Statistics associated with the lethality of COVID-19 by age group and gender in Mexico

We analyzed outcomes of 102,985 SARS-CoV-2 confirmed cases of patients at- tending the IMSS (Mexican Institute for National Insurance) from January 2 to August 3, 2020. We calculated relative IFR by age group and gender and intro- duced the concept of adjusted lethalities, that can be used to project the burden of the disease for a population with different demographic characteristics.

COVID-19, SARS-CoV-2, IFR, Lethality, Age, Gender, Adjusted lethality 1. Introduction Since it was first identified in pneumonia patients in Wuhan, China, the coro- navirus disease 2019 (COVID-19) by severe acute respiratory syndrome coron- avirus 2 (SARS-CoV-2) has been characterized by its fast-spreading and high related disease burden [1]. The spectrum of symptoms is wide and ranges from5 asymptomatic infection to severe respiratory illness [2]. By August 4, 2020, al- most 20 million confirmed cases of COVID-19 had been reported globally and a fatal outcome was registered in nearly a half million of them [3]. Gender and age- related differences in disease severity and risk of death have been documented [4].10 ∗Corresponding author Email addresses: [email protected] (Carlos Hernandez-Suarez), [email protected] (Efren Murillo-Zamora) Preprint submitted to medRxive August 8, 2020 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. The lethality of a disease, also known as Infection Fatality Rate (IFR) is the fraction of infected individuals that die from the disease. It’s estimation is of the upmost importance for the design of and application of containment measures and to decide if lockdowns are implemented as when these should be reinforced or lifted. Unfortunately, our data does not come from a random sample and we15 cannot estimate the IFR, instead, we estimate the relative share of the IFR by age group and gender and introduce the concept of adjusted lethalities that can be used to project the burden of the disease for a population whose demographic characteristics is known. Methodology20 We used the database of the Instituto Mexicano de Seguro Social (IMSS, acronym for Mexican Institute for National Insurance) with confirmed SARS- CoV-2 cases. The IMSS provides health services to about 10% of the population in Mexico, over 12 million persons. The database on SARS-CoV-2 we used contains confirmed cases from January 2 to June 23, 2020. We included only25 cases with disease outcome as dead or recovered, leaving a database with 102,985 cases, from which 55 % were males and 45% females. When a patient is diagnosed with COVID-19, it follows one of the paths depicted in Figure 1. With this data we constructed Table 1 after dividing the population in seven age categories and two genders.30 Table 2 shows a processing of the information in Table 1. Vectors h, c, d and dc in Table 2 are described as follows: h = relative frequency of hospitalized patients. c = fraction requiring ICU among those that went into hospitalization.35 d = fraction dying among those that went into hospitalization. dc = fraction dying among those that went into ICU. As mentioned before, it is not possible to estimate the IFR from the data 2 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint N Hospital Dead Home Health servicesICUN1N2N3 N4 N5 N6 N0 Figure 1: Transitions in our model: N0 + N1 = N, N2 + N3 + N4 = N1, N5 + N6 = N3 available (Table 1) since the death rates are conditional on patients mostly40 symptomatic and thus they are not a representative sample of the response to an infection. Nevertheless, there is a couple of things that we can obtain from Table 2. The fist one is the relative lethality and the second adjusted lethality. 