US stats confirm link between rises in influenza vaccinations and Covid-19 mortality rates
Dr Grahame Blackwell
A Pan-American Study incorporating data from 200 million subjects
See also this Pan-European Study incorporating data from over 350 million subjects

Summary

An objective analysis of data relating to around 200 million US citizens in 31 states shows a highly significant link between percentage of vaccinations of children (6 months - 17 years) for influenza and overall death rates from Covid-19 across the whole population in those states. This link is best modelled as a quadratic curve - i.e. the mortality rate rises with the square of (vacc.% - 60 [approx]) in states where that rate is 60% or more.
[Note: 'states' here includes Washington DC, as this is included in the CDC state-by-state statistics.]

This follows a previous study showing an exponential rise in death rates in European countries when correlated with percentage influenza vaccination rates for over-65s in those countries - a study that incorporated a total population of over 350 million people in those countries.
[Some form of correlation is consistent with a Jan 2020 study in the journal Vaccine linking influenza vaccinations with 36% increased susceptibility to coronavirus (pre-Covid-19).]

This analysis is presented in a form that is hopefully relatively easy for non-technical readers to follow. In addition, all the necessary information is provided to enable those readers to check the results for themselves using data and tools freely available on the internet.
In this way readers should be empowered to draw their own conclusions, from totally unbiased objective sources, in relation to this issue.

Data on Covid-19 mortality rates in US states was collected, also latest available data on percentage vaccination rates for each state for over-65s and children 6 months - 17 years. These figures are listed below, in addition to figures derived from them for use in the calculations.

The analysis was then undertaken as follows:
(1) Identify whether Seniors' or Children's vaccination data, or both, are correlated to a significant degree with Covid-19 mortality data;
(2) Where applicable, check whether there is an upper or lower threshold, or tipping-point, for any such correlation;
(3) Identify whether this correlation is best modelled by a linear relationship or some other mathematical 'fit';
(4) Calculate the Correlation Coefficient, R, for the best form of fit;
(5) Test the null hypothesis ("no actual connection") by checking the probability that this value for R could occur by chance;
(6) After eliminating any outliers (data points significantly distant from the pattern defined by the data-set as a whole), calculate the line of best fit for that adjusted data-set and re-calculate the R-value.

For a quadratic fit the probability of "no actual connection" turns out to be less than 0.00001 - so we must reject that hypothesis in favour of the alternative hypothesis: "Overall mortality rates from Covid-19 do increase in line with the square of increases in percentage child vaccination rates".
We can then add the information given by R2, the Coefficient of Determination: the significance of this figure is given at the bottom of this page.

Conclusion: Rate of total deaths/million of population from Covid-19 rises as the square of increases in rate of percentage child influenza vaccinations across US states above 62%. This could be cause-and-effect, or it could be due to some as-yet unidentified third factor linking these two.

It's difficult to imagine what that third factor might be, to give a quadratic connection.
=============================

[See notes on Statistical Inferencing, in relation to this analysis, here.

Data is listed below state-by-state, in order of children's percentage vaccination rates (apart from the two starred sets of figures at the end, for reasons explained below): Junior percentage vaccination rates; Senior percentage vaccination rates; overall deaths per 100,000 population from Covid-19. Beside the figures for each state are added both log[to base 10] and square-root of each mortality figure, to test for exponential and quadratic relationships respectively (both can be obtained from a calculator, or more quickly column-by-column using formulae in Excel).

Mortality rates were tested for linear regression against percentage rates for seniors using a statistical tool to be found here: simply copy-&-paste 'Over-65s Vacc %' column and 'deaths/100,000' column into 'X-Values' and 'Y-Values' boxes respectively and press 'śCalculate'. [You can skip past all the 'Calculations' stuff; press 'Reset' to repeat with other sets of figures]. No significant relationship was found with original mortality figures, square-root or log figures.

