The disproportionate case–fatality ratio of COVID-19 between countries with the highest vaccination rates and the rest of the world

Highlights • We compared the vaccination rates and case–fatality rates (CFRs) for coronavirus disease 2019 (COVID-19) for various countries on 31 December 2022.• 260 COVID-19 vaccine doses (/100 population) were administered in the 20 countries with the highest vaccination rates countries are 260.• In the rest of the world and Sub-Saharan Africa, 152 doses and 51 doses have been administered per 100 population.• The mean CFR of COVID-19 in the top 20 vaccinated countries decreased by 69%.• The mean CFR decreased by 27% in the rest of the world and by 8% in Sub-Saharan Africa.

COVID-19 vaccines are not distributed equitably in the world [11] . Although COVID-19 vaccines were developed at an unprecedented rate through the advancement of science and global cooperation, the distribution of COVID-19 vaccines across the world is questionable [12] . Current global vaccination rates are approximately 6.7 million doses per day, and the vaccine distribution is absent or very limited in many low-income countries. Experts anticipated that 80% of the population in low-income countries would not have received any doses of COVID-19 vaccine by the end of 2021 [12] , and this has proved to be the case.
As the world faces the third year of the COVID-19 pandemic, as of 31 December 2022, more than 660.35 million confirmed cases of COVID-19, including 6.69 million deaths, have been reported to WHO [13] . Globally, rollout of COVID-19 vaccination has progressed at varying rates, and the impact of mass vaccination on CFR should be explored in order to inform global access to the vaccine. To this end, this study compared the global rCFRs between the 20 countries with the highest vaccination rates (minimum 196.9 doses/100 population), sub-Saharan Africa (SSA) and the rest of the world, before and after commencement of vaccination programmes. In addition, associations between vaccination and other control measures and COVID-19 CFR and excess mortality were explored.

COVID-19 data
The necessary COVID-19-related data, including daily reported new cases, daily reported new deaths, reported total deaths, reported total deaths per million inhabitants and vaccination (number of doses of any COVID-19 vaccine administered/100 population), were collected from the WHO daily COVID-19 situation reports of 210 countries from 1 January 2020 to 31 December 2022 [14] . On 8 December 2020, the first approved COVID-19 vaccine was administered to a human [15] . Twenty-eight days after 8 December 2020 was considered as the cut-off to compare the pre-vaccine period (1 January 2020-5 January 2021) and the post-vaccine period (6 January 2021-31 December 2022). In total, data were obtained from 159 countries for analysis after the exclusion of countries with population < 1 million. Of the 159 countries,

Identifying the top 20 vaccinated countries
The top 20 countries were those countries that consistently remained in the top 20 in terms of the weekly vaccination rate (/100 population) during the period 5 January 2021-31 December 2022. A count variable was used to identify the top 20 vaccinated countries each week, with a score of 1 if a country was listed in the top 20 countries in a particular week and zero otherwise. This procedure was repeated for each week until 31 August 2022. Finally, the 20 countries with the highest aggregated scores for weekly vaccination rate were selected. The 20 countries with the highest COVID-19 vaccination rates were (doses/100 popula-

Reported case-fatality ratio
The daily cumulative COVID-19 rCFR was calculated, as described previously [6] , as the number of reported COVID-19-attributed deaths per 100 COVID-19 confirmed cases [i.e. rCFR = (weekly reported COVID-19 attributed deaths/weekly reported COVID-19 confirmed cases) x100]. As the numbers of reported cases and deaths both represent a fraction of the total numbers of cases and deaths globally, the term 'rCFR' was used [6] .

Excess mortality
Excess mortality is used to describe the number of deaths from all causes during a particular period that is higher than expected under 'normal' circumstances [16] . Excess mortality was calculated as the difference between the recorded number of fatalities in a certain week or month (depending on the country) between January 2021 and December 2022, and an estimate of the projected deaths for that time period if the COVID-19 pandemic had not happened [ 17 , 18 ]. There are major difficulties associated with obtaining excess mortality data from many countries; however, 'Our World in Data' tracked data from different sources, and the authors were able to extract excess mortality data from 159 countries for the period from 5 January 2021 to 31 December 2022 [19] .

