Abstract

Introduction: This study seeks to model Covid-19 cases and deaths and excess all-cause mortality in 19 European countries over the period 2020-2023, using a number of socio-demographic factors as independent variables.

Methods: We used QSAR (Quantitative Structure-Activity Relationship) multiple linear regression modelling to examine which of over 20 socio-demographic factors best modelled the data. The Minitab ‘Best Subsets’ routine was used to select the best descriptor sets for each model.

Results: We were unable to obtain good QSAR correlations for cases, probably because of significant under-reporting of Covid-19 infections. Despite some under-reporting of Covid-19 deaths, they were well modelled with two factors, namely a pollution index and levels of Cardiovascular problems (CHD, CVD, stroke), both of which increased Covid-19 deaths.

Excess all-cause mortality is now regarded as a more accurate indication of deaths, and we obtained very good QSAR models for seven publicly available excess all-cause mortality data in the 19 European countries. Modelling selected the same two factors in each case, namely level of Covid-19 vaccination and latitude N (north), both with negative signs.

Discussion and conclusion: The models show that Covid-19 deaths appeared to be controlled largely by levels of pollution and of cardiovascular diseases. Excess all-cause mortality during the pandemic was modelled best by vaccination levels and latitude north. The rôle of latitude N is not clear, but we suggest that it could be a proxy for exercise levels and temperature, both of which correlate reasonably well with latitudes of the 19 European countries.

Keywords: Covid-19; Cases; Deaths; Excess all-cause mortality; Modelling; QSAR.

Introduction

The viral infection Severe Acute Respiratory Syndrome 2 (SARS-Cov2), generally referred to as Covid-19, is a severe viral infection that started in Wuhan, China, in late 2019, and spread rapidly throughout the world. It was declared a pandemic by the World Health Organisation (WHO) on 12 March 2020 [1]. The western world in particular was totally unprepared for this catastrophe, as the last time such a huge event had occurred was a severe influenza outbreak, the so-called Spanish flu, in 1918, which killed at least 50 million people worldwide [2].

In the months following the initial outbreak of Covid-19, a number of possible factors that could affect infection and death rates were proposed in scientific reports and in the media; these included the effect of vitamin D on reducing infection rates [3] and a range of socio-demographic factors such as obesity and levels of smoking.

In an attempt to elucidate which if any of these factors were contributing to the pandemic, we used the QSAR (Quantitative Structure-Activity Relationship) approach [4] to correlate cumulative Covid-19 cases and deaths per million inhabitants in 20 European countries up to 9th May 2020 with 20 potential factors [5]. We found that a key factor in infection rates was, as Ilie et al. [3] had reported, levels of vitamin D in populations. Other controlling factors for infection rates were levels of stroke deaths, levels of smoking and levels of respiratory deaths. Covid-19 death rates were found to correlate best with population densities, proportions of elderly (>65) people and levels of inactivity.

It must be pointed out that such modelling requires the input data to be as accurate as possible. However, it is known that the numbers of both cases and deaths in the pandemic almost certainly contain considerable error. For example, Starnini et al. [6], focussing on Italy and Spain, found “several biases of case-based surveillance data and temporal and spatial limitations in the data”, and called for “an improvement in the process of COVID-19 data collection, management, storage, and release”. Kobak [7] stated that “for many countries the reported numbers of cases and deaths can be gross underestimations”. In some instances, the opposite is the case; for example, in the United Kingdom if a person died in hospital with Covid-19, the death was reported as a Covid death even if the person died of something else. Nevertheless, we believe that QSAR modelling of Covid-19 cases and deaths should yield indications of which socio-demographic factors are important in controlling the development of the pandemic.

The present work extends that previously reported [5] by using Covid-19 cumulative cases and deaths per million inhabitants on two additional dates: 5th May 2023 (the date on which the WHO declared the pandemic to be over) and 7th November 2021 (midway between the other two dates), for 19 European countries. Turkey was removed from our original list of 20 countries because it is partly in Europe and partly in Asia, and it was not always clear whether Turkish data related only to its European area or to the whole of Turkey.