 




















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##
##
##
##
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##
##
##
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##
##
##
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##
##
##
##
##
##
**
**
Juniors
Vacc %
=======
46
48.8
50.3
51.8
54.5
54.7
55.2
55.5
55.7
55.8
55.9
56
56.5
56.6
56.7
57
59.4
59.7
60
60.1
60.3
60.7
61
61.8
61.8
62.1
62.9
63.3
63.5
63.5
63.8
64.5
64.5
64.8
64.9
65.4
65.8
66
67
67.2
67.5
69.2
69.6
69.7
73.8
74.5
75.1
78
81.1
69.6
72.8
Seniors
Vacc %
=======
52.9
60
53
59.5
52.8
49
63.5
52.6
57.4
52.8
50.6
64.5
45.7
46.9
51.9
61.2
54.4
58.4
45.4
55.4
55.8
58
49.2
45.2
52.7
48.1
48.5
56.3
54.9
47.6
58.4
55.9
59.1
59.4
57.5
65.6
59.7
58.3
50.7
51.1
53.2
57.9
58.9
59.7
55.3
56.5
59.8
51.1
54.5
44.8
63.7
Deaths/
100,000
=======
5
68
14
33
41
4
9
43
8
11
60
16
95
46
66
22
9
42
17
62
32
39
9
34
3
19
9
14
28
19
23
33
31
18
16
22
31
61
31
17
33
19
28
58
125
60
84
96
128
169
179
Log(10)
d/h-thou
=======
0.699
1.8325
1.1461
1.5185
1.6128
0.6021
0.9542
1.6335
0.9031
1.0414
1.7782
1.2041
1.9777
1.6628
1.8195
1.3424
0.9542
1.6232
1.2304
1.7924
1.5051
1.5911
0.9542
1.5315
0.4771
1.2788
0.9542
1.1461
1.4472
1.2788
1.3617
1.5185
1.4914
1.2553
1.2041
1.3424
1.4914
1.7853
1.4914
1.2304
1.5185
1.2788
1.4472
1.7634
2.0969
1.7782
1.9243
1.9823
2.1072
2.2279
2.2529
Sq. root
d/h-thou
=======
2.2361
8.2462
3.7417
5.7446
6.4031
2
3
6.5574
2.8284
3.3166
7.746
4
9.7468
6.7823
8.124
4.6904
3
6.4807
4.1231
7.874
5.6569
6.245
3
5.831
1.7321
4.3589
3
3.7417
5.2915
4.3589
4.7958
5.7446
5.5678
4.2426
4
4.6904
5.5678
7.8102
5.5678
4.1231
5.7446
4.3589
5.2915
7.6158
11.1803
7.746
9.1652
9.798
11.3137
13
13.3791


(You can try those last two by pasting the 'log' or 'sq-rt' column into the 'Y-Values' box.)

Using the same web tool, those Deaths/100,000 (Y-Values) were then tested against Juniors vacc % rates (X-Values). Simple linear regression gave an R-value of 0.5 with a p-value of 0.00018 (i.e. greater than 99.98% probability of a link; logs of deaths (Y-Value) against Juniors vacc % (X-Value) gave a slightly less good fit.
[For p-value scroll down to the bottom to find 'Click here to calculate a p-value'. On the next page N is the number of data pairs - 51 in this case.]

From the scattergram it was apparent that a pattern began to appear for vaccination percentages upward of 60%. Regression analysis just for those 33 states with children's vacc % upwards of 60% confirmed this with an R value of 0.68 for a linear fit, slightly less good for a log fit.

Since there was a clear up-turn in the scatter-gram, a fit of sq-root[deaths] (Y-Values) against Juniors vacc % (X-Values) was tested, as a simple linear check for a quadratic relationship [If Sq-root(Y) varies with X then Y varies with X2]: this gave R = 0.704 with
p < 0.00001 - clear evidence of a quadratic fit.
The straight line given by the square-root values is shown on the left.
[You can see the same result: just copy-&-paste Juniors vacc % and Sq.root figures from all rows marked ## or ** into 'X-Values' and 'Y-Values' columns and press 'Calculate.]