Time series model to predict the trend
Three time series models [i.e. auto-regressive integrated moving average (ARIMA), automatic time-series forecasting model also known as 'Prophet model', and simple exponential smoothing (SES)] were used to identify the global trends in COVID-19 rCFR and excess mortality. The details of the SES, ARIMA and Prophet models are discussed elsewhere [6] .

Outcome and predictor variables
Data on selected predictor variables were collected from the World Bank or other United Nations sources and from 'Our World in Data', including population density [20] , percentage of people aged ≥ 65 years [21] , Gross Domestic Product (GDP) [22] , worldwide governance indicators [23] , Global Health Security Index [24] , and prevalence of obesity [ 25 , 26 ] for analysis. In addition, country-specific prevalence rates of diabetes [26] and cardiovascular disease [26] were included to explain the variation in COVID-19 rCFRs. The 'Stringency Index' from the Oxford COVID-19 Government Response Tracker was used [27] .

Empirical evaluation
The ARIMA and Prophet models were assessed by comparing their results with the benchmark model, the SES model [28] . The SES model is the most appropriate non-seasonal model for each series, allowing for any kind of error or trend component. Next, the performances of the time series models were analysed and compared with some commonly used measures to evaluate the significance of predictions, including coefficient of determination ( R 2 ), root mean square error (RMSE) and mean absolute error (MAE).

Generalized linear mixed model
A generalized linear mixed model (GLMM) with beta distribution was developed to identify whether the explanatory variables were associated with the country's COVID-19 rCFR and excess mortality. The GLMM is an extension of the generalized linear model that allows the analysis of clustered categorical data, as in the case of repeated responses from different subjects [29] . One of the key advantages of the GLMM is that it separates the levels of the models to account for the group effect nesting the lower-level observations. In the present study, there were several observations within the variable 'locations (country or territory)'. While the location data are assumed to be time-invariant, the independent data are assumed to be universal over the whole study area at a certain time point. The model describes a beta distribution family that has a logit link.
Although the variables were selected carefully, and consistency was maintained with previous publications on the subject [6] , the authors were not able to add some potential confounding variables, including the median age of cases in each country. All analyses were undertaken using R Version 3.5.2.2 [30] .

Statistical analysis
Summary statistics of vaccine doses/100 population and rCFR were obtained by country for the 20 countries with the highest vaccination rates ( Figure 1 ), SSA and the rest of the world before and after commencement of vaccination programmes, and the mean and standard error (SE) were reported. COVID-19 rCFR and excess mortality changed over time ( Figure 2 ). The use of time series models alone would not enable identification of the reasons for the increasing and decreasing trends in COVID-19 rCFR and excess mortality.

Factors associated with rCFR and excess mortality
In the GLMM, the estimated effect of each variable is presented as the odds ratio ( ( Table 2 ). Table 2 includes various covariates and the random intercept in the model. The intraclass correlation coefficient of 0.682 was calculated by dividing the variance of the random effect by the total variance. Thus, the spatial unit effects account for approximately 68.2% of the total variance in weekly rCFR, which suggests moderate reliability on location effects on weekly rCFR. It is also to be noted that with the introduction of a random intercept, 'vaccination', 'population density', 'GDP', 'weeks' and 'Stringency Index' had significant negative effects on weekly rCFR, and 'percentage of people aged ≥ 65 years' had a significant positive effect.

Trend of global COVID-19 rCFR
The ARIMA and Prophet models found a strong declining trend in COVID-19 rCFR between observed and predicted global COVID-19 rCFR with R 2 , RMSE and MAE of 99.97% and 99.50%, 0.029 and 0.113, and 0.008 and 0.059, respectively ( Table 3 ). The observed and predicted rCFR and observed and predicted excess mortality had fair agreement ( Figure 4 ). In terms of accuracy, the ARIMA model performed better that the Prophet and SES models (with better R 2 , RMSE and MAE). The coefficient of determination of the ARIMA model was larger and errors were lower compared with the Prophet and SES models. According to the forecast in both models, the ratio of COVID-19 rCFR is expected to decrease considerably in the coming 10 days ( Figure 1 ).      The SES, ARIMA and Prophet models used daily cumulative reported casefatality ratio (rCFR) data.