We also modelled all-cause excess mortality in the selected 19 European countries during periods in late 2020 to late 2022. This statistic is defined as the increase in all-cause mortality relative to the expected mortality [8]. It is regarded as “a more comprehensive measure of the total impact of the pandemic than the confirmed Covid-19 death count alone. It captures not only the confirmed deaths, but also COVID-19 deaths that were not correctly diagnosed and reported as well as deaths from other causes that are attributable to the overall crisis conditions” [9].

Methods

Cumulative Covid-19 cases and deaths per million inhabitants were taken from Wikipedia [10]. Excess mortalities were taken from seven sources: Office for National Statistics (ONS) [11]; Our World in Data (OWID) [12]; Eurostat (Euro) [13]; Organisation for Economic Co-operation and Development (OECD) [14]; The Collaborators (Coll) [15]; The Economist (Econ) [16]; World Health Organization (WHO) [17]. Data for the potential socio-demographic factors (descriptors) for the 19 European countries were taken from Dearden and Rowe [5]. Two of them require explanation: HDI is a Human Development Index, a composite index of life expectancy, education and per capita income [18]; UHC (Universal Health Coverage) is a measure of access to the full range of quality health services without financial hardship [19]. Lengths (days) of the first and second lockdowns (LD1 and LD2) were also included as descriptors [20], as were three datasets giving Covid-19 vaccination levels; the percent percentage of people fully vaccinated in July 2022 (VaccJ22) [21] and in December 2022 (VaccD22) [22], and the number of vaccinations per 100 people by late 2022-early 2023 (Vacc22/23) [23]. Statistical analysis of the data was performed with Minitab statistical software, version 20.0 [24], using the best sub-sets routine to find the factors (descriptors) that best modelled the Covid-19 data. For 19 objects (in this case countries) no more than three or four descriptors should be used in a model, to minimise the risk of chance correlations [25]. It should be noted that almost all types of data contain error, particularly in vivo data, so a good statistical model should have a coefficient of determination (r2) in the region of 0.7-0.8, and a predictive r2 (termed q2) of ≥0.5. The probability (p) of each of the descriptors in a correlation being there by chance should be ≤0.05 (≤1 in 20).

European countries were not fully vaccinated against Covid-19 until the spring of 2022 [26]. Therefore, in order to assess the effect of vaccination on the progress of the pandemic, cumulative cases/million and deaths/million for 5th July 2022 were subtracted from those for 5th May 2023.

Results

Table 1 shows the cumulative cases and deaths per million inhabitants for the 19 European countries.

Table 1: Cumulative Covid cases and deaths per million inhabitants for 19 European countries.

Correlations between cases and deaths are: for 09.05.20, r² = (+) 0.425; for 07.11.21, r² = (+) 0.425; for 05.05.23, r² = (-) 0.100.

Table 2: Cumulative Covid cases and deaths per million inhabitants for 19 European countries from the start of full vaccination.

Table 3 gives the r2 values of correlations of Covid-19 cases and deaths with each socio-demographic factor separately.

Table 4 gives the excess all-cause mortality (EACM) values for the 19 European countries from seven different sources.

Table 5 gives the correlation matrix of each set of values in Table 4.

Table 3: Single correlations (r2) of cases/million and deaths/million with socio-demographic descriptors (signs in brackets indicate a positive or negative correlation).

Table 4: EACM figures for the 19 European countries, from seven different sources.

Table 5: Correlation matrix (r2) of seven sets of EACM data.

Table 6 gives the Covid vaccination figures for the three sets of vaccination data that we used.

Table 7 gives the r2 values of correlations of EACM with each socio-demographic factor separately.

The best QSARs for cumulative cases and deaths on each of the three selected dates are given below. The statistical data are: n=number of countries; r2=coefficient of determination; q2=predictive coefficient of determination; s=standard error of prediction; F=variance ratio or Fisher coefficient (a measure of goodness of fit); p=probability of chance correlation (range 0 to 1).

