Epidemiological Risk Factors of SARS-Cov-2 Infections

Since the first governmental recognitions of the pandemic characteristic of the SARS-Cov-2 infections, public health agencies have warned about the dangers of the virus to persons with a variety of underlying physical conditions, many of which are more commonly found in persons older than 50 years old. To investigate the statistical, rather than physiological basis of such warnings, this study examines correlations on a nation-by-nation basis between the statistical data concerning covid-19 fatalities among the populations of the ninety-nine countries with the greatest number of SARS-Cov-2 infections plus the statistics of potential co-morbidities that may influence the severity of the infections. It examines reasons that may underlie of the degree to which advanced age increases the risk of mortality of an infection and contrasts the risk factors of SARS-Cov-2 infections with those of influenzas and their associated pneumonias.


Introduction and Context
The SARS-Cov-2 virus has spread in only a few months around the world and in late winter (2020) was designated as a worldwide epidemic by the World Health Organization. The virus causes the covid-19 infection that can manifest in mild flu-like symptoms or far more seriously as a severe respiratory disease with pneumonia Since the outset of the covid-19 pandemic, the public has been treated to numerous speculations concerning the degree to which age or various the CDC as increasing risk include cancer, chronic kidney disease, obesity, coronary disease, Type 2 diabetes mellitus, and sickle cell disease. CDC also warns that asthma, hypertension, and liver disease among others might subject a person to increased risk. One notes that sickle cell disease is most commonly found among persons whose ancestors come from Africa and Mediterranean countries where malaria is a prevalent affliction.
As many of the diseases cited by the CDC are more common in persons in late middle age and older, a warning common early in the course of the pandemic was that SARS-Cov-2 presented a particular danger to persons over 50 years old. Indeed, very early, as in the initial wave of cases in China [2] and the strong wave of cases in Italy, the probability of death due to covid-19 was judged to be a strong function of a patient's age, being only a few percent for those under 50 and rising to nearly 20% for patients over 80. Certainly the large number of fatalities [3] in care homes seen in New York, the United Kingdom and elsewhere have fueled speculations about the potential of comorbidities frequently seen in the elderly to make contracting covid-19 fatal.
Why is covid-19 more dangerous to the elderly than to younger persons? To complicate answering this question, the actual mortality rate of covid-19 is highly uncertain, as the prevalence of asymptomatic infections has been estimated to be 5 to 10 times more than infections with definitive symptoms.
An exemplary source of testing-based data was provided by the passengers aboard the Princess Line cruise ship, the Diamond Princess on which half of the passengers who tested positive for covid-19 were asymptomatic. [4] To some degree that uncertainty might explain the very wide distributions of reported (or apparent) rate of mortality of covid-19 in countries ranging from < 0.03% (Singapore) to almost 30% (Yemen).
For a less anecdotal (and less speculative) assessment of risk factors for serious consequences of covid-19, a data-driven examination of national statistics seems to be in order with the goal of identifying strong correlations of mortality due to covid-19 with other potential co-morbidities. This manuscript presents a set of calculations of such correlations.

Methods of Analysis
From the outset one must keep in mind that the following analysis is not based on clinical or physiological considerations but on national epidemiological statistics. Unless otherwise indicated, the following assumptions underlie the subsequent calculations: 1. The apparent mortality outcomes are a viable proxy for actual rates of infection, death, and correlation with co-morbidities; we define The apparent mortality and case number data used in the following analysis are accurate as of 30 August 2020. 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 October 5, 2020. . https://doi.org/10.1101/2020.09.30.20204990 doi: medRxiv preprint sets: One may estimate the statistical significance of calculated correlations by computing r for two variables that are uncorrelated by construction; i.e., apparent covid-19 mortality and a random variable in the range from 1 to 100.
Once linear correlations have been examined, the next step is evaluating cross-correlations among variables and performing a multivariate analysis.
The 99 countries sampled in this study were selected as having the largest number of reported covid-19 infections. The countries listed in Table 1 represent five regions, Americas, Asia, Europe, Africa, and Middle East plus Central Asia. Their combined population of nearly 5.5 billion accounts for the strong preponderance of all cases reported worldwide. Table 1. The countries sampled grouped into regions. As Yemen is a statistical outlier in apparent mortality, many plots omit its data point for visual clarity.
. CC-BY-NC-ND 4.0 International license It 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 October 5, 2020. .  A possible limitation of this approach is that all mortality data are given equal weight in the calculation of correlation. One check of whether this Ansatz introduces a bias is computing the correlation between apparent national mortality rates and national populations. Doing so yields a value of 0.56%.
Another possible way to attribute a weighting that is not arbitrary is to plot the variation of covid-19 deaths per capita against the possible risk factor.
However, the number of covid-19 deaths per capita depends strongly on national public health policies, on national efforts to prevent spread of the SARS-Cov-2 virus, on GDP and other considerations that are non-medical.
The differences between Norway and Sweden are a case in point