Discussion
The global COVID-19 rCFR has been declining since May 2020, stabilizing or increasing slightly with the emergence of different variants of concern (VOCs), particularly the Delta variant [ 31 , 32 ]. Following the rollout of COVID-19 vaccines, rCFR started to decline, although the rates differed between the top 20 vaccination countries (69% decrease) and the rest of the world (27% decrease). In SSA, where the vaccine rollout has not yet reached a satisfactory level, COVID-19 rCFR only decreased by 8%. Excess mortality, on the other hand, decreased by 49% in the top 20 vaccinated countries, 62.5% in the rest of the world and 60.71% in Sub-Saharan Africa. Many factors affect the reduction of rCFR; however, the present results indicate that vaccination and the stringency of control measures influence the reduction in rCFR. A study on the global impact of COVID-19 vaccination showed that vaccination averted 14.4 million reported deaths (or 19.8 million excess deaths) due to COVID-19 in the first year of vaccination (8 December 2020-8 December 2021) [11] . This analysis complements previous findings showing a disproportionate decline in rCFR and excess mortality in countries with various vaccination coverage levels, indicating the importance of equitable distribution of COVID-19 vaccines.
This study found an overall decreasing trend of excess mortality in the postvaccination period. In SSA, in contrast to the negligible decline in rCFR, a marked decrease in excess mortality was noted. Excess mortality during the COVID-19 pandemic was affected by various factors, and not merely by transmission of COVID-19 and vaccination coverage. Some of these factors (e.g. shielding elderly people) may have even contributed to the reduction in excess mortality. The differential impact of these factors made the use of excess mortality an unpredictable estimator of the severity of COVID-19 [33] . This study did not compare excess mortality data at country level. Although differences in data and methodology preclude direct comparisons between the present results and those of the above studies, it should be noted that none of the top 20 countries for excess mortality were in SSA. Although it is beneficial to increase vaccination coverage where possible, this may not be the only reason why the mortality rate in SSA, where the majority of the population are aged < 65 years, has decreased markedly since 2021. It is known that survival from COVID-19 is higher in younger age groups [ 6 , 34 ]. The positive association between Stringency Index and excess mortality is surprising and needs further study. An earlier study showed chaotic behaviour of COVID-19 data when compared with the Stringency Index [35] , and a weaker relationship with the mortality rate [36] . Excess mortality decreased by 48.6% in the top 20 vaccinated countries, 62.5% in the rest of the world and 60.7% in SSA. Excess mortality showed a different pattern compared with COVID-19 rCFR. This may be because of differences in population age structures between high-income countries and the rest of the world including SSA, rather than the actual impact of lockdown-related control measures estimated in the Stringency Index; there is a need for a well-designed study to investigate this further.
The negative correlation between doses of COVID-19 vaccine given per 100 population, rCFR and excess mortality indicate the benefit of vaccines. Thus, the vaccine has been considered as a pathway out of this pandemic, but strong, innovative policies that ensure fast and equitable distribution are absent [ 11 , 12 ]. Vaccinating the world serves global interests of protecting each other's health and economies [12] . The present analysis showed a large disparity in vaccine rollout between the top 20 vaccinated counties (260 doses/100 population) and low-income countries (e.g. 51 doses/100 population in SSA) by 31 December 2022. In high-income countries, the administration of a third or even fourth COVID-19 vaccine dose is ongoing [37] , whereas > 60% of the population in SSA have not yet received a single dose (as of 31 December 2022).
COVID-19 vaccination, Stringency Index and GDP were found to be significantly associated with the reduction in COVID-19 rCFR. The main vaccines (mRNA or adenovirus vector) have been found to be highly effective in reducing hospital admissions and deaths, although some vaccines were not very effective at limiting infection [38] . Thus, the vaccine rollout helped high-income countries to reduce the burden of patients in hospitals rapidly, thus limiting the number of COVID-19 deaths. However, in the rest of the world, where vaccine rollout is still far from satisfactory (defined as 70-85% of people are fully vaccinated) [12] , CFR has not declined markedly in comparison to the top 20 vaccinated countries. On the other hand, the results from different surveys suggest that natural immunity has reached a state where it is limiting spread and reducing the overall burden of the pandemic in many countries in SSA [39] . More than 28% of people in Brazzaville, Republic of Congo [40] , 64.9% of blood donors in Malawi [41] and 74% of community residents in the Central African Republic have been found to have antibodies to SARS-CoV-2 [42] . The country's GDP is another indicator associated with a reduction in COVID-19 rCFR. Countries with higher national income deployed vaccines at a faster rate, which reduced local transmission and the rate of hospitalization, allowing these countries to concentrate on the vulnerable population; these factors acted synergistically to reduce the number of COVID-19-related deaths. Earlier studies have also identified these variables as risk factors for mortality/fatality ratio of COVID-19 [ 6 , 43 , 44 ].
Equitable distribution of COVID-19 vaccines is crucial to ending the pandemic [ 11 , 45 ]. The circulation of SARS-CoV-2 across the world among the large unvaccinated populations may allow the virus to mutate into a new VOC. Furthermore, many animal species are susceptible to SARS-CoV-2, including mink, primates, rodents, cats and dogs [46] . Several animal species have been linked with the emergence of SARS-CoV-2 VOCs, including dogs for the Alpha variant [47] and rodents for the Omicron variant [48] . Thus, it is important to reduce the circulation of SARS-CoV-2 in human and animal populations in order to avoid further epidemics caused by emergence of new VOCs. Equitable and faster vaccine rollout is key to reducing the circulation of SARS-CoV-2 across the world [11] .
The model was adjusted for the number of tests/100 population in each country. Some countries do not report the daily testing number, while some countries share their test numbers irregularly. Testing is an important variable, and failure to adjust for it may result in the identification of spurious relationships. The denominator of rCFR (cases of COVID-19) is entirely predicated on the number of tests that a country has reported. As such, it is possible that the lower rCFRs in higher vaccination countries are simply reflective of greater testing capacity, and thus a larger denominator for the same number of deaths. Thus, only those countries that reported test data regularly were included in the analysis.
This study has several limitations. The main limitation is the dependence of the number of cases on the intensity of testing; as such, countries with low levels of testing missed fatal cases due to COVID-19. In countries where people undergo testing for travelling, working, moving, accessing health care etc., which tend to be higher-income countries where vaccine rollout was faster, large numbers of asymptomatic people are tested daily, which may result in the identification of large numbers of asymptomatic infections. These are then counted as COVID-19 cases, but these people are merely clinically ill. Thus, only some individuals in these countries are actually true cases, because a large proportion of positive cases are asymptomatic and are, therefore, infected. This may increase the denominator of the proportion artificially lowering the CFR. In contrast, it is likely that in SSA, the proportion of apparently healthy individuals who are tested is much lower, leading to apparently lower rCFRs in these countries. The associations reported in this study between COVID-19 rCFR/excess mortality and explanatory variables are statistical associations, and should not be interpreted as causal. Finally, differ-ent VOCs of SARS-CoV-2 have different rCFRs, and the VOCs circulated at different times in different countries [32] ; it was not possible to adjust for these factors in the analysis.

Conclusion
More than 260 doses of COVID-19 vaccines have been given per 100 population in the 20 countries with the highest vaccination rates, compared with 152 doses in the rest of the world and 51 doses in SSA as of 31 December 2022. Vaccination is negatively correlated with rCFR ( r = -0.36) and excess mortality ( r = -0.32), which is likely to reflect a contribution of vaccines to the reduction in COVID-19-related deaths. Excess mortality and COVID-19 rCFR have continued to decline since February 2021, although at a disproportionate rate between the top 20 vaccinated countries and the rest of the world. However, rCFR has decreased dramatically (69.3%) in the 20 countries with the highest vaccination rates (70%) and quite markedly in the rest of the world (30.0%), whereas it has only decreased by 7.6% in SSA. COVID-19 vaccination, Stringency Index and GDP were associated with a reduction in COVID-19 rCFR. Vaccine equity and faster rollout across the world is critically important to reduce COVID-19 transmission and CFR.

Funding
None.

Ethical approval
This study does not include any individual-level data and thus did not require ethical approval.

Data availability
All data presented in this manuscript are publicly available on the 'Our World in Data', WHO or United Nations webpages. However, the corresponding author can be contacted regarding specific queries on the data sources.