Table 6: Covid vaccination data.

*(%) means percentage of people fully vaccinated; (/100) means average number of vaccinations per 100 of population.

Cases/million 9.5.20 = 12773 – 75.7 vitamin D – 76.2 stroke – 217.5 >65 (1)

n = 19 r² = 0.677 q² = 0.502 s = 938.3 F = 10.5 All p≤0.047

Deaths/M 9.5.20 = – 3325 + 13.42 pollution index + 37.47 UHC index (2)

n = 19 r² = 0.737 q² = 0.626 s = 121.6 F = 22.4 All p < 0.001

Deaths/M 9.5.20 = 242 – 15.89 stroke + 12.70 pollution index (3)

n = 19 r² = 0.722 q² = 0.632 s = 125.0 F = 20.8 All p < 0.001

Deaths/M 9.5.20 = 73 – 13.51 stroke + 10.56 pollution index + 4.82 inactivity (4)

n = 19 r² = 0.797 q² = 0.701 s = 110.4 F = 19.7 All p≤0.033

Cases/M 31.1.21 No good models with r² ≥ 0.6

Deaths/M 31.1.21 = – 142 + 42.06 pollution index – 5.62 exponential index (5)

n = 19 r² = 0.710 q² = 0.000 s = 324.8 F = 19.1 All p≤0.039

Cases/M 7.11.21 No good models with r² ≥ 0.6

Deaths/M 7.11.21 = – 769 + 7.12 CHD + 56.12 pollution index (6)

n = 19 r² = 0.793 q² = 0.723 s = 446.7 F = 30.7 All p≤0.008

Table 7: Single correlations (r2) of all-cause mortality values with socio-demographic descriptors.

Deaths/M 7.11.21 = – 1000 +33.1 stroke + 52.00 pollution index (7)

n = 19 r² = 0.782 q² = 0.708 s = 458.3 F = 28.8 All p≤0.013

Cases/M 5.5.23 No good models with r² ≥ 0.6

Deaths/M 5.5.23 = – 872 + 64.6 stroke + 50.24 pollution index (8)

n = 19 r² = 0.811 q² = 0.744 s = 516.6 F = 34.4 All p< 0.001

Deaths/M 5.5.23 = – 367 + 13.01 CHD + 58.58 pollution index (9)

n = 19 r² = 0.802 q² = 0.718 s = 528.8 F=32.1 All p<0.001

For both (cases/M 5.5.23 – cases/M 5.7.22) and (deaths/M 5.5.23 – deaths/M 5.7.22) no satisfactory models were found.

The best QSARs for excess mortality are given below.

ONS = 35.76 – 0.0583 Vacc22/23 – 0.264 Lat N (10)

n = 19 r² = 0.680 q² = 0.528 s = 2.085 F = 17.0 All p≤0.002

ONS = 42.31 – 0.240 VaccJ22 – 0.286 Lat N (11)

n = 19 r² = 0.624 q² = 0.421 s = 2.260 F = 13.3 All p≤0.002

OWID = 105.6 – 0.182 Vacc22/23 – 0.832 Lat N (12)

n = 18 r² = 0.713 q² = 0.608 s = 6.217 F = 18.7 All p≤0.001

OWID = 128.9 – 0.784 VaccJ22 – 0.912 Lat N (13)

n = 18 r² = 0.674 q² = 0.517 s = 6.632 F = 15.5 All p≤0.001

EURO = 41.45 – 0.0674 Vacc22/23 – 0.323 Lat N (14)

n = 17 r² = 0.688 q² = 0.574 s = 2.576 F = 15.4 All p≤0.002

EURO = 39.9 – 0.0690 Vacc22/23 + 0.0192 Lockdown2 – 0.303 Lat N (15)

n = 17 r² = 0.769 q² = 0.599 s = 2.301 F = 14.4 All p≤0.050

OECD = 1158 – 6.51 VaccJ22 – 10.43 Lat N (16)