Examination of linear correlations
To gain confidence in this statistical approach one can plot two variables for which one may expect to see a correlation ( Figure 2). Here the value is quite high, 62.5%. Examining Fig. 2 more closely suggests a limitation of the method. The countries circled in red show a strong correlation while those in the green circle that show scarcely any correlation of a nation's wealth with the age of its population. A refinement of the statistical approach is needed.
By identifying the data underlying each point with each country's region reveals that median age and national wealth are essentially uncorrelated for European nations but strongly correlation for countries in Africa and Asia.
Regional grouping was thus adopted throughout this study.
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The copyright holder for this preprint this version posted October 5, 2020. . From the outset of the pandemic, national health authorities have warned the public about the increase risk of mortality for persons 60 years old and older.
One can see in Figure 5 an example of the basis for such warnings in the data provided by the UK Office of National Statistics in September 2020 [5]. Again one asks why should the seriousness of covid-19 be a function of age? From such data, one might expect a very strong correlation between the national apparent mortality rate and the median age of a country's population. Even accepting the hypothesis of universality for the data of That plot ( Figure 6a) shows a surprising result. The low correlation, 12.9%, is even less pronounced when one examines the data region by region.
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The copyright holder for this preprint this version posted October 5, 2020. Instead of plotting mortality to covid-19 versus national median age, one might have examined the dependence on the percentage of the population of age 65 or greater (figure 6b). That correlation is somewhat larger (22.0%), consistent reference [5], but also the result of strong regional variations.
The national rate of confirmed cases of covid-19 with respect to the percentage of population older than 65 (Figure 7) displays a negative correlation (-14.8%) that is driven primarily by data from the Middle East. If one removes those countries with large numbers of young, foreign workers that correlation drops to -0.03%.
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The copyright holder for this preprint this version posted October 5, 2020.  One may hypothesize that the "care home effect," i.e., the large numbers of deaths seen in nursing homes in Italy, the U.K. and N.Y. was more the result of poor hygiene practices than by an extreme dependence of the lethality of covid-19 infections on specific underlying disorders. That hypothesis will be investigated in the following analysis.
The linear correlations of age with various potential causal factors shown in Figure 8 suggest candidates to examine to explain the "care home effect." In addition to particular underlying factors, the "care home effect" also reflects a generally very weakened physical condition of many occupants of care homes that would render any pneumonia-inducing disease lethal.
Finally, the data of Figure 8 show no evidence that age alone influences the probability of a person becoming infected by the SARS-Cov-2 virus.
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The copyright holder for this preprint this version posted October 5, 2020. . https://doi.org/10.1101/2020.09.30.20204990 doi: medRxiv preprint As suggested by the results in Figure 8, an example ( Figure 9) illustrates the utility of the statistical approach used herein. In contrast with infections due to SARS-Cov-2, the incidence of death from influenza-induced pneumonia is highly correlated (-65.2%) with the median age of the population. The correlation also displays a strong regional dependence. As the covid-19 often presents as a severe respiratory disease and strengthened by the results in Figure 9, one asks whether the seriousness of the covid-19 infections is correlated with incidence of asthma. As Figure 10 indicates, asthma neither increases the likelihood of SARS-Cov-2 infection nor does it seem to affect the seriousness of the disease in an infected patient. In case of asthma, the contrast with influenza related pneumonia (Figure 11) is striking. The overall correlation of 46.2% is seen in all regions. Referring to covid-19 as a "flu-like" infection is definitely misleading.
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The copyright holder for this preprint this version posted October 5, 2020. . https://doi.org/10.1101/2020.09.30.20204990 doi: medRxiv preprint Figure 11. The incidence of death from flu related pneumonia is relatively strong.
Another early warning of the U.S. Centers for Disease Control was that obesity could represent a serious underlying factor that would lead to serious consequences of covid-19. However, once again actual the national data of ( Figure 12) display essentially no (1.9%) correlation. The contribution of obesity to the outcome of other pulmonary disorders is significantly different as is displayed in Figure 13. Curiously, obesity has a significant correlation (nearly 40%) with the risk of contracting infection from SARS-Cov-2, although not with the apparent outcome of the infection. The observation of increased risk of infection (although not its outcome) has been previously reported in [6]. Unlike this study, reference [6] reports increased . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted October 5, 2020. . https://doi.org/10.1101/2020.09.30.20204990 doi: medRxiv preprint risk of infection (32.9%) for people with chronic kidney disease. One might speculate that as a chronic respiratory disorder involving the airways in the lungs, asthma may increase the seriousness of consequences of covid-19 and its induced pneumonias, but Figure 14 shows no such significant correlation (2.6%). Examining the correlation of covid-19 mortality with other lung diseases (Figure 15) also shows minimal if any correlation (2.5%). In contrast, the relationship of influenza-induced pneumonias with asthma and other lung diseases presents a correlation that is quite high, 61.0% and 34.8% respectively. With respect to their effects on patients with underlying conditions, influenza and covid-19 are very different diseases. Figure 14. Correlation of asthma with apparent covid-19 mortality rate.
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An early warning to persons with underlying conditions concerned diabetes mellitus. That suspicion is echoed by the strong dependence with age shown in Figure 8. Whether one measures the incidence of diabetes by deaths due to diabetes or to the reported national rates of diabetes in adults (20 to 79 years of age), the correlation with covid-19 mortality is similarly low (~11%). In otherwise healthy persons, diabetes does not appear to be a significant risk factor with respect to the serious of infection by SARS-Cov-2. Figure 16 and Table 2 summarize the linear correlations of apparent covid-19 mortality with several underlying medical and economic conditions considered herein.  CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted October 5, 2020. . https://doi.org/10.1101/2020.09.30.20204990 doi: medRxiv preprint As the shown in Figure 8 most strongly correlated with age correlated at best weakly with covid-19 mortality, one may surmise that poor health care management played a very large role in the "care home effect."