2. Relative lethality Table 2 tells us, for instance, that the probability that a female person in45 age group 40-49 that is hospitalized from infection with SARS-CoV-2 dies is 0.3548, but this does not provides information on the probability that a female infected person in age group 40-49 dies from the disease. Nevertheless, observe that if fij is the fraction in the population of individuals of gender i,i = 1, 2 and group age j,j = 1, 2,..., 7., and we assume that everyone is equally likely50 to become infected but there is a differential response to the disease, then, if p is the fraction of individuals in the population that is infected and βij is the fraction of infected individuals of gender i and age group j that become hospitalized, then: 3 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint fij p βij∝hij (1) Wherehij is the fraction of hospitalized that belong to age groupi and genderj.55 Now, if αij is the fraction of individuals hospitalized that die from COVID-19, then fij p βijαij∝hijdij (2) where dij is the fraction of individuals of these hospitalized that dies. Letθij be the lethality or infection fatality rate of gender i and age group j, then, the lethality of gender i and age group j can be written as:60 θij =βijαij. (3) Thus, the IFR by gender and group age follows this relationship: θij∝hijdij/fij. (4) The reason why we only establish that θij is proportional to some value is because we ignore the value of p, the true proportion of infected individuals in the population. Thus, we define θ∗ ij as the relative lethalitiy : θ∗ ij =hijdij/fij (5) Even although the value of p is not known, the ratio of any two relative lethalities θ∗ ij/θ∗ kl reflects the ratio of the true lethalities, that is: θ∗ ij/θ∗ kl =θij/θkl, therefore this quotient can be used to compare the lethality of any two groups.65 Table 3 shows in the last column the relative infection fatality rates in (5) , after normalization. In this table f M and f F are the relative frequencies by age group and gender in the Mexican population. In this table we can see, for instance, that the lethality of COVID-19 in age group 60+ is 0 .37511/0.19795 = 1.9 times higher in males than in females, and that the lethality in the 60+ group70 compared to the group with less than 20 years age is: 4 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint 0.37511 + 0.19705 0.00068 + 0.00024 + 0.00041 + 0.00048= 317.7 times larger. Table 3 also shows that the lethality among people 50 years or older is about 6 times larger than among people less than 50 years old. 3. Adjusted lethality It is possible to estimate the true values of θM andθF . The lethality of the75 disease is the probability that a person at random that has been infected with SARS-CoV-2 dies, which is: IFR = f′ MθM + f′ FθF (6) which assumes all individuals are equally likely to become infected. If we have an estimate of the lethality of the disease, θ, then we can rescale θ∗ M and θ∗ F multiplying by a constant c so that80 θ =c f′ Mθ∗ M +c f′ Fθ∗ F (7) Some estimates of the IFR are in the range 0 .05%− 0.25% [5, 6, 7]. Here we will use the lethality reported by [5] of 86 in 100, 000 (about 0.1%) because it is a more recent study with a large sample size, thus, we use θ = 0.001. The adjusted lethalities by age group and gender are shown in Table 4. One immediate application of Table 4 is the possibility of projecting the85 IFR for another population whose demographics by age and gender are known. Consider for instance the demographics of the Za’atari refugee camp, in Jordan1, which is shown in Table 5. We use θM andθF from Table 4 and the fM and fF from the camp’s demographic and thus the IFR projected for this camp is: IFR = f′ MθM + f′ FθF = 0.00037 1https://data2.unhcr.org/en/situations/syria/location/53 5 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint Observe this adjusted lethality is about 2.7 times smaller than the overall90 IFR, which is due to the fact that Za’atari refugee camp is a young population with 3/4 of the refugees being less than 30 years old. Although this comparison used θ = 0.001 as the overall IFR of SARS-CoV-2, the observed ratio of 2.7 is independent of this value because the adjusting constant c in 7 cancels out. Clearly, this projection includes only demographic factors and not other health95 and socioeconomic factors or availability of health services. Figure 2 shows a comparison between the demographics of the Za’atari camp and the Adjusted lethalities from Table 4 by age group and gender. 0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% 0.8% 0.9% 1.0% 1 2 3 4 5 6 7 Male Female Figure 2: Population frequency in Za’atari camp (left) and Adjusted lethalities from Table 4 (right) by age and gender. For this particular camp, the lethality affects a group of individuals that are found at a very low frequency in the camp. The distribution of deaths across age groups and gender. Another use of the adjusted lethalities in Table 4 is the estimation of the100 distribution of deaths across group ages and genders. The question we want to answer is: what is the probability that a dead individual belongs to a particular gender and age group? This is clearly given by fM◦θM and fF◦θF after normalization. For the Mexican population, a plot of this distribution is given in Figure 3.105 6 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 Male Female Figure 3: The projected distribution of deaths across age groups and gender for Mexico’s population. 4. Bibliography [1] F. Zhou, T. Yu, R. Du, G. Fan, Y. Liu, Z. Liu, J. Xiang, Y. Wang, B. Song, X. Gu, et al., Clinical course and risk factors for mortality of adult inpatients with covid-19 in wuhan, china: a retrospective cohort study, The lancet. [2] K. Gostic, A. C. Gomez, R. O. Mummah, A. J. Kucharski, J. O. Lloyd-110 Smith, Estimated effectiveness of symptom and risk screening to prevent the spread of covid-19, Elife 9 (2020) e55570. doi:10.7554/eLife.55570. [3] World Health Organization, Coronavirus disease (COVID-2019) situation reports: Situation report - 150, June 18, 2020, Accessed on June 19, 2020. URL https://www.who.int/docs/default-source/coronaviruse/115 situation-reports/20200618-covid-19-sitrep-150.pdf?sfvrsn= aa9fe9cf_2 [4] W. Tian, W. Jiang, J. Yao, C. J. Nicholson, R. H. Li, H. H. Sigurslid, L. Wooster, J. I. Rotter, X. Guo, R. Malhotra, Predictors of mortality in hospitalized covid-19 patients: A systematic review and meta-analysis, Jour-120 nal of Medical Virologydoi:10.1002/jmv.26050. 7 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint [5] C. Erikstrup, C. E. Hother, O. B. V. Pedersen, K. Mølbak, R. L. Skov, D. K. Holm, S. Sækmose, A. C. Nilsson, P. T. Brooks, J. K. Boldsen, C. Mikkelsen, M. Gybel-Brask, E. Sørensen, K. M. Dinh, S. Mikkelsen, B. K. Møller, T. Haunstrup, L. Harritshøj, B. A. Jensen, H. Hjalgrim,125 S. T. Lillevang, H. Ullum, Estimation of SARS-CoV-2 infection fatal- ity rate by real-time antibody screening of blood donors, medRxiv doi: 10.1101/2020.04.24.20075291. [6] H. Streeck, B. Schulte, B. Kuemmerer, E. Richter, T. Hoeller, C. Fuhrmann, E. Bartok, R. Dolscheid, M. Berger, L. Wessendorf, M. Eschbach-Bludau,130 A. Kellings, A. Schwaiger, M. Coenen, P. Hoffmann, M. Noethen, A.-M. Eis-Huebinger, M. Exner, R. Schmithausen, M. Schmid, B. Kuemmerer, Infection fatality rate of SARS-CoV-2 infection in a german community with a super-spreading event, medRxivdoi:10.1101/2020.05.04.20090076. [7] J. Ioannidis, The infection fatality rate of COVID-19 inferred from sero-135 prevalence data, medRxivdoi:10.1101/2020.05.13.20101253. Conflicts of interest Authors declare no conflict of interest. Funding and study approval This work is part of the program “Building the Evidence on Protracted140 Forced Displacement: A Multi-Stakeholder Partnership”. The program is funded by UK aid from the United Kingdom’s Department for International Develop- ment (DFID), it is managed by the World Bank Group (WBG) and was estab- lished in partnership with the United Nations High Commissioner for Refugees (UNHCR). The scope of the program is to expand the global knowledge on145 forced displacement by funding quality research and disseminating results for the use of practitioners and policy makers. This work does not necessarily reflect 8 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint the views of DFID, the WBG or UNHCR. This study had approval R-2020-601- 07 by the Health Research Ethics Committee (601) of the IMSS. 9 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint Table 1: Number of transitions between compartments in Figure 1 by age group and gender. Males Age N N 0 N1 N2 N3 N4 N5 N6 0-9 256 97 159 116 20 23 14 6 10-19 367 261 106 83 6 17 3 3 20-29 5,627 4,585 1,042 852 8 182 6 2 30-39 10,829 7,706 3,123 2,289 29 805 14 15 40-49 11,788 6,153 5,635 3,539 65 2,031 32 33 50-59 11,566 3,799 7,767 3,914 65 3,788 24 41 60 + 16,392 2,599 13,793 4,407 111 9,275 27 84 Total 56,825 25,200 31,625 15,200 304 16,121 120 184 Females Age N N 0 N1 N2 N3 N4 N5 N6 0-9 205 90 115 81 17 17 14 3 10-19 423 316 107 80 3 24 2 1 20-29 5,778 4,972 806 684 15 107 13 2 30-39 9,894 8,211 1,683 1,330 29 324 23 6 40-49 10,128 6,868 3,260 2,260 22 978 8 14 50-59 8,274 3,515 4,759 2,755 33 1,971 13 20 60 + 11,458 2,068 9,390 3,600 54 5,736 12 42 Total 46,160 26,040 20,120 10,790 173 9,157 85 88 10 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint Table 2: Statistics associated with the transition of COVID-19 patients between compartments in Figure 1. h = distribution of patients arriving to hospitals. c = probability of requiring ICU among those that went into hospitalization; d = probability of dying among those that went into hospitalization; dc = probability of dying among those that went into ICU. Males Age h c d d c 0-9 0.0031 0.1258 0.1824 0.3000 10-19 0.0020 0.0566 0.1887 0.5000 20-29 0.0201 0.0077 0.1766 0.2500 30-39 0.0604 0.0093 0.2626 0.5172 40-49 0.1089 0.0115 0.3663 0.5077 50-59 0.1501 0.0084 0.4930 0.6308 60 + 0.2666 0.0080 0.6785 0.7568 Females Age h c d d c 0-9 0.0022 0.1478 0.1739 0.1765 10-19 0.0021 0.0280 0.2336 0.3333 20-29 0.0156 0.0186 0.1352 0.1333 30-39 0.0325 0.0172 0.1961 0.2069 40-49 0.0630 0.0067 0.3043 0.6364 50-59 0.0920 0.0069 0.4184 0.6061 60 + 0.1815 0.0058 0.6153 0.7778 11 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint Table 3: Normalized relative lethalities. “ ◦” and “ ⊘” are the Hadamard element-by-element multiplication and division respectively. Males θ∗ M Age f M h d h ◦ d⊘ f M 0-9 0.09871 0.00307 0.18239 0.00052 10-19 0.09976 0.00205 0.18868 0.00036 20-29 0.08130 0.02014 0.17658 0.00403 30-39 0.07203 0.06035 0.26257 0.02029 40-49 0.05566 0.10890 0.36628 0.06609 50-59 0.03851 0.15010 0.49298 0.17722 60 + 0.04218 0.26656 0.67853 0.39548 Females θ∗ F Age f F h d h ◦ d⊘ f F 0-9 0.09577 0.0022 0.1739 0.00037 10-19 0.09824 0.0021 0.2336 0.00045 20-29 0.08709 0.0156 0.1352 0.00223 30-39 0.07908 0.0325 0.1961 0.00744 40-49 0.06096 0.0630 0.3043 0.02900 50-59 0.04225 0.0920 0.4184 0.08399 60 + 0.04846 0.1815 0.6153 0.21252 12 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint Table 4: Adjusted lethalities by age group and gender for the Mexican population( M=male, F =female). The adjusted lethalities are obtained from rescaling the unadjusted lethalities in Table 3, so that f′ M θM + f′ F θF = 0.001.Age θM θF 0-9 0.00001 0.00001 10-19 0.00001 0.00001 20-29 0.00009 0.00005 30-39 0.00045 0.00016 40-49 0.00145 0.00064 50-59 0.00389 0.00184 60 + 0.00868 0.00467 Table 5: Population structure of Syrian refugees in Jordan. Age fM fF 0-9 0.1934 0.1823 10-19 0.1190 0.1116 20-29 0.0714 0.0794 30-39 0.0574 0.0611 40-49 0.0337 0.0348 50-59 0.0127 0.0171 60 + 0.0110 0.0150 Total 0.4987 0.5013 13 . CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted August 11, 2020. ; https://doi.org/10.1101/2020.06.28.20142117doi: medRxiv preprint