n = 18 r² = 0.769 q² = 0.690 s = 51.81 F = 24.9 All p < 0.001

OECD = 1136 – 6.39 VaccD22 – 10.15 Lat N (17)

n = 18 r² = 0.763 q² = 0.657 s = 52.45 F = 24.1 All p < 0.001

Collaborators = 1611 + 6.51 % smoking – 17.96 HDI (18)

n = 19 r² = 0.820 q² = 0.749 s = 41.04 F = 36.4 All p≤0.010

Collaborators = 504.2 + 1.336 CHD – 8.93 Lat N (19)

n = 19 r² = 0.815 q² = 0.747 s = 41.60 F = 35.2 All p < 0.001

Economist = 923.1 – 6.646 VaccD22 – 5.35 Lat N ,(20)

n = 19 r² = 0.808 q² = 0.737 s = 34.75 F = 73.7 All p < 0.001

Economist = 945.9 – 6.775 VaccJ22 – 5.64 Lat N (21)

n = 19 r² = 0.822 q² = 0.753 s = 33.50 F = 36.9 All p < 0.001

WHO = 728.2 – 4.852 VaccD22 – 5.37 Lat N (22)

n = 19 r² = 0.761 q² = 0.699 s = 35.55 F = 25.5 All p < 0.001

WHO = 739.3 – 4.879 VaccJ22 – 5.57 Lat N (23)

n = 19 r² = 0.758 q² = 0.691 s = 32.75 F = 25.1 All p < 0.001

Discussion

Correlation between cases and deaths

If figures for cases and deaths were both recorded accurately, it would be reasonable to expect these to be positively correlated. The negative correlation seen for the 2023 data strongly suggests that by that year, one, or possible both, sets of data were no longer being reliably and consistently recorded in European nations.

Correlation of cases with potential contributory factors

Among equations 1-9 linking cases and deaths to possible factors, there are only two cases where an acceptable relationship for cases could be established. In contrast, eight such equations emerged for deaths. The correlation coefficients between cases and deaths had already created doubt about one or both of these measures, and this finding casts particular suspicion on the data for cases.

In our previous study of the modelling of Covid-19 cases and deaths in 20 European countries, we used the Box and Cox apapproach [27] to transform the Covid-19 data and the potential descriptors. Best sub-sets regression analysis yielded two models, one selecting vitamin D levels, stroke deaths/100K and respiratory deaths/100K, and the other selecting vitamin D levels, smoking % prevalence and HDI.

In the present work, we studied only 19 European countries, and found (Equation 1) that whilst vitamin D level was again selected as a good descriptor for the 9^th May 2020 cases data, other selected descriptors were different from those previously selected. Nevertheless, stroke deaths/100K correlated well (r²=0.750) with CVD deaths/100K, so the contributions of those two descriptors could be similar. However, in equation 1 both the stroke and >65 terms are negative, which is contrary to expectation. No reliance can therefore be placed on Equation 1.

For all dates other than 9th May 2020, no good or even satisfactory models could be obtained for cases. The reason is likely to be inaccuracies in the data; on later dates infections by the Covid-19 Omicron variant were generally much milder, which led to many fewer cases being reported. Several studies have examined the effects of inaccurate data on Covid-19 policies [28-30].

From the above, it is clearly necessary that great improvements in the accuracy of the numbers of both cases and deaths from a pandemic need to be made.

Correlation of deaths with potential contributory factors

In stark contrast to the modelling of Covid-19 cases, that of Covid-19 deaths shows that very similar descriptors were selected for each of the three dates (Equations 2-9). Pollution index was selected in each of those QSARs; CVD deaths/100K and stroke deaths/100K were also selected several times. It can be inferred that Covid-19 deaths in European countries were much better reported than were cases, although it is claimed [31] that there was under-reporting of Covid-19 deaths. Nevertheless, it can be concluded that the main factors affecting Covid-19 deaths in European countries were pollution and cardiovascular problems. This confirms what has observed elsewhere for pollution [32] and for cardiovascular disease [33,34]. It should be noted that the study by Ssentongo et al. [34] found, when examining the effects of 11 comorbidities on Covid-19 mortality, that cardiovascular disease had the greatest effect, increasing mortality by 125%.

