Alternative Global Health Security Indexes for Risk Analysis of COVID-19

Given the volume of research and discussion on the health, medical, economic, financial, political, and travel advisory aspects of the SARS-CoV-2 virus that causes the COVID-19 disease, it is essential to enquire if an outbreak of the epidemic might have been anticipated, given the well-documented history of SARS and MERS, among other infectious diseases. If various issues directly related to health security risks could have been predicted accurately, public health and medical contingency plans might have been prepared and activated in advance of an epidemic such as COVID-19. This paper evaluates an important source of health security, the Global Health Security Index (2019), which provided data before the discovery of COVID-19 in December 2019. Therefore, it is possible to evaluate how countries might have been prepared for a global epidemic, or pandemic, and acted accordingly in an effective and timely manner. The GHS index numerical scores are calculated as the arithmetic (AM), geometric (GM), and harmonic (HM) means of six categories, where AM uses equal weights for each category. The GHS Index scores are regressed on the numerical score rankings of the six categories to check if the use of equal weights of 0.167 in the calculation of the GHS Index using AM is justified, with GM and HM providing a check of the robustness of the arithmetic mean. The highest weights are determined to be around 0.244–0.246, while the lowest weights are around 0.186–0.187 for AM. The ordinal GHS Index is regressed on the ordinal rankings of the six categories to check for the optimal weights in the calculation of the ordinal Global Health Security (GHS) Index, where the highest weight is 0.368, while the lowest is 0.142, so the estimated results are wider apart than for the numerical score rankings. Overall, Rapid Response and Detection and Reporting have the largest impacts on the GHS Index score, whereas Risk Environment and Prevention have the smallest effects. The quantitative and qualitative results are different when GM and HM are used.


Introduction
There is no doubt that the COVID-19 disease, and the SARS-CoV-2 virus that causes it, have captured the world's attention. With the exception of some countries where the leadership has tried to downplay, distort, and seemingly ignore its presence, most countries seem to have taken the coronavirus seriously from a public health and community safety perspective. Under such circumstances, it can be difficult to maintain a semblance of sanity when it is easy to entertain the alternative of panic.
At the time of writing, there is still no safe, reliable, efficient, and timely vaccine for the SARS-CoV coronavirus that caused SARS from 2002 to 2003, and for the MERS-CoV coronavirus that has continued to cause MERS since 2012. Therefore, it is difficult to feel optimistic about the discovery of a vaccine for COVID-19 in the foreseeable future.
Despite the volume of research and discussion on the health, medical, economic, financial, political, and travel advisory aspects of COVID-19, it is essential to enquire if an outbreak of the epidemic, which was belatedly classified as a global pandemic by the World Health Organization on 11 March 2020, might have been anticipated, given the well-documented history of SARS and MERS.
For there to be a foreseeable and predictable outcome based on observable and credible data, rather than on possibly misguided perceptions and "hunches" that do not necessarily rely on provable facts, it is essential to consider a well-documented source of publicly available information about what might have been anticipated about epidemics such as COVID-19. If various issues directly related to health security risk could have been predicted accurately, public health and medical contingency plans might have been prepared and activated well in advance of the onset of a pandemic such as COVID-19.
The purpose of this paper is to critically evaluate an important source of health security, namely the Global Health Security Index (2019). The data in the 2019 Report were available before the discovery of COVID-19 as pneumonia of unknown form in December 2019. Therefore, it is possible to evaluate how countries might have been prepared for a global epidemic, or pandemic, and acted accordingly.
The GHS Index numerical score rankings are obtained from [15] Global Health Security Index (2019), and are presented in Appendix A, while the GHS Index ordinal rankings are presented in Appendix B.
The remainder of the paper is as follows. Section 2 presents the Global Health Security (GHS) Index that is based on six broad categories. Section 3 provides an empirical evaluation of the numerical GHS scores and their respective rankings, as well as the corresponding ordinal rankings. Two regression models are estimated by least squares using both the numerical score and ordinal rankings, and optimal weights are assigned to each of the six categories in calculating the GHS Index. A conclusion and discussion of relevance are given in Section 4.

