Weak or No Correlation Between Recent COVID-19 Data and Vaccination Rates in France

Since August 9, the "health pass" became mandatory in France and applies to many economic sectors and social activities such as commercial catering, trade fairs and exhibitions, healthcare services and medical-social centres, public long-distance transport, and some stores and shopping malls. In addition, since September 30, 2021, the "health pass" has been made compulsory for minors aged 12 and two months to 17 years old. The aim is to better control the spread of the Sars-Cov-2 virus by forcing the entire population to be vaccinated in order to reduce the effects of the epidemic. Since vaccination is currently the only pursued strategy to fight against COVID-19 in the world, we were interested in verifying the explanation often put forward to justify the improvement (due to high vaccination rate) or the recrudescence (due to low vaccination percentage) of the health situation linked to COVID-19. At the same time, several developed countries have launched the injection of a third dose of vaccines following a substantial increase in COVID-19 cases. In this regard, we have studied the correlation between the levels of vaccination coverage (percentage of the vaccinated population) and the various epidemiological variables of COVID-19 in the 101 French departments (territories) during the month of September 2021. The findings of the study indicate no significant relationship between vaccination rates and COVID-19 data.


Methodology
The epidemiological data 2 used in this study are published by Santé France and made available as of October 4th and 5th 2021. We have calculated the hospitalisation (tx_hosp), ICU admissions (tx_rea) and daily mortality ratios (tx_dchosp or tx_dc 3 ) per 100 thousand people for each territory. COVID-19 incidence ratios (tx_incid), positivity percentages (tx_pos) and reproduction ratio (R0) are provided by Santé France.
The correlation or statistical relationship between these variables and the levels of vaccination (D1 for Dose 1 & D2 for Dose 2) is investigated through an affine relation estimated by linear regression. The Pearson's correlation coefficient "R" is then calculated as the covariance of two variables divided by the product of their standard deviations. Its sign indicates whether higher values of one variable correspond "on average" to higher or lower values for the other variable. It is +1 in the case of a perfect increasing linear association, -1 in the case of a perfect decreasing linear association. For all other cases, a value between -1 and +1, indicating the degree of linear relationship between the variables. The closer the coefficient is to -1 or +1, the higher the correlation between the variables. As it approaches zero, there is weak or no relationship. The Coefficient of Determination "R 2 " represents the ratio of the variation of the Y variable that is being explained by the X variable.
The table below summarises the different correlation levels for a linear regression of the population P (sample S) defined as follows: H0: β1 = 0 We test the Alternative Hypothesis Ha defined as: There is a moderate or strong or very strong decreasing correlation between COVID-19 epidemiological dependent variables (Y-axis) and the vaccination rates (independent variables, Xaxis) in France during September 2021 (R < 0 AND R 2 > 0.423).
Ha: β1 ≠ 0 The outcome of the test is either the rejection of the Null Hypothesis or the failure to reject H0 at 5% level of significance.

General Results
For the whole country, Figure 1 shows a very strong decreasing relationship (R = -0.9980, R 2 > 0.99) between the incidence ratio (tx_incid) and the percentages of vaccination during the month of September. The incidence ratio (infection cases per 100 thousand people) decreases while the vaccination rate increases. However, the daily mortality ratio (tx_dc) plot shows weak association (R = -0.4799 vs. D2 -p-value < 0.001; R = -0.4902 vs. D1 -p-value < 0.001) with the vaccination rates ( Figure 2).
France has a percentage of the population fully vaccinated between 66% and 72. However, for the daily mortality rate, there is an insignificant association (R = -0.4038 vs. D1 -p-value = 0.000; R = -0.4039 vs. D2 -p-value = 0.000) with the percentage of the vaccinated population, throughout September 2021, which accounts for only R 2 =16.3% for each dose (Figure 4), i.e., the variation -decrease of the daily mortality ratio can only be explained by 16% of the progression of vaccination rate.
The same analysis -weak relationship -applies to the ratios of hospitalised patients (tx_hosp) and ICU admissions (tx_rea) per 100 thousand people, shown in Figures 7 & 8, where the effect of vaccination is less than 38% and less than 32% in their decrease respectively.
For September 30, data show slightly moderate decreasing association between the vaccination percentages and the hospitalized patients (0.44 < R 2 < 0.47 -p-value = 0.000) according to Figure 9. Although there is weak association regarding the incidence, the daily mortality, and the ICU admissions as per Figures 5, 6 & 10 (0.20 < R 2 < 0.36 -pvalue = 0.000).