If the effects of any future similar pandemic are to be contained, it is clear that much work needs to be done in reducing levels of pollution and cardiovascular disease.

Correlation of excess all-cause mortality with potential contributory factors

The strong positive correlations among most of the measures of excess deaths (Table 5) suggest that they are all measuring essentially the same thing, although the data from The Collaborators [15] correlate less well with the other measures, leaving the possibility that this data set is measuring something slightly different.

In contrast to numbers of cases and deaths, the data on excess deaths are well modelled using a limited number of variables (only eight appear in equations 10-23), and these are dominated by various measures of vaccination levels, all of which show negative correlation with excess deaths, as might be expected, and by latitude N, which also has a negative sign.

Latitude N must be a proxy for one or more other factors. Of the other factors that we have used, latitude N correlates best with exercise levels (r2=0.537) and HDI (r2=0.357), which is understandable. However, it occurred to us that two other factors, happiness and temperature, could possibly affect excess all-cause mortality. The Bible tells us [35] that: “A cheerful heart is good medicine, but a crushed spirit dries up the bones”. Happiness levels are available [36], and these correlated well with latitude N (r2=0.543) for our 19 European countries. Temperature also is known to affect excess mortality [37], although there are very few studies in this area. Mean national temperatures were taken from [38].

Table 8 gives the data for these factors.

Table 8: Latitude N and factors for which it may be a proxy.

The only measures of excess deaths that were not modelled by vaccination levels and latitude N were those from The Collaborators [15]. However, it has already been commented that this data-set may be measuring something slightly different from the others.

We checked whether any of the above factors could be important by best sub-sets modelling of EACM without using latitude N as a factor. The best resulting QSARs were:

EACM (ONS) = 24.1 – 0.0480 Vacc22/23 – 0.119 Exercise (24)

n = 19 r² = 0.634 q² = 0.384 s = 2.230 F = 13.8 All p≤0.005

EACM (ONS) = 20.63 – 0.0691 Vacc22/23 + 0.451 Temperature (25)

n = 19 r² = 0.609 q² = 0.378 s = 2.304 F = 12.5 All p≤0.009

EACM (OWID) = 57.62 – 0.220 Vacc22/23 + 1.588 Temperature (26)

n = 18 r² = 0.695 q² = 0.540 s = 6.414 F = 17.1 All p≤0.002

EACM (OWID) = 69.3 – 0.147 Vacc22/23 – 0.393 Exercise ,(27)

n = 18 r² = 0.691 q² = 0.511 s = 6.460 F = 16.8 All p≤0.002

EACM (EURO) = 27.3 – 0.0540 Vacc22/23 – 0.150 Exercise (28)

n = 17 r² = 0.649 q² = 0.491 s = 2.729 F = 13.0 All p≤0.006

EACM (EURO) = 22.97 – 0.0794 Vacc22/23 + 0.534 Temperature (29)

n = 17 r² = 0.595 q² = 0.423 s = 2.932 F = 10.3 All p≤0.016

EACM (OECD) = 644 – 9.21 VaccJ22 + 21.29 Temperature (30)

n = 18 r² = 0.760 q² = 0.675 s = 52.74 F = 23.8 All p<0.001

EACM (OECD) = 629 – 8.85 VaccD22 + 20.17 Temperature (31)

n = 18 r² = 0.743 q² = 0.652 s = 54.62 F = 21.7 All p<0.001

EACM (COLLAB) = 1611 – 17.96 HDI + 6.51 Smoking (32)

n = 19 r² = 0.820 q² = 0.749 s = 41.04 F = 36.4 All p≤0.010

EACM (ECON) = 1652 – 4.803 VaccJ22 – 12.58 HDI (33)

n = 19 r² = 0.848 q² = 0.782 s = 30.96 F = 44.6 All p<0.001

EACM (ECON) = 1103 – 5.507 VaccJ22 – 77.6 Happiness (34)

n = 19 r² = 0.838 q² = 0.746 s = 31.92 F = 41.5 All p<0.001

EACM (WHO) = 473.5 – 6.550 VaccJ22 + 12.22 Temperature (35)

n = 19 r² = 0.808 q² = 0.753 s = 29.21 F = 41.5 All p<0.001

EACM (WHO) = 567.0 – 6.356 VaccD22 + 11.49 Temperature (36)

n = 19 r² = 0.799 q² = 0.744 s = 29.86 F = 31.8 All p<0.001

The above models indicate that latitude N is a proxy mainly for exercise and temperature, and possibly for happiness, all of which correlate well with latitude N (r=0.733, -0.874 and 0.737 respectively). In order to reduce EACM, governments and other bodies must stress the vital importance of exercise for everyone. That would, or course, lead also to better health in general, thereby lowering the cost of illness and other morbidities.

It can be seen from equation 32 that, the Collaborators data yielded a different model, again indicating that those data are measuring something different from the other data-sets. Note that we were able to obtain only one good QSAR model with The Collaborators data-set.

The Collaborators [15] used a Least Absolute Shrinkage and Selection Operator (LASSO) regression to select a list of contributory factors that “have sensible direction of effect on the excess mortality rate”. They selected 15 such factors, seven of which are similar or identical to the factors that we have used, namely CVD death rate (positive), healthcare access and quality index (negative), mobility (positive), proportion of population over age 75 (positive), smoking prevalence (positive), UHC (negative), and average absolute latitude (positive). These yielded a model that accounted for 69.1% (i.e. r2=0.691) of the variation in excess all-cause mortality, which is good considering that their study involved many more countries and regions than does our study. Our latitude N factor had a negative sign, but the difference in sign is probably because The Collaborators’ study included a large number of countries covering a wide range of latitudes, some of which were south of the equator.

A review published by the British Office for National Statistics [39] reviewed a number of published studies of possible factors affecting excess all-cause mortality during the Covid-19 pandemic. They reported that cardiovascular diseases, diabetes, chronic obstructive pulmonary disease, dementia, obesity, smoking, age and ethnicity had all been found to affect excess all-cause mortality. Whilst our models for The Collaborators’ data-set (equations 18 and 19) incorporate some of the above factors, it is striking that our models for the other excess all-cause mortality data-sets do not incorporate any of them.

Conclusion

The three outcomes that we have attempted to model have yielded very variable levels of success. Numbers of cumulative cases produced only two acceptable equations, but numbers of cumulative deaths generated far more, although the factors entering into these were rather variable, and in a number of models the signs on coefficients were counter-intuitive, perhaps indicating that data error could be responsible. Excess deaths were modelled in a far more satisfactory way, and showed a strong and consistent influence of vaccination levels, as well as of the proxy factor latitude N. Intuitively, this pattern probably accords with the relative difficulties in obtaining reliable and consistent measures of the three outcomes. Numbers of cumulative cases are likely to be particularly problematic at later time points, as governments had little need to record these once the lethality of the disease had declined. Numbers of cumulative deaths would have been recorded more accurately, but ascertaining numbers specifically due to Covid-19 is more problematic. Excess deaths data should be the most reliable as they only require total numbers of deaths in the Covid-affected years and in preceding years. Our analysis leads us to conclude that excess all-cause mortality is controlled largely by vaccination levels and factors such as exercise and temperature.

To reduce the impact of any future respiratory pandemics, great improvements should be made in levels of exercise, and in reduction of cardiovascular diseases and levels of pollution. Data collection needs to be improved, in order to follow the progress of a pandemic more accurately.

Declarations

Disclaimer: The submitted article is our own, and is not an official position of our institution.

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