at all
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ages above 30 years. The source code to create this chart is
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[covid_vs_flu.py](covid_vs_flu.py). The COVID-19 IFR curves represent various
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estimates:
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1. ENE-COVID Spanish serosurvey (calculated by `calc_ifr.py`, see next section)
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1. [US CDC](https://web.archive.org/web/20200911222029/https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html) (table 1)
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1. [Verity et al.: Estimates of the severity of coronavirus disease 2019: a model-based analysis](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099%2820%2930243-7/fulltext) (table 1)
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1. [Levin et al.: Assessing the age specificity of infection fatality rates for COVID-19: systematic review, meta-analysis, and public policy implications](https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v5) (table 3)
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1. [Perez-Saez et al.: Serology-informed estimates of SARS-CoV-2 infection fatality risk in Geneva, Switzerland](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30584-3/fulltext)
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1. [Poletti et al.: Age-specific SARS-CoV-2 infection fatality ratio and associated risk factors, Italy, February to April 2020](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.31.2001383) (table 1, column "Any time")
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1. [Picon et al.: Coronavirus Disease 2019 Population-based Prevalence, Risk Factors, Hospitalization, and Fatality Rates in Southern Brazil](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7493765/) (table 2)
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1. [Gudbjartsson et al.: Humoral Immune Response to SARS-CoV-2 in Iceland](https://www.nejm.org/doi/full/10.1056/NEJMoa2026116),
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specifically [Supplementary Appendix 1](https://www.nejm.org/doi/suppl/10.1056/NEJMoa2026116/suppl_file/nejmoa2026116_appendix_1.pdf) (table S7)
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1. [PHAS - Public Health Agency of Sweden: The infection fatality rate of COVID-19 in Stockholm – Technical report](https://www.folkhalsomyndigheten.se/contentassets/53c0dc391be54f5d959ead9131edb771/infection-fatality-rate-covid-19-stockholm-technical-report.pdf) (table B.1)
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1. [O’Driscoll et al.: Age-specific mortality and immunity patterns of SARS-CoV-2 infection in 45 countries](https://www.medrxiv.org/content/10.1101/2020.08.24.20180851v1) (table S4)
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1. [Ward et al.: Antibody prevalence for SARS-CoV-2 in England following first peak of the pandemic: REACT2 study in 100,000 adults](https://www.medrxiv.org/content/10.1101/2020.08.12.20173690v2),
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specifically [Supplementary Appendix](https://www.medrxiv.org/highwire/filestream/93745/field_highwire_adjunct_files/0/2020.08.12.20173690-1.docx) (table S2a, column "Based on confirmed COVID-19 deaths")
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1. [Yang et al.: Estimating the infection fatality risk of COVID-19 in New York City during the spring 2020 pandemic wave](https://www.medrxiv.org/content/10.1101/2020.06.27.20141689v2) (table 1)
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1. [Molenberghs et al.: Belgian Covid-19 Mortality, Excess Deaths, Number of Deaths per Million, and Infection Fatality Rates](https://www.medrxiv.org/content/10.1101/2020.06.20.20136234v1) (table 6)
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The seasonal influenza IFR curves represent data from the US CDC on multiple seasons of flu:
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1. [2018-2019 influenza burden](https://www.cdc.gov/flu/about/burden/2018-2019.html)
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1. [2017-2018 influenza burden](https://www.cdc.gov/flu/about/burden/2017-2018.htm)
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1. [2016-2017 influenza burden](https://www.cdc.gov/flu/about/burden/2016-2017.html)
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1. [2015-2016 influenza burden](https://www.cdc.gov/flu/about/burden/2015-2016.html)
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1. [2014-2015 influenza burden](https://www.cdc.gov/flu/about/burden/2014-2015.html)
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However, these CDC statistics (eg. table 1 in "2018-2019 influenza burden",)
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only give the estimated number of symptomatic illnesses. We must account for
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asymptomatic ones as well to calculate the IFR.
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In [Key Facts About Influenza
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(Flu)](https://www.cdc.gov/flu/about/keyfacts.htm) the CDC implies 55-60% of
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illnesses are symptomatic:
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> «on average, about 8% of the U.S. population gets sick from flu each season,
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> with a range of between 3% and 11%, depending on the season.
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> [...]
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> The commonly cited 5% to 20% estimate was based on a study that examined both
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> symptomatic and asymptomatic influenza illness, which means it also looked at
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> people who may have had the flu but never knew it because they didn’t have
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> any symptoms. The 3% to 11% range is an estimate of the proportion of people
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> who have symptomatic flu illness.»
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Thus, the CDC acknowledges that 55-60% of illnesses are symptomatic (3/5 = 60%,
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and 11/20 = 55%.) We use the mid-point, 57.5%, to infer the number of asymptomatic
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illnesses:
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total_illnesses = symptomatic_illnesses / .575
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# Age-stratified IFR applied to countries' population pyramids
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The script [apply_ifr.py](apply_ifr.py) uses a handful of age-stratified
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IFR estimates and applies them to countries' population pyramids, to
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IFR estimates (from the chart above) and applies them to countries' population pyramids, to
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find their expected overall IFR assuming equal prevalence of the disease among all
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age groups.
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@@ -18,16 +75,6 @@ Of course, the real-world overall IFR will dependent on many factors: varying
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prevalence among age groups, underlying health conditions, access to
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healthcare, socioeconomic status, ethnicity, etc.
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IFR estimates come from:
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1. ENE-COVID Spanish serosurvey (calculated by `calc_ifr.py`, see next section)
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1. [US CDC](https://web.archive.org/web/20200911222029/https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html) (table 1)
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1. [Verity et al.: Estimates of the severity of coronavirus disease 2019: a model-based analysis](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099%2820%2930243-7/fulltext) (table 1)
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1. [Levin et al.: Assessing the age specificity of infection fatality rates for COVID-19: systematic review, meta-analysis, and public policy implications](https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v5) (table 3)
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1. [Gudbjartsson et al.: Humoral Immune Response to SARS-CoV-2 in Iceland](https://www.nejm.org/doi/full/10.1056/NEJMoa2026116),
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[Supplementary Appendix 1](https://www.nejm.org/doi/suppl/10.1056/NEJMoa2026116/suppl_file/nejmoa2026116_appendix_1.pdf) (table S7)
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1. [O’Driscoll et al.: Age-specific mortality and immunity patterns of SARS-CoV-2 infection in 45 countries](https://www.medrxiv.org/content/10.1101/2020.08.24.20180851v1) (table S4)
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Data for the population pyramids comes from the
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[United Nations](https://population.un.org/wpp/Download/Standard/Population/),
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specifically the first sheet of [Population by Age Groups - Both Sexes](https://population.un.org/wpp/Download/Files/1_Indicators%20%28Standard%29/EXCEL_FILES/1_Population/WPP2019_POP_F07_1_POPULATION_BY_AGE_BOTH_SEXES.xlsx). This excel file was converted to CSV format:
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Executable
+375
@@ -0,0 +1,375 @@
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#!/usr/bin/python3
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#
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# Author: Marc Bevand — @zorinaq
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import sys
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import matplotlib.pyplot as plt
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import matplotlib.ticker as ticker
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import numpy as np
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import scipy.stats
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from scipy.optimize import curve_fit
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maxage = 100
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# Age-stratified IFR estimates for COVID-19
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ifrs_covid = [
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# Calculated from Spanish ENE-COVID study
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# (see calc_ifr.py)
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('ENE-COVID', {
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(0,9): 0.003,
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(10,19): 0.004,
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(20,29): 0.015,
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(30,39): 0.030,
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(40,49): 0.064,
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(50,59): 0.213,
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(60,69): 0.718,
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(70,79): 2.384,
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(80,89): 8.466,
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(90,maxage): 12.497,
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}),
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# US CDC estimate as of 10 Sep 2020
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# https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html
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# (table 1)
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('US CDC', {
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(0,19): 0.003,
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(20,49): 0.02,
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(50,69): 0.5,
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(70,maxage): 5.4,
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}),
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# Verity et al.
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# https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30243-7/fulltext
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# (table 1)
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('Verity', {
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(0,9): 0.00161,
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(10,19): 0.00695,
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(20,29): 0.0309,
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(30,39): 0.0844,
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(40,49): 0.161,
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(50,59): 0.595,
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(60,69): 1.93,
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(70,79): 4.28,
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(80,maxage): 7.80,
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}),
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# Levin et al.
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# https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v5
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# (table 3)
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('Levin', {
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(0,34): 0.004,
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(35,44): 0.06,
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(45,54): 0.2,
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(55,64): 0.7,
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(65,74): 2.3,
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(75,84): 7.6,
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(85,maxage): 22.3,
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}),
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# Perez-Saez et al.
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# https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30584-3/fulltext
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('Perez-Saez', {
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(5,9): 0.0016,
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(10,19): 0.00032,
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(20,49): 0.0092,
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(50,64): 0.14,
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(65,maxage): 5.6,
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}),
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# Poletti et al.
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# https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.31.2001383
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# (table 1, column "Any time")
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('Poletti', {
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(0,19): 0,
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(20,49): 0,
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(50,59): 0.46,
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(60,69): 1.42,
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(70,79): 6.87,
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(80,maxage): 18.35,
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}),
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# Picon et al.
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# https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7493765/
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# (table 2)
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('Picon', {
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(20,39): 0.08,
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(40,59): 0.24,
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(60,maxage): 4.63,
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}),
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# Gudbjartsson et al.: Humoral Immune Response to SARS-CoV-2 in Iceland
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# https://www.nejm.org/doi/full/10.1056/NEJMoa2026116
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# Supplementary Appendix 1
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# https://www.nejm.org/doi/suppl/10.1056/NEJMoa2026116/suppl_file/nejmoa2026116_appendix_1.pdf
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# (table S7)
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('Gudbjartsson', {
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(0,70): 0.1,
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(71,80): 2.4,
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(81,maxage): 11.2,
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}),
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# Public Health Agency of Sweden
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# https://www.folkhalsomyndigheten.se/contentassets/53c0dc391be54f5d959ead9131edb771/infection-fatality-rate-covid-19-stockholm-technical-report.pdf
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# (table B.1)
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('PHAS', {
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(0,49): 0.01,
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(50,59): 0.27,
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(60,69): 0.45,
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(70,79): 1.92,
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(80,89): 7.20,
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(90,maxage): 16.21,
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}),
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# O’Driscoll et al.: Age-specific mortality and immunity patterns of SARS-CoV-2 infection in 45 countries
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# https://www.medrxiv.org/content/10.1101/2020.08.24.20180851v1
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# (table S4)
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('O’Driscoll', {
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(0,4): 0.002,
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(5,9): 0,
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(10,14): 0,
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(15,19): 0.002,
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(20,24): 0.004,
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(25,29): 0.009,
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(30,34): 0.017,
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(35,39): 0.029,
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(40,44): 0.053,
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(45,49): 0.086,
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(50,54): 0.154,
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(55,59): 0.241,
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(60,64): 0.359,
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(65,69): 0.642,
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(70,74): 1.076,
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(75,79): 2.276,
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(80,maxage): 7.274,
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}),
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# Ward et al.: Antibody prevalence for SARS-CoV-2 in England following first peak of the pandemic: REACT2 study in 100,000 adults
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# https://www.medrxiv.org/content/10.1101/2020.08.12.20173690v2
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# Supplementary Appendix
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# https://www.medrxiv.org/highwire/filestream/93745/field_highwire_adjunct_files/0/2020.08.12.20173690-1.docx
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# (table S2a, column "Based on confirmed COVID-19 deaths")
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('REACT2', {
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(15,44): 0.03,
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(45,64): 0.52,
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(65,74): 3.87,
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(75,maxage): 18.71,
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}),
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# Yang et al.: Estimating the infection fatality risk of COVID-19 in New York City during the spring 2020 pandemic wave
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# https://www.medrxiv.org/content/10.1101/2020.06.27.20141689v2
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# (table 1)
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('Yang', {
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(0,24): 0.0097,
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(25,44): 0.12,
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(45,64): 0.94,
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(65,74): 4.87,
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(75,maxage): 14.17,
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}),
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# Molenberghs et al.: Belgian Covid-19 Mortality, Excess Deaths, Number of Deaths per Million, and Infection Fatality Rates
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# https://www.medrxiv.org/content/10.1101/2020.06.20.20136234v1
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# (table 6)
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('Molenberghs', {
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(0,24): 0.0005,
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(25,44): 0.017,
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(45,64): 0.21,
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(65,74): 2.24,
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(75,84): 4.29,
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(85,maxage): 11.77,
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}),
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]
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# In the CDC influenza burden pages (eg. table 1 in
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# https://www.cdc.gov/flu/about/burden/2018-2019.html), only symptomatic
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# illnesses are estimated. We must account for asymptomatic ones as well.
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#
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# In https://www.cdc.gov/flu/about/keyfacts.htm the CDC implies 55-60% of
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# illnesses are symptomatic:
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#
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# «on average, about 8% of the U.S. population gets sick from flu each season,
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# with a range of between 3% and 11%, depending on the season.
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# [...]
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# The commonly cited 5% to 20% estimate was based on a study that examined both
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# symptomatic and asymptomatic influenza illness, which means it also looked at
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# people who may have had the flu but never knew it because they didn’t have
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# any symptoms. The 3% to 11% range is an estimate of the proportion of people
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# who have symptomatic flu illness.»
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#
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# The CDC thus acknowledges that 55-60% of illnesses are symptomatic:
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# 3/5 = 60%
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# 11/20 = 55%
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#
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# We use the mid-point, 57.5%, as an estimate to account for both symptomatic
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# and asymptomatic illnesses.
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cdc_sympt = .575
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# Age-stratified IFR estimates for seasonal influenza
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ifrs_flu = [
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# US CDC 2018-2019 influenza burden
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# https://www.cdc.gov/flu/about/burden/2018-2019.html
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('US CDC 2018-2019', {
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(0,4): 266/3_633_104 * 100 * cdc_sympt,
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(5,17): 211/7_663_310 * 100 * cdc_sympt,
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(18,49): 2_450/11_913_203 * 100 * cdc_sympt,
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(50,64): 5_676/9_238_038 * 100 * cdc_sympt,
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(65,maxage): 25_555/3_073_227 * 100 * cdc_sympt,
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}),
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# US CDC 2017-2018 influenza burden
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# https://www.cdc.gov/flu/about/burden/2017-2018.htm
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('US CDC 2017-2018', {
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(0,4): 115/3_678_342 * 100 * cdc_sympt,
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(5,17): 528/7_512_601 * 100 * cdc_sympt,
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(18,49): 2_803/14_428_065 * 100 * cdc_sympt,
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(50,64): 6_751/13_237_932 * 100 * cdc_sympt,
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(65,maxage): 50_903/5_945_690 * 100 * cdc_sympt,
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}),
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# US CDC 2016-2017 influenza burden
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# https://www.cdc.gov/flu/about/burden/2016-2017.html
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('US CDC 2016-2017', {
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(0,4): 126/2_381_218 * 100 * cdc_sympt,
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(5,17): 125/6_452_110 * 100 * cdc_sympt,
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(18,49): 1_365/9_292_804 * 100 * cdc_sympt,
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(50,64): 3_780/7_448_184 * 100 * cdc_sympt,
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(65,maxage): 32_833/3_646_206 * 100 * cdc_sympt,
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}),
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# US CDC 2015-2016 influenza burden
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# https://www.cdc.gov/flu/about/burden/2015-2016.html
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('US CDC 2015-2016', {
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(0,4): 180/2_195_276 * 100 * cdc_sympt,
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(5,17): 88/4_140_269 * 100 * cdc_sympt,
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(18,49): 1_703/9_121_242 * 100 * cdc_sympt,
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(50,64): 3_277/6_640_358 * 100 * cdc_sympt,
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(65,maxage): 17_458/1_407_174 * 100 * cdc_sympt,
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}),
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# US CDC 2014-2015 influenza burden
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# https://www.cdc.gov/flu/about/burden/2014-2015.html
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('US CDC 2014-2015', {
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(0,4): 396/3_207_314 * 100 * cdc_sympt,
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(5,17): 407/6_388_401 * 100 * cdc_sympt,
|
||||
(18,49): 985/8_606_083 * 100 * cdc_sympt,
|
||||
(50,64): 4_780/7_283_766 * 100 * cdc_sympt,
|
||||
(65,maxage): 44_808/4_679_888 * 100 * cdc_sympt,
|
||||
}),
|
||||
|
||||
]
|
||||
|
||||
def col(is_covid, i):
|
||||
if is_covid:
|
||||
return plt.cm.OrRd(255 - i * 8)
|
||||
else:
|
||||
return plt.cm.Blues(255 - i * 30)
|
||||
|
||||
def plot(ax, ifrs, is_covid):
|
||||
lstyles = ('solid', 'dashed', 'dashdot', 'dotted')
|
||||
markers = ('o', 's', 'v', '^', '<', '>', 'P', '*', 'X', 'D', 'p')
|
||||
i = 0
|
||||
for ifr in ifrs:
|
||||
name, ifr_by_age = ifr
|
||||
x, y = [], []
|
||||
for age_group, ifr_val in sorted(ifr_by_age.items()):
|
||||
# place the marker at the middle (mean) of the age group
|
||||
x.append(np.mean(age_group))
|
||||
y.append(ifr_val)
|
||||
ax.plot(x, y, color=col(is_covid, i), label=name, lw=1, alpha=.8,
|
||||
marker=markers[i % len(markers)], ms=4,
|
||||
ls=lstyles[i % len(lstyles)])
|
||||
i += 1
|
||||
|
||||
def interpolate(age, x1, y1, x2, y2):
|
||||
def func_exp(x, a, b):
|
||||
return a * (b ** x)
|
||||
popt, pcov = curve_fit(func_exp, [x1, x2], [y1, y2])
|
||||
return func_exp(age, *popt)
|
||||
|
||||
def ifr_for_model(age, ifr_model):
|
||||
# calculate IFR for age <age>
|
||||
m_prev = ifr_prev = None
|
||||
# iterate over the age groups in order
|
||||
for age_group, ifr in sorted(ifr_model[1].items()):
|
||||
m = np.mean(age_group)
|
||||
if m == age:
|
||||
return ifr
|
||||
if m > age:
|
||||
if ifr_prev == None:
|
||||
sys.stderr.write(f'{ifr_model[0]}: no data, age {age} too young\n')
|
||||
return None
|
||||
if ifr_prev == 0 or ifr == 0:
|
||||
sys.stderr.write(f'{ifr_model[0]}: ignoring IFR zero for age {age}\n')
|
||||
return None
|
||||
return interpolate(age, m_prev, ifr_prev, m, ifr)
|
||||
m_prev, ifr_prev = m, ifr
|
||||
sys.stderr.write(f'{ifr_model[0]}: no data, age {age} too old\n')
|
||||
return None
|
||||
|
||||
def mean_ifr(age, ifr_models):
|
||||
# calculate the geometric mean of IFR estimates in <ifr_models> for age <age>
|
||||
values = []
|
||||
for ifr_model in ifr_models:
|
||||
ifr = ifr_for_model(age, ifr_model)
|
||||
if ifr != None:
|
||||
values.append(ifr)
|
||||
return scipy.stats.gmean(values)
|
||||
|
||||
def plot_comp(ax):
|
||||
for age in np.arange(30, 90, 10):
|
||||
y1 = mean_ifr(age, ifrs_flu)
|
||||
y2 = mean_ifr(age, ifrs_covid)
|
||||
assert not np.isnan(y1) and not np.isnan(y2)
|
||||
ax.annotate(s='', xy=(age, y1), xytext=(age, y2),
|
||||
arrowprops=dict(arrowstyle='|-|', shrinkA=0, shrinkB=0,
|
||||
alpha=.7))
|
||||
ax.text(age, y1 * .6, f'{y2/y1:.1f}×', ha='center', va='top',
|
||||
weight='bold', size=12, alpha=.7)
|
||||
|
||||
def main():
|
||||
(fig, ax) = plt.subplots(dpi=300, figsize=(8,6))
|
||||
# plot ifrs_covid
|
||||
plot(ax, ifrs_covid, True)
|
||||
ax.text(3, 35, 'COVID-19:')
|
||||
handles, labels = fig.gca().get_legend_handles_labels()
|
||||
first_legend = ax.legend(handles=handles, labels=labels, loc='upper left',
|
||||
frameon=False, fontsize='x-small', handlelength=5)
|
||||
fig.gca().add_artist(first_legend)
|
||||
# plot ifrs_flu
|
||||
plot(ax, ifrs_flu, False)
|
||||
# plot vertical comparison bars
|
||||
plot_comp(ax)
|
||||
ax.semilogy()
|
||||
ax.grid(True, which='minor', linewidth=0.1)
|
||||
ax.grid(True, which='major', linewidth=0.3)
|
||||
ax.spines['top'].set_visible(False)
|
||||
ax.spines['bottom'].set_visible(True)
|
||||
ax.spines['left'].set_visible(True)
|
||||
ax.spines['right'].set_visible(False)
|
||||
ax.set_ylabel('IFR (%)')
|
||||
ax.set_xlabel('Age')
|
||||
ax.set_xlim(left=0)
|
||||
ax.xaxis.set_minor_locator(ticker.MultipleLocator(base=5))
|
||||
ax.xaxis.set_major_locator(ticker.MultipleLocator(base=10))
|
||||
ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g'))
|
||||
ax.text(75, .0016, 'Seasonal Influenza:')
|
||||
handles, labels = fig.gca().get_legend_handles_labels()
|
||||
x = len(ifrs_flu)
|
||||
ax.legend(handles=handles[-x:], labels=labels[-x:], loc='lower right',
|
||||
frameon=False, fontsize='x-small', handlelength=5)
|
||||
fig.suptitle('Infection Fatality Ratio of COVID-19 vs. Seasonal Influenza')
|
||||
ax.text(0, -0.11,
|
||||
'Source: https://github.com/mbevand/covid19-age-stratified-ifr\n'
|
||||
'Note: the vertical lines on two COVID-19 IFR curves (Poletti and O’Driscoll) are caused by the IFR being\n'
|
||||
'estimated to be zero by Poletti for age groups 0-19 and 20-49, and by O’Driscoll for 5-9 and 10-14.\n',
|
||||
transform=ax.transAxes, fontsize='small', verticalalignment='top',
|
||||
)
|
||||
ax.text(1, 1, 'Created by: Marc Bevand — @zorinaq',
|
||||
transform=ax.transAxes, fontsize='xx-small', va='top', ha='right')
|
||||
fig.savefig('covid_vs_flu.png', bbox_inches='tight')
|
||||
plt.close()
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
||||
Reference in New Issue
Block a user