Cross-correlations and multivariate analysis
Before investigating cross-correlations as a way of searching for root causes, one might want to perform a multivariate analysis of covid-19 mortality against a common trio of risk factors commonly found together in patients in nursing and convalescent homes-namely Diabetes mellitus,  Table 3.
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The copyright holder for this preprint this version posted October 5, 2020. . Other calculations of multivariate correlations with the apparent national mortality rates of covid-19 are presented in Table 4.

Cross-correlations
As the previous section argues and as Figure 17 illustrates, the contrast with covid-19 in the correlations of influenza/pneumonia with other potential underlying conditions is striking. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted October 5, 2020.  Although obesity appears correlated with SARS-Cov-2 contagion, it appears uncorrelated with the outcome of covid-19 infections. Figure 13 shows that lack of such correlation does not appear with respect to influenza, malnutrition and asthma, although in those three cases the coefficient is negative. Understanding the correlations of obesity calls for a deeper look at the relationship of obesity with the conditions that show the most influence. Already in the case of contagion, regional differences make for a substantial fraction of the apparent effect (Figure19). Figure 19. Is the correlation with obesity merely due to regional differences with other underlying influences? . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted October 5, 2020. . https://doi.org/10.1101/2020.09.30.20204990 doi: medRxiv preprint These regional differences could be due to factors such as national median age (Figure 20) or it may be influenced by national wealth reckoned in terms of per capita GDP-PPP (Figure 23).  . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted October 5, 2020. . conditions. The correlation with covid-19 mortality is the purple bar.

Factors related to national economics and public health policies
The differences in the magnitude, outcomes, and characteristics of waves of   . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted October 5, 2020. . mortality is presented in Table 5. As the mortality rate varies in time and seems to decline as the pandemic progresses (at least in the Northern Hemisphere) the mortality rate has been benchmarked as of August 30, 2020. The surprising negative correlation in contagion with the percentage of the urban population living in slums is due to the trend in Africa that the smaller the fraction of a nation's population living in cities, the more likely it is that they live in slums. That characteristic is displayed in Figure 25.
The correlation level with respect to GDP is explained by the correlation of GDP-PPP with percentage of population over the age 65. The substantial . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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Summary and conclusions
This statistical study covering countries with ~70% of the world's population confirms the early clinical observation that infection by the SARS-Cov-2 virus presents a great risk to persons over the age of 65.
However, it does not support the suggestions presented by government agencies early in the pandemic that the risks are much greater for persons with certain common potential co-morbidities. Many of the early deaths of elderly patients early in the course of the pandemic took place in circumstances that likely promoted rather than impeded the spread of the virus among person who were generally in a poor state of health.
A commonly heard claim by persons who object to strict measures to prevent the spread of the SARS-Cov-2 virus has been that the resulting . CC-BY-NC-ND 4.0 International license It 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 October 5, 2020. . https://doi.org/10.1101/2020.09.30.20204990 doi: medRxiv preprint disease is similar to influenza and should be treated in the same manner as influenza as a matter of public policy. The comparison of the severity of medical outcomes of covid-19 with those caused influenza strains and their resulting pneumonias displays dramatic differences. Promulgating the idea that covid-19 a "flu-like disease" spreads gross misinformation to the detriment of the public health worldwide.
One may ask what governmental actions can reduce the seriousness of Presently authoritative data on a worldwide country-to-country basis are not available to evaluate the effectiveness of prevention and treatment modalities.