Lethality model for COVID-19 based on social determinants of health: an approximation in 67 countries

Fred G. Manrique-Abril; Mario J. Pacheco-López; Cristian F. Téllez-Piñerez; Felipe Ortíz-Rico; Juan D. Sarmiento-Páramo

doi:10.12688/f1000research.26055.1

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Lethality model for COVID-19 based on social determinants of health: an approximation in 67 countries

[version 1; peer review: 1 approved, 1 approved with reservations]

Fred G. Manrique-Abril ^1,2, Mario J. Pacheco-López³, Cristian F. Téllez-Piñerez³, Felipe Ortíz-Rico³, Juan D. Sarmiento-Páramo³

Fred G. Manrique-Abril ^1,2, Mario J. Pacheco-López³, [...] Cristian F. Téllez-Piñerez³, Felipe Ortíz-Rico³, Juan D. Sarmiento-Páramo³

PUBLISHED 30 Oct 2020

Author details Author details

¹ Facultad de Enfermería, Universidad Nacional de Colombia, Bogotá,, Colombia
² Facultad de Ciencias de la Salud, Universidad Pedagógica y Tecnológica de Colombia,, Tunja, Boyacá, Colombia
³ Facultad de Estadistica, Universidad Santo Tomas, Bogotá, Colombia

Fred G. Manrique-Abril
Roles: Conceptualization, Data Curation, Formal Analysis, Funding Acquisition, Investigation, Methodology, Writing – Original Draft Preparation, Writing – Review & Editing

Mario J. Pacheco-López
Roles: Data Curation, Formal Analysis, Investigation, Software, Supervision, Validation, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

Cristian F. Téllez-Piñerez
Roles: Data Curation, Formal Analysis, Investigation, Methodology, Software, Validation, Writing – Original Draft Preparation, Writing – Review & Editing

Felipe Ortíz-Rico
Roles: Conceptualization, Data Curation, Funding Acquisition, Project Administration, Resources, Supervision, Writing – Original Draft Preparation

Juan D. Sarmiento-Páramo
Roles: Data Curation, Investigation, Methodology, Resources, Software, Visualization, Writing – Original Draft Preparation

OPEN PEER REVIEW

REVIEWER STATUS

This article is included in the Emerging Diseases and Outbreaks gateway.

This article is included in the Coronavirus (COVID-19) collection.

Abstract

Background: Social, geographic, economic, demographic, and health factors were analysed to identify some social determinants related to case fatality of COVID-19 in 67 countries.
Methods: A mixed generalized linear model with beta distribution with random intercept was used to estimate the effects of the explanatory variables on the lethality for COVID-19 in 67 countries.
Results: The case fatality rate (CFR) was highest in the countries with the highest percentages of people over 60 years of age, the highest number of hospital beds,the highest mortalit yrate from diabetes, and the highest number of COVID-19 tests. Additional increases were seen based on literacy rates, health investment, death rate from cardiovascular disease, poverty rate, ratio of men, number of air passengers mobilized, number of days from the ﬁrst reported case to the start of quarantine, death rate from respiratory infections, and percentage of people living in urban areas.
Conclusions: The statistical model used to predict lethality is novel because it allows the magnitude of the CFR to be analysed over a logistic model that classiﬁes countries considering the presence and absence of deaths. When considering a beta distribution with excess zeros, the model also allows countries without reported deaths due to COVID-19 at the analysed cut-off date to be included.

Keywords

COVID-19 Pandemic, Beta Regression, Lethality, social determinants.

Corresponding author: Fred G. Manrique-Abril

Competing interests: No competing interests were disclosed.

Grant information: The author(s) declared that no grants were involved in supporting this work.

Copyright: © 2020 Manrique-Abril FG et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: Manrique-Abril FG, Pacheco-López MJ, Téllez-Piñerez CF et al. Lethality model for COVID-19 based on social determinants of health: an approximation in 67 countries [version 1; peer review: 1 approved, 1 approved with reservations]. F1000Research 2020, 9:1285 (https://doi.org/10.12688/f1000research.26055.1) First published: 30 Oct 2020, 9:1285 (https://doi.org/10.12688/f1000research.26055.1) Latest published: 30 Oct 2020, 9:1285 (https://doi.org/10.12688/f1000research.26055.1)

Introduction

COVID-19 is an infectious disease caused by the SARS-CoV-2^1,2 virus that originated in early December 2019 from the city of Wuhan, the capital of Hubei Province, in China^3,4. Its virulence and reproducibility gave the virus a special character, and the WHO declared the disease a pandemic on March 11, 2020⁵, due to the high number of infected people and deaths that it had caused around the world. In comparison, the 2003 outbreak of severe acute respiratory syndrome (SARS) had a fatality rate of about 10% (8,098 cases and 774 deaths), and Middle East respiratory syndrome (MERS) killed 34% of people with the disease between 2012 and 2019 (2,494 cases and 858 deaths)⁶.

However, even though its death rate is minuscule, COVID-19 so far has caused more deaths (1871) than SARS and MERS combined (1632)⁶. As such, many epidemiologists, statisticians, mathematicians, and other researchers have focused on forecasting the number of new cases at the regional or global level^4,5,7–9 and on detecting possible measures to decrease the probability of contagion and death in the most vulnerable populations^3,10. Few studies can determine with sufficient statistical rigour which factors decrease the probability of death from COVID-19 with any level of statistical significance.

The SIR model is on the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments:

S: The number of susceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment. I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals. R for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called "recovered" or "resistant". This model is reasonably predictive for infectious diseases that are transmitted from human to human.⁵. With these models, indicators of lethality are also calculated by dividing the number of deaths by the total number of those infected. This simple calculation is called the case fatality rate (CFR).

In practice, when a pandemic enters a territory, the susceptible often do not get sick, do not infect themselves, and do not die as established in the SIR model. Thus, one assumes that other factors are included in the SIR or susceptible, exposed, infected, recovered (SEIR) models (a compartmental deterministic model) that determine the infection and mortality. This would substantially modify the CFR, which is a measure of a disease’s severity and indicates the disease’s importance in terms of its ability to produce death. Given this order of ideas, lethality is calculated as CFR:

C F R = \frac{N d}{N c} \times 100

Where Nd=Number of deaths from a disease in a given period and Nc=Number of cases diagnosed with the same disease in the same period.

Since each country has different characteristics in terms of the social determinants and the cases and deaths COVID-19 pandemic report is uniform, it is necessary to collect the available information to model the virus’s CFR and identify the factors that statistically increase or modify the risk of death. A model will give researchers a powerful tool to estimate the probability of death from COVID-19 and its causes will give researchers a powerful tool, alongside the existing ones for predicting the number of cases, for decision-making aimed at alleviating the consequences of deadly events. That is why, in this article, we propose to model the CFR for COVID-19 using a mixed beta model and adjust it for some social, geographic, economic, health and demographic variables as social determinants in the global context of the COVID-19 pandemic.

Methods

Based on the assumptions that the CFR by country can be affected by socioeconomic factors and by health and non-pharmaceutical measures, and that its behaviour may have varied since the start of the pandemic, a mixed beta¹¹ regression model with random intercept was used to estimate the effects of the explanatory variables on the CFR for COVID-19 in 67 countries. A significance level of 10% was used to identify factors that had a statistically significant relationship with the COVID-19 CFR worldwide, see Table 1.

Table 1. Explanatory variables for COVID-19 case fatality rate.

Variable	Description
CFR (response)	Corrected case fatality rate: measured nine times,on April 8, 15, 22 and 29; May 6, 13, 20 and 27; and June 3
Explanatory
60years	People aged over 60 years (%)
Literacy	Literacy rate
Beds	Number of hospital beds per 10000 inhabitants
Health	Investment in health as a percentage of GDP
Obesity	Prevalence of obesity
Test	COVID-19 tests per million inhabitants
Diabetes	Diabetes mellitus mortality rate
Respiratory diseases	Respiratory diseases mortality rate
HIV/AIDS	HIV/AIDS mortality rate
Respiratory infection	Respiratory infection mortality rate
Cardiovascular	Cardiovascular disease mortality rate
Poverty	Percentage of people below the poverty line
Sex	Sex ratio (men/women)
Doctors	Number of doctors per 1000 inhabitants
Passengers	Annual volume of air passengers (%)
Quarantine	Days until quarantine decree
GDP	Gross domestic product
Tobacco	Smoker between 15 and 60 years old (%)
Urban population	Population living in urban areas (%)
Height	Height above sea level (meters above the sea level.)
Density	Population density
Nurses	Number of nurses per 1000 inhabitants

Data source

Data on the number of daily cases and deaths from COVID-19 were obtained from the Johns Hopkins University repository to construct the CFRs by country. The possible predictors of the CFR by country were obtained from the repositories of Population Pyramid, the Word Bank, the World Health Organization and the Topographic Mission Radar Shuttle, as well as from health policy, news and macro data. The seven-day corrected fatality rate was calculated nine times: on April 8, 15, 22 and 29; May 6, 13, 20 and 27; and June 3.

