BMJ publication: Dr Allan Cunningham has collected data from reliable sources for 20 European countries. He's listed this in a
Rapid-Response document published in the BMJ.

That document can be seen here.

Dr Cunningham suggests applying a statistical correlation calculation to these 20 data pairs to see whether there's any connection
between percentage of over-65s receiving the Influenza vaccine in a country and the death rate per million in that country from Covid-19.
[It seems likely that he's done this himself and found the results 'interesting' enough for him to encourage others to do it for themselves.]

Happily, it's quite simple for anyone, even those with no experience of statistical methods, to do exactly that.

[See notes on Statistical Inferencing, in relation to this analysis, here.
See here for follow-up Advanced Analysis. ]

The simplest form of relationship between two sets of figures (in this case vaccination rates and mortality rates) is a 'linear', or straight-line
relationship. This means it's represented by a straight line through the data plotted as X-Y points on a graph. A straight-line fit is based on
the idea that when X doubles, Y also doubles; when X is five times as much, Y is five times as much; etc (roughly, for real-life data - that's why
the X-Y points are scattered around the line). We'll do a linear relationship fit first, then show that an exponential graph fits the data even better.

Linear Fit

=======

The figures collected and listed by Dr Cunningham are copied below for your convenience, so that they can be cut-and-pasted into
a statistical analysis tool you can find here.
Simply copy-and-paste the column of figures headed 'X' (the percentage vaccination rates) into the box headed 'X Values' and the column
of figures headed 'Y' (the death rates per million) into the box headed 'Y Values'.

[Don't copy the X or Y, and be sure to copy all the numbers - preferably in one go.]

X

20.3

13.4

52.0

37.6

4.8

64.0

48.4

34.4

49.7

60.8

34.8

13.0

26.8

11.8

57.6

53.7

52.7

49.4

7.7

72.6

Y

28

22

97

174

48

337

55

43

431

125

99

5

49

51

319

596

535

384

12

531

Once you've pasted both sets of 20 figures into the 'X Value' and 'Y Value' boxes (you'll see slider bars on both boxes, that's ok) just click on the 'Calculate R' button. This will produce the Pearson's Correlation Coefficient, referred to as 'R': it should give you a value of 0.7299, which is pretty high for a set of 20 data pairs.

R can vary between +1 and -1. +1 is a 100% positive correlation between X and Y, meaning that as X goes up Y also goes up in exact correspondence with it; -1 is a 100% negative correlation between X and Y, meaning that as X goes up Y goes

If you scroll down past the calculations (which you don't need - they've done them for you), you'll find it says: "This is a moderate positive correlation...". HOW moderate doesn't just depend on that 0.07299, it also depends on the number of data pairs - 20 in this case.

To get a figure for statistical significance of this result, click on the link that says: "Click here to calculate a p value". You'll be asked to input the R value (0.7299) and the number of data pairs (20) [You can also choose a significance level if you like - if so, choose 0.01 - but we'd really need a 0.001 option for the significance of this result!]

The calculator will give you the exact probability of this R for 20 data pairs: 0.000259. That's less than 3 in 10,000 likelihood that this result could happen by chance - in other words, a 99.97% probability that

So now we know there's a very high probability that these two sets of figures are linked. We can improve on even that, though, by refining our model - in other words, a graph (and a formula) that represents the relationship better.

Look at these two graphs:

The first is a linear (straight-line) 'best fit' to the data, as used in our calculation above.

The second is a linear best-fit of**logarithms** (to base 10) of death rates against vaccination percentages.

It's very clear, just by looking at them, that the second graph is a better straight-line fit than the first.

If**logarithms** of the Y-axis data are a good straight-line fit to the X-values, this tells us that Y is **exponentially** related to X.

In other words, our deaths-per-million show an**exponential** increase in relation to increases in vaccination percentages.

Exponential Fit

==========

So now we'll repeat our earlier test, but using the**logarithms** of our deaths-per-million for our Y values.

Those logarithm values can be read off any student calculator: just press the 'log' button, enter the original Y-value, and you get the log Y-value.

For example, our first original Y-value was 28. So we press 'log', tap in '28', and press '='. We get the answer 1.44716 (when rounded).

This has all been done for you, in the Y-values below (though you can check them). You just have to copy-and-paste the X's and the Y's, as before.