1.
Prevention: Prevention of the emergence or release of pathogens; 2.
Detection and Reporting: Early detection and reporting for epidemics of potential international concern; 3.
Rapid Response: Rapid response to and mitigation of the spread of an epidemic; 4.
Health System: Sufficient and robust health system to treat the sick and protect health workers; 5.
Compliance with International Norms: Commitments to improving national capacity, financing plans to address gaps, and adhering to global norms;

6.
Risk Environment: Overall risk environment and country vulnerability to biological threats.
The GHS Index is a comprehensive assessment, developed as a collaboration between the Nuclear Threat Initiative, Johns Hopkins Center for Health Security, and the Economist Intelligence Unit, covering global health security capabilities in 195 countries. The GHS Index lists the countries that are best prepared for an epidemic or pandemic. "The average overall GHS Index score is 40.2 out of a possible 100. While high-income countries report an average score of 51.9, the Index shows that collectively, international preparedness for epidemics and pandemics remains very weak. Overall, the GHS Index finds severe weaknesses in a country's abilities to prevent, detect, and respond to health emergencies; severe gaps in health systems; vulnerabilities to political, socioeconomic, and environmental risks that can confound outbreak preparedness and response; and a lack of adherence to international norms." (https://www.ghsindex.org/report-model/). As part of China, Hong Kong was not included in the GHS Index as a country, while Taiwan was not included undoubtedly for political reasons. The data for the 195 countries are reported on pages 20-29 at: https://www.ghsindex.org/wp-content/uploads/2019/10/2019-Global-Health-Security-Index.pdf, which provides a numerical Average Overall score and separate numerical scores for each of the six categories. The seven numerical score rankings are obtained from Global Health Security Index (2019), and are reported in Appendix A, while the seven ordinal rankings are presented in Appendix B.