Beta mixed models

The parameterized beta probability density function, denoted by Y ∼ β(µ, ϕ), in terms of its mean (µ) and precision (ϕ) parameters,¹², is given by

f (y | μ, ϕ) = \frac{γ (ϕ)}{γ (μ ϕ) γ ((1 - μ) ϕ)} y^{μ ϕ - 1} {(1 - y)}^{(1 - μ) ϕ - 1}

0 < y < 1, with 0 < µ < 1,ϕ > 0, E(Y) = µ, Var(Y) = µ(1 − µ)/(1 + ϕ), and γ is as the Gamma function. For a random sample from Y_i ∼ β(µ, ϕ), and assuming ϕ is constant, the beta regression model¹³ is specified by $g (μ_{i}) = x_{i}^{τ} β = η_{i},$ with β =(β₁, β₂, ..., β_p)^τ being a vector of the (p) unknown regression coefficients, x_i = (x_i₁ ,..., x_i_p)^τ being a vector of (p) known covariates and η_i being a linear prediction. The model specification is completed by the choice of a link function, g(_∗) : (0, 1) → IR. We adopt the Logit function g(µ) = log(µ/(1 − µ)). This model does not contemplate possible dependencies such as those induced by multiple measurements on the same observational unit or time.

Including latent random effects on a grouped data structure is a parsimonious strategy, as compared to adding parameters to the fixed part of the model, while still accounting for nuisance effects.

Let Y_ij denote an observation j = 1, . . . , n_i within group i = 1, . . . , q and y_i denote a n_i -dimensional vector of measurements from the i-th group. Let b_i be a q-dimensional vector of random effects, and assume the responses Y_{i j} are conditionally independent with density

f_{i} (y_{i j} | b_{i}, β, ϕ) = \frac{γ (ϕ)}{γ (μ_{i j} ϕ) γ ((1 - μ_{i j}) ϕ)} y_{i j}^{μ_{i j} ϕ - 1} {(1 - y_{i j})}^{(1 - μ_{i j}) ϕ - 1}

and a link function $g (μ_{i}) = x_{i}^{τ} β = η_{i},$ vectors of known covariates x_{i j} and z_{i j} with dimensions (p) and (q), respectively, a (p) -dimensional vector of unknown regression parameters β and the precision parameter ϕ. The model specification is completed by b_i|Σ ∼ N(0, Σ) Gaussian random effects.

Preparation of the model

A model was developed that accounted for the variables’ nature, which is bounded in the interval [0, 1]. A mixed beta model was then assumed to model the CFR, and a step procedure did what for the final selection. The statistical software R version 3.6.3 was used to fit the model, specifically the GAMLSS function. See 14 for more technical details.

Results

The distribution of CFR by country is shown in Figure 1. For June 3, high CFR stand out in countries like Belgium, France, Mexico, England, Italy, Hungary, Holland and Sweden, as do the low values in Russia, Australia, New Zealand, Malaysia, Chile and Israel.

Figure 1. COVID-19 case fatality, as of June 3.

According to the adjusted model (Figure 2), The variables with greater statistical significance in the model were three (60years, Health and Sex), the CFR increases inversely with health expenditure; and directly the CFR is higher where more people over 60 years of age live and there is a male population predominance.

So too does CFR increase, if the number of beds increases, if there are more diabetes mortality or greater death rate from cardiovascular diseases or death rate from respiratory infections. The CFR increase if there are a greater number of tests for SARS-CoV-2. The register lethality change with the literacy proportion in the country; the CFR increase with poverty, with a greater number of air passengers mobilised, number of days from the first case reported until the beginning of the quarantine, and percentage of people living in the urban area.

Figure 2. Results of the adjusted model.

According to the model, the CFR decreased in the countries with the low death rate from respiratory diseases, low obesity rate, low death rate from HIV/AIDS, low physicians per thousand inhabitants, low GDP in health care, low population density and a high number of nurses per thousand inhabitants.

Discussion

Economic Commission for Latin America and the Caribbean (ECLAC) studied the relationship between mortality in Latin American countries with some characteristics of their social development. A set of four social indicators (hospital beds per 1000 inhabitants, protein consumption, literacy and proportion of households with drinking water) have high linear correlations with life expectancy at birth (r = 0.94)¹⁵.

This global analysis of the socioeconomic determinants of COVID-19 mortality had several limitations. Countries had clear differences in their stage of historical development, with different modes of production being found. On the other hand, mortality was highly heterogeneous mortality between countries and in different populations within each country. Finally, the review of the available information indicates that the analysis is not systematic or complete, particularly for the most important analysis categories.

Nevertheless, the available data allow us to reach some important conclusions. For example, adjustment of the presented model allows factors related to COVID-19 case fatality to be identified. The methodology can be replicated with different cut-off dates, include more related factors or be used at sub-national levels.

The calculated case fatality differs from another model’s fatality proposed by researchers at the University Hospital of Lausanne and collaborators (15), who estimated a CFR of 3.59% as of March 1, 2020, considering that an adjustment must be made for the 14 previous days before death to coincide with the date of infection spread and infection, representing the maximum incubation period for the virus. The findings show that current figures may underestimate the potential threat of COVID-19 in symptomatic patients¹⁶.

Conclusions

The statistical model used to model fatalities is novel because it allows to analyse the magnitude of the fatality rate over a logistic model that classifies the countries considering the presence and absence of fatalities. Additionally, when considering a beta distribution with excess zeros, countries without reported deaths due to COVID-19 at the analysed cut-off date can be included. Finally, the variability obtained from the partial estimates made by the countries on different dates can be analysed.

The model’s results may have a high sensitivity to the data on reported case fatality from COVID-19, due to the sub-registry inherent to the measurement of infected people, because of the small number of tests carried out in some countries. However, the modelling strategy used is optimal for the type of information considered and can be replicated with new updates to the lethality measurement¹⁷.

Data availability

Source data

The population, cases, test number and deaths number by country were obtained from the repository Johns Hopkins University (JHU) at https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data.

World Bank data were obtained using the following program: https://github.com/vincentarelbundock/WDI.

Extended data

R analysis code for this study is available at: https://github.com/DataStatistic/covid19model.

Archived code at time of publication: http://doi.org/10.5281/zenodo.4007005¹⁸.

License: Creative Commons Attribution 4.0 International license.

Faculty Opinions recommended

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Comments on this article Comments (0)

Version 1

VERSION 1 PUBLISHED 30 Oct 2020

Author details Author details

Fred G. Manrique-Abril
Roles: Conceptualization, Data Curation, Formal Analysis, Funding Acquisition, Investigation, Methodology, Writing – Original Draft Preparation, Writing – Review & Editing

Mario J. Pacheco-López
Roles: Data Curation, Formal Analysis, Investigation, Software, Supervision, Validation, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

Cristian F. Téllez-Piñerez
Roles: Data Curation, Formal Analysis, Investigation, Methodology, Software, Validation, Writing – Original Draft Preparation, Writing – Review & Editing

Felipe Ortíz-Rico
Roles: Conceptualization, Data Curation, Funding Acquisition, Project Administration, Resources, Supervision, Writing – Original Draft Preparation

Juan D. Sarmiento-Páramo
Roles: Data Curation, Investigation, Methodology, Resources, Software, Visualization, Writing – Original Draft Preparation

Competing interests

No competing interests were disclosed.

Grant information

The author(s) declared that no grants were involved in supporting this work.

Article Versions (1)

version 1

Published: 30 Oct 2020, 9:1285

https://doi.org/10.12688/f1000research.26055.1

© 2020 Manrique-Abril FG et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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how to cite this article

Manrique-Abril FG, Pacheco-López MJ, Téllez-Piñerez CF et al. Lethality model for COVID-19 based on social determinants of health: an approximation in 67 countries [version 1; peer review: 1 approved, 1 approved with reservations]. F1000Research 2020, 9:1285 (https://doi.org/10.12688/f1000research.26055.1)

NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article.

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PUBLISHED 30 Oct 2020

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Reviewer Report 26 Mar 2021

Hector Florez, Universidad Distrital Francisco Jose de Caldas, Bogota, Colombia

Approved with Reservations

https://doi.org/10.5256/f1000research.28754.r81713

The article presents a mixed generalized linear model with beta distribution with a random intercept to estimate the effects of the explanatory variables on the CFR for COVID-19 in 67 countries.
It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.
I suggest describing how the explanatory variables in table 1 were selected.
I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"
Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Bioinformatics, data science, computer science, mathematics

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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Author Response 28 Jul 2021

Fred Manrique-Abril, Facultad de Enfermería, Universidad Nacional de Colombia, Bogotá,, Colombia

28 Jul 2021

Author Response

It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.
... Continue reading It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.

Given that the response variable (Covid fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.