X

20.3

13.4

52.0

37.6

4.8

64.0

48.4

34.4

49.7

60.8

34.8

13.0

26.8

11.8

57.6

53.7

52.7

49.4

7.7

72.6

Y

1.44716

1.34242

1.98677

2.24055

1.68124

2.52763

1.74036

1.63347

2.63448

2.09691

1.99564

0.69897

1.69020

1.70757

2.50379

2.77525

2.72835

2.58433

1.07918

2.72509

As before paste both sets of 20 figures into the 'X Value' and 'Y Value' then click on the 'Calculate R' button. This will produce the Pearson's Correlation Coefficient, as before: this time it should give you a value of 0.8249, which is**very** high for a set of 20 data pairs.

Scroll down past the calculations and you'll find it says: "This is a strong positive correlation...".

To get a figure for statistical significance of this result, click on the link that says: "Click here to calculate a p value". You'll be asked to input the R value (0.8249) and the number of data pairs (20) [You can also choose a significance level if you like - if so, choose 0.01 - but we'd really need a 0.00001 option for the significance of this result!]

The calculator will tell you the probability of this R for 20 data pairs: <0.00001. That's less than 1 in 100,000 likelihood that this result could happen by chance - in other words,**a 99.999% probability that there's an exponential link between over-65s
influenza vaccination rate and Covid-19 death rate per million of population**.

This graph shows the calculated best-fit exponential line relating death rate to vaccination rate.

Now, we're always told to remember that "Correlation doesn't necessarily imply causation". We've shown that the link between these two factors is very, very unlikely to be coincidence (it's significant at 4.25-sigma level, for those who are into stats, and that's pretty significant) - it's very difficult to imagine what other factor could cause these two to be so strongly linked. (There will of course be other local factors which would make this less than an absolute '+1' correlation).

We shouldn't forget, either, a previous finding reported in this study showed 36% increase in risk of coronavirus (Prior to Covid-19) and 51% increased risk of another virus in those who'd been give influenza vaccine, compared to unvaccinated subjects. This tends to reinforce the likelihood of the influenza vaccine being a causative, or at least contributory, factor for other illnesses.

**The Bottom Line: There is very significant evidence that death rate from Covid-19 is exponentially linked to over-65s influenza vaccination rate, compared across Europe.
**

The first is a linear (straight-line) 'best fit' to the data, as used in our calculation above.

The second is a linear best-fit of

It's very clear, just by looking at them, that the second graph is a better straight-line fit than the first.

If

In other words, our deaths-per-million show an

Exponential Fit

==========

So now we'll repeat our earlier test, but using the

Those logarithm values can be read off any student calculator: just press the 'log' button, enter the original Y-value, and you get the log Y-value.

For example, our first original Y-value was 28. So we press 'log', tap in '28', and press '='. We get the answer 1.44716 (when rounded).

This has all been done for you, in the Y-values below (though you can check them). You just have to copy-and-paste the X's and the Y's, as before.

X

20.3

13.4

52.0

37.6

4.8

64.0

48.4

34.4

49.7

60.8

34.8

13.0

26.8

11.8

57.6

53.7

52.7

49.4

7.7

72.6

Y

1.44716

1.34242

1.98677

2.24055

1.68124

2.52763

1.74036

1.63347

2.63448

2.09691

1.99564

0.69897

1.69020

1.70757

2.50379

2.77525

2.72835

2.58433

1.07918

2.72509

As before paste both sets of 20 figures into the 'X Value' and 'Y Value' then click on the 'Calculate R' button. This will produce the Pearson's Correlation Coefficient, as before: this time it should give you a value of 0.8249, which is

Scroll down past the calculations and you'll find it says: "This is a strong positive correlation...".

To get a figure for statistical significance of this result, click on the link that says: "Click here to calculate a p value". You'll be asked to input the R value (0.8249) and the number of data pairs (20) [You can also choose a significance level if you like - if so, choose 0.01 - but we'd really need a 0.00001 option for the significance of this result!]

The calculator will tell you the probability of this R for 20 data pairs: <0.00001. That's less than 1 in 100,000 likelihood that this result could happen by chance - in other words,

This graph shows the calculated best-fit exponential line relating death rate to vaccination rate.

Now, we're always told to remember that "Correlation doesn't necessarily imply causation". We've shown that the link between these two factors is very, very unlikely to be coincidence (it's significant at 4.25-sigma level, for those who are into stats, and that's pretty significant) - it's very difficult to imagine what other factor could cause these two to be so strongly linked. (There will of course be other local factors which would make this less than an absolute '+1' correlation).

We shouldn't forget, either, a previous finding reported in this study showed 36% increase in risk of coronavirus (Prior to Covid-19) and 51% increased risk of another virus in those who'd been give influenza vaccine, compared to unvaccinated subjects. This tends to reinforce the likelihood of the influenza vaccine being a causative, or at least contributory, factor for other illnesses.