The next step is to eliminate any outliers - data points that lie so far out of the pattern set by the other points that they are clearly being heavily influenced by other factors, and so can't be regarded as part of that pattern.

[The following text, in maroon, can be skipped unless you're particularly interested in calculations for outliers.]

This involves first calculating distances of all the points from the line. It's not intended to cover the maths for that here, those interested (and slightly mathematical!) can find the necessary info here.

To check for outliers we next have to calculate upper and lower quartiles for this set of distances, and from these the interquartile range (having first put those distances into order, either way round). Again, info on these can be found here: in simple terms, upper and lower quartiles (UQ and LQ) are values that mark off the top and bottom values for the 'middle half' of the Y-values - i.e. cutting off the top quarter and the bottom quarter.

The interquartile range (IQR) is UQ - LQ; outliers are defined as values greater than UQ+1.5xIQR (or smaller than LQ-1.5xIQR, where small values could also show abnormal situations; that can't apply here, as small values represent data points very close to the regression line).

In brief: the topmost two points, for New York & New Jersey, do turn out to be outliers (as one might suspect from the graph above), no other points do. So our correlation calculations shouldn't include the figures for NY & NJ, as they will distort the result.

The final step is to find the actual quadratic line-of-best-fit, using this facility. The column of figures for 'Juniors Vacc %', just for those lines marked ##, are copied and pasted into the first box of the 'X' column on that page; they will fill that column downward. The column of figures for 'Deaths/100,000' (just from the ## lines) are likewise copied and pasted into the first 'Y' box, to fill that column. After checking that both columns are filled to the same length, the 'Execute' button is then pressed.

The software tool shows a best-fit line; it also gives the A, B and C values for the equation: Y = A + BX +CX2. Putting this the usual way round (i.e. reverse of that order), we get in this case:     Y = 0.3083X2 - 38.14X + 1204     , or
Y = 0.3083(X - 61.855)2 + 24.4     [showing that approx-62% tipping point]
where X is the Juniors percentage vaccination rate and Y is Deaths per 100,000. We're also told that the Correlation Coefficient, R, is 0.839, which is very high for 31 pairs of data, amply confirming our previous finding of
p < 0.00001: there is 99.999% certainty that this is a genuine link - effectively zero probability of it just happening by chance.

R2:   The Coefficient of Determination

R-Squared - which is literally the square of the Correlation Coefficient, R - is a measure of how much the variation in the dependent variable (in our case deaths/million) is related to variation in the independent variable (in our case % vaccination of Juniors). In this case R = 0.839, giving R2 = 0.704; this in turn gives an Adjusted R2 = 0.694*, or 69.4%. In other words, variation in mortality rate from Covid-19 across US states is almost 70% attributable to its 99.999%-certain quadratic (X2) link with vaccination rates of Juniors, in those states where that rate is 60% or more. Barely 30% of that variation in death rate is attributable to other factors.
[* Giving increased precision.]

Note the careful wording here: The stats do not tell us that higher vaccination rates are the cause of higher death rates; stats cannot tell us causes - they can only tell us about connections. But the whole point of identifying connections - and the strength of those connections - is to inform us about things that merit our serious attention. The very fact that this strong connection exists tells us that we need to investigate it: either it is causal or there is some third factor linking these two. To ignore this warning, or to assume "It can't be that, there must be another factor" without checking is both highly irresponsible and highly un-scientific. Without clear evidence to the contrary (such as an obvious provable third factor linking these two) the Precautionary Principle requires that we act on the basis that it's very likely that higher vaccination rates could be causing higher mortality rates - increasingly higher mortality rates.

If this is so, then that quadratic factor would imply that those vaccinated are not just at risk themselves, they are also acting as 'propagators' to spread the disease.

The Bottom Line: There is very significant evidence that death rates from Covid-19 rises quadratically with (i.e. as the square of) Juniors' excess influenza vaccination rates above a 'tipping point' of 62%, compared across states in the USA.