Empirical Evaluation
This section provides an empirical evaluation of the numerical GHS scores according to seven data series, namely the numerical scores for Average Overall and 6 categories, and the respective numerical score rankings, as well as the corresponding ordinal rankings for the Average Overall and six categories. Two empirical models are estimated using the numerical score rankings and ordinal rankings, with the GHS Index regressed on the respective numerical score rankings and ordinal rankings of each of the six categories.
The GHS Average Overall Index is the arithmetic mean numerical value that is calculated from the six numerical scores categories. The equal weight that is used for each category is 0.167. The abbreviations used are as follows: AO = Average Overall, PR = Prevention, DR = Detection and Reporting, RR = Rapid Response, HS = Health System, CO = Compliance, and RE = Risk Environment.
The descriptive statistics for the numerical score rankings are given in Table 1, which reports the mean, standard deviation, minimum and maximum values, and the range. The highest mean score is RE, and the lowest is HS. The highest standard deviation is DR, and the lowest is CO. The highest minimum is CO, and the lowest is HS. The highest maximum is DR, and the lowest HS. The largest range is DR and the lowest is CO. It is instructive to present the 10 leading countries according to the AO numerical scores, together with the associated 6 category scores, namely: The USA has the highest scores in five categories, but has an outlying score at 19 in Risk Environment (RE). The UK and Thailand also have apparent outliers in RE, with scores of 26 and 93, respectively. The Netherlands and Denmark have what seem to be outliers in Compliance (CO), at 32 and 28, respectively. Australia, Canada, and Sweden have relatively uniform scores in all six categories. South Korea has two outlying scores in CO and RE at 23 and 27, respectively. Finland has an outlier in Detection and Reporting (DR) at 45.
In the presence of outliers, the arithmetic mean can give a distorted measure of the central tendency of the individual components. Consequently, it is worth calculating the arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM) using the numerical scores and ordinal rankings of each of the six categories for the 195 countries' data for purposes of comparison. The GHS Index reported in the Global Health Security Index (2019) is calculated using the arithmetic mean, and is called AO.
The Pythagorean means are special cases of the generalized, power, or Hölder means, which can extend the three means discussed above to weighted power means, such as the quadratic and cubic means. In the interest of keeping the empirical analysis manageable, only the three Pythagorean means will be used in the paper.
The three classical Pythagorean means satisfy the inequality.
The AM (=AO) of the numerical scores of the six categories is defined as: where the subscript i = 1, 2, . . . , 6 represents PR, DR, RR, HS, CO and RE, respectively. The AM score might be referred to as GHS(AM), but we will continue to use AO, as given in the Global Health Security Index (2019). Two new alternative GHS mean scores are as follows. The geometric mean of the GHS scores, which is an arithmetic mean of the logarithms of the six GHS scores when all the observations are positive, is defined as: where the subscript i = 1, 2, . . . , 6 represents PR, DR, RR, HS, CO and RE, respectively.
The harmonic mean, which measures the reciprocal of the arithmetic mean of the reciprocals of the six GHS scores, is defined as: where the subscript i = 1, 2, . . . , 6 represents PR, DR, RR, HS, CO and RE, respectively.
In the empirical analysis, the new GHS average scores, GM and HM will be analyzed together with AO. According to the inequality in Equation (1), the three means satisfy.
If the rankings of all three means in Equation (5) are similar, according to the pairwise correlation coefficients, the use of AO would seem to be reasonable, although arbitrary. However, if the pairwise correlations are dissimilar, then the use of AO would be questionable, especially given the outliers among the six GHS rankings. This is especially the case when the chosen rankings would depend on an arbitrary selection of a Pythagorean mean.
Returning to Table 1, the means satisfy the condition in Equation (5), as do the minimum values of the numerical scores. The standard deviations are in reverse order to the respective means, as is the range. The maximum values of the numerical scores are similar.
The correlations of the numerical score rankings are given in Table 2. The correlations among AO, GM, and HM are high in the range (0.982, 0.997), with GM and HM having the highest correlation at 0.997. The correlation between DR and RR is very high at 0.987. The next highest correlations are between AO and PR, HS, DR and RR, with all values above 0.89. The correlations of GM and HM with these categories are similar to those of AO. The lowest correlations are between RE and CO, DR and RR, with all values below 0.44. The correlations of the ordinal rankings are given in Table 3, which qualitatively match the results in Table 2. The correlations among AO, GM, and HM are high in the range (0.950, 0.987), with GM and HM having the highest correlation at 0.987. The correlation between DR and RR is 0.999, which means that the two categories are virtually identical. The next highest correlations are between AO and HS, DR, RR and PR, with all values above 0.88. The correlations of GM and HM with these categories mirror those of AO. The lowest correlations are between RE and CO, RR and DR, with all values below 0.39.
The numerical score GHS Index is regressed on the numerical score rankings of the six categories in Table 4 to check if equal weights in the calculation of the GHS Index are justified. Given the high correlation between DR and RR in Table 2, it is not surprising that RR is statistically insignificant in the first column in Table 4. Each DR and RR are deleted in the second and third columns in Table 4, where the other variable is found to be statistically significant. The highest weights in each case are determined to be RR at 0.325, while the lowest weights are for PR at 0.186 and RE at 0.128. Therefore, Rapid Response has a large impact on the GHS Index numerical score.  The quantitative and qualitative results for GM and HM in Tables 5 and 6 are quite different from those of AO in Table 4. Both DR and RR are significant for GM, whereas RR is insignificant for HM. The highest weight for GM is RR at 0.42, while the lowest weights are RE at 0.109 and CO at 0.13, which are markedly different from the weights for AO. The highest weights for HM is RR at 0.398 and HS at 0.366, while the lowest weights are RE at 0.076 and CO at 0.096, which are substantially lower than the corresponding weights for AO, as well as lower than for GM.
Overall, the range in the weights is much greater for both GM and HM than they are for AO, although RR has the highest weights for each of the three means.
The ordinal GHS Index is regressed on the ordinal rankings of the six categories in Table 7 to check for the optimal weights in the calculation of the ordinal GHS Index. Given the correlation of 0.999 between DR and RR in Table 3, it is not surprising that both categories are insignificant for AO in the first column when they appear simultaneously, while RR is only marginally significant. Deleting DR and RR in turn leads to the estimates in the second and third columns in Table 7, respectively, which show that the estimates for AO are identical, a result that is mirrored for GM and HM. With AO as the dependent variable, the highest weights are for DR and RR at 0.368, while the lowest is for RE at 0.142.
Broadly similar results hold for GM and HM in Tables 8 and 9, respectively. The categories DR and RR also have the highest weights for GM and HM, but with higher numerical values of 0.382-0.383 for GM, and a lower numerical value of 0.341 for HM. However, unlike the case for AO where the lowest weight was for RE at 0.142, the lowest weight for GM is PR at 0.175. The lowest weight for HM is also PR, but at much lower weights of 0.118-0.119. It is clear that the ordinal rankings differ more widely across AO, GM and HM than they did for the GHS numerical score rankings.
Overall, Rapid Response and Detection and Reporting have strong impacts on the GHS Index ordinal ranking, regardless of whether the mean is AO, GM, or HM. While Risk Environment has the smallest impact on the GHS Index ordinal score for AO, Prevention has the smallest impact for GM and HM.

Conclusions
Given the volume of research and discussion on the health, medical, economic, financial, political, and travel advisory aspects of COVID-19, it is essential to enquire if an outbreak of the epidemic might have been anticipated, in light of the well-documented history of SARS and MERS. If various issues directly related to health security risks could have been predicted accurately, public health and medical contingency plans might have been prepared and activated well in advance of the onset of an epidemic such as COVID-19.
In this light, this paper critically evaluated an important source of health security, namely the Global Health Security Index (2019), which provided data before the discovery of COVID-19 in January 2020. Therefore, it is possible to evaluate how countries might have been prepared for a global epidemic, or pandemic, and acted accordingly.
The GHS Index numerical score is the arithmetic mean of the data for six categories, and hence uses equal weights for each category. The AO of the GHS Index score was regressed on the numerical score rankings of the six categories to check if the use of equal weights of 0.167 in the calculation of the GHS Index was justified. The highest weights were determined to be around 0.244-0.246, while the lowest weights were around 0.186-0.187.
Two alternative mean scores, namely the geometric mean (GM) and harmonic mean (HM), were also calculated from the numerical GHS Index scores. In addition to presenting alternative means of the GHS scores, they also provide a check of the robustness of the arithmetic mean score (AO) in the Global Health Security Index (2019). Although the three means suggested that Rapid Response had the largest impact, albeit with different weights, AO found the smallest impact from Prevention and Risk Environment, whereas both GM and HM found Compliance and Risk Environment had the smallest impacts.
The ordinal GHS Index was regressed on the ordinal rankings of the six categories to check for the optimal weights in the calculation of the ordinal GHS Index. The highest weight was 0.368, while the lowest was 0.142, so the estimated results are wider apart at 0.226 than for the numerical score rankings. The range was smaller for GM at 0.180 and for HM at 0.199.
Overall, Rapid Response and Detection and Reporting have the largest impacts on the GHS Index score, regardless of whether AO, GM, or HM were used, albeit with different weights. Risk Environment has the smallest impact on the GHS Index score when AO is used, whereas Prevention has the lowest impacts for GM and HM.
In preparing for an epidemic or pandemic, the order and importance of risk factors need to be known so that public health and medical contingency plans can be coordinated and activated effectively and in a timely manner. In such an environment, it is revealing that Rapid Response and Detection and Reporting have the largest impacts.

Conflicts of Interest:
The authors declare no conflict of interest.