Given that the response variable (Covid fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
Competing Interests: No competing interests were disclosed. Close
Report a concern
Author Response 21 Sep 2021

Fred Manrique-Abril, Facultad de Enfermería, Universidad Nacional de Colombia, Bogotá,, Colombia

21 Sep 2021

Author Response

Given that the response variable (COVID-19 fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting ... Continue reading Given that the response variable (COVID-19 fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
Given that the response variable (COVID-19 fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
Competing Interests: No competing interests were disclosed. Close
Report a concern
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Author Response 28 Jul 2021

Fred Manrique-Abril, Facultad de Enfermería, Universidad Nacional de Colombia, Bogotá,, Colombia

28 Jul 2021

Author Response

It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.
... Continue reading It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.

Given that the response variable (Covid fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.

Given that the response variable (Covid fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
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Author Response 21 Sep 2021

Fred Manrique-Abril, Facultad de Enfermería, Universidad Nacional de Colombia, Bogotá,, Colombia

21 Sep 2021

Author Response

Given that the response variable (COVID-19 fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting ... Continue reading Given that the response variable (COVID-19 fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
Given that the response variable (COVID-19 fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895
Competing Interests: No competing interests were disclosed. Close
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Reviewer Report 13 Nov 2020

Ahmed M. Abbas, Department of Obstetrics & Gynecology, Faculty of Medicine, Assiut University, Assiut, Egypt

Approved

https://doi.org/10.5256/f1000research.28754.r74024

The topic is interesting and the authors covered the aspects of the paper successfully. The research methods are appropriate and the results are presented in a clear manner. Discussion and conclusions are sufficient. Citations are updated and covering the topic. ... Continue reading

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Obstetrics and Gynecology

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.

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Ahmed M. Abbas, Assiut University, Assiut, Egypt
Hector Florez, Universidad Distrital Francisco Jose de Caldas, Bogota, Colombia

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26 Mar 2021 | for Version 1

Hector Florez, Universidad Distrital Francisco Jose de Caldas, Bogota, Colombia

17 Views Cite this report Responses(2)

Approved With Reservations

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Bioinformatics, data science, computer science, mathematics

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Author Response

28 Jul 2021

Fred Manrique-Abril, Facultad de Enfermería, Universidad Nacional de Colombia, Bogotá,, Colombia

It is not clear why the authors concluded that a mixed generalized linear model with beta distribution with a random intercept is a proper model to perform the desired analysis.

Given that the response variable (Covid fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895

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Competing Interests

No competing interests were disclosed.

Author Response

21 Sep 2021

Fred Manrique-Abril, Facultad de Enfermería, Universidad Nacional de Colombia, Bogotá,, Colombia

Given that the response variable (COVID-19 fatality rate) is observed for each country on more than one occasion, it is necessary to control the effect of the country in adjusting a model that explains said response variable. This requires a random intercept model.

Most variables have an effect around zero except for three variables (60years, Sex, Health). Based on this result, can someone interpret that just these three variables are worth to be analyzed? I am afraid that this result deserves a deeper discussion.

In the model adjustment, 20 variables out of a total of 22 explanatory variables turn out to be significant and due to the nature of each variable, the parameter associated with each explanatory variable can have a value close to zero without this meaning that the variable does not have an effect. on the response variable. For example, the variable People aged over 60 years (%) has a different nature than Sex ratio (men / women) and these in turn have a very different nature from Investment in health as a percentage of GDP, therefore they are not comparable their effects on each other.

I suggest extending the explanation of the equations presented in the subsection "Beta mixed models"

The proposed beta regression model allows the adjustment of a model that establishes the relationship between the 22 proposed explanatory variables in which the effect of the country on lethality can be controlled and separated from the effect of each explanatory variable.

For a more detailed explanation of the model see Verkuilen J, Smithson M. Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution. Journal of Educational and Behavioral Statistics. 2012;37(1):82-113. doi:10.3102/1076998610396895

View more View less

Competing Interests

No competing interests were disclosed.

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Reviewer Report

20 Views

13 Nov 2020 | for Version 1

Ahmed M. Abbas, Department of Obstetrics & Gynecology, Faculty of Medicine, Assiut University, Assiut, Egypt

20 Views Cite this report Responses(0)

Approved

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Obstetrics and Gynecology

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.

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Alongside their report, reviewers assign a status to the article:

Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested

Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.

Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions

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Lethality model for COVID-19 based on social determinants of health: an approximation in 67 countries

Abstract

Keywords

Introduction

Methods

Table 1. Explanatory variables for COVID-19 case fatality rate.

Data source

Beta mixed models

Preparation of the model

Results

Figure 1. COVID-19 case fatality, as of June 3.

Figure 2. Results of the adjusted model.

Discussion

Conclusions

Data availability

Source data

Extended data

References

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