More Findings
Comparing the most with the least vaccinated territories (62 in total), we observe opposite results. For September 30, the incidence, hospitalisation, and ICU ratios tended to increase with the vaccination percentages ( Figures  11a,12a & 13a). Although, such association is insignificant (0.01 < R 2 < 0.14 vs. D2; 0.04 < R 2 < 0.23 vs. D1), it shows that a relationship between the variables of the COVID-19 epidemy and the vaccination rates is unlikely to exist (pvalue > 0.05).
The same applies for the daily mortality ratio (R 2 = 0.094 vs. D2 -p-value = 0.094; R 2 = 0.075 vs. D1 -p-value = 0.135) even though there is a decreasing but no significant relationship with the vaccine coverage in the 31 most vaccinated territories (Figure 14a).
The obtained results of mortality, hospitalization, and incidence ratios, shown in the below tables for the most vaccinated territories (September 30), demonstrate that they (Y dependent variable) are unrelated to the vaccination rates (X independent variable). Such absence of impact means the null hypothesis H0 (No correlation) cannot be rejected for those territories. For instance, p-value = 0.094 means that it is quite likely if β1 equals zero to get a slope b1 = -1.613 for the daily mortality ratio, since the 95% Confidence Interval [-3.52; 0.29] includes zero.

Conclusion and Proposal
The weak or slightly moderate decreasing relationship found between the epidemiological variables of COVID-19 and the vaccination rates (D1 & D2) in France during September 2021, is due to territories with very low rate of vaccinated population (7 territories still had less than 60% of population fully vaccinated by September 30).
The above findings indicate no correlation between tested COVID-19 data and vaccine coverage for the 31 territories whose population is the most vaccinated (more than 76% fully vaccinated). The more the vaccination rate increases, the more the association with the epidemiological variables of COVID-19 weakens (p-value = 0.591 for tx_incid; pvalue = 0.458 for tx_hosp; p-value = 0.094 for tx_dchosp vs. D2) as shown in the above Tables.
Recently, Subramanian and Kumar have found no discernible relationship between new COVID-19 cases and percentage of population fully vaccinated in 68 countries as of September 3, 2021. There also appears to be no significant signalling of COVID-19 cases decreasing with higher percentages of population fully vaccinated in 2947 counties in the US [1].
It has been widely reported that vaccines against COVID-19 had greatly contributed to reducing the number of severe disease and therefore hospitalizations and mortality [2,3] but have failed in preventing the spread of the SARS-CoV-2 variants. However, the lack of correlation between the epidemiological variables of COVID-19 and vaccine coverage in France is certainly attributed to the combination of several factors, such as the gradual decline of vaccine efficacy [4,5,6,7]; lower vaccine's effectiveness against highly infectious spread of new SARS-CoV-2 variants, as well as the improvement of medical care for COVID-19 patients, and probably a fairly significant development of natural immunity.
In addition, the decrease of the population's vigilance (especially, those vaccinated) with regard to barrier and hygiene measures, could explain -at least partially -the growth of SARS-CoV-2 infections. A study has found in the United States that adherence to mask wearing and acceptance of vaccines are correlated, which makes the vaccine efficacy estimation from real-world data biased by a significant amount [8]. Therefore, the lack of correlation with vaccine coverage suggests that herd immunity threshold would not be reached without respecting barrier gestures.
Assuming the Null Hypothesis (No correlation) cannot not be rejected as explained above, and using the regression line trend equations, we have estimated the mean of the epidemiological variables based on different vaccination rates (for vaccine coverage > 50% with D2 and > 60% with D1), such as shown in Figures 15, 16, 17 & 18.
The exercise consists in determining the main variables ratios, as per equation (2), such that the linear regression line follows a slightly decreasing trend (R < 0, whenever it is possible) with a coefficient of determination (R 2 ) very close to zero. For instance, the obtained values (as shown in Figures 17 & 18    If the unique pursued strategy is that of vaccination, a reasonable objective would be around 60% to 70% coverage, in a homogeneous manner and across all territories. Thus, an optimal vaccination plan would be as follows: