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UK Data: Impact of vaccines on deaths. Part 2: Fully vaccinated (both doses)

Updated: Nov 27, 2021

This is part 2 in a 4 part blog post series exploring what the data posted by the UK's Office of National Statistics (ONS) on November 1st tell us about the effect of the national vaccination program on death rates.

Part 1 focused on COVID-19 deaths. Here we focus on all-cause deaths. It is important to look at all-cause deaths for two reasons:

  1. Deaths caused by COVID-19 are not always accurately attributed as such on the death certificate, and those that aren't are lost to the COVID-19 death analysis.

  2. If the vaccines cause serious adverse events or other medical complications leading to deaths in some, then these will also be captured in the all cause deaths analysis.

Fortunately, the UK has posted a data set they posted on November 1 looking at deaths in the UK from January 2, 2021 through September 24, 2021 split out by age and vaccination status. Here is a link to the Excel spreadsheet containing the data.

Table 4 in the spreadsheet contains weekly data from the UK including all cause death counts split out by age group (10-59, 60-69, 70-79, 80+) and vaccination status (unvaccinated, 1st dose within past 21 days, 1st dose >21 days ago, 2nd dose). They also have the population number for each vaccinated status from each age group for each week that can be used to compute standardized death rates as well as to track the proportion of that age group in each vaccination status over time.

This is one of the few large-scale data sets I've seen in which all cause death is reported over time, split out by vaccination status and age, the key factors that MUST be accounted for in order to begin to make any valid assessment of the real-world effect on vaccinations.

It is possible to fit rigorous statistical models to disentangle all of the confounding factors of vaccination rate, age, time, and vaccination status to tease out valid real-world effectiveness measurements, and some excellent papers have done so.

However, to keep things simple and accessible, I will not do that here. Instead, I will simply plot the all-cause death rates over time for each age group and vaccination status. If done carefully, these plots can parse out the confounding effects and provide a clear visual picture of the effect of vaccination on all-cause death in the UK in 2021. This data set runs through late September, allowing enough time to accurately assemble the death data for the November 1st release. Keep in mind, there still may be some confounding factors remaining in the data that could impact risk of death, including pre-existing medical conditions, socioeconomic status, vocation, and other demographic factors. However, by accounting for age and time confounding, these plots should give us a reasonable idea of that is going on.

To make the plots maximally informative, the data are plotted as follows:

  • As mentioned above, I will plot all cause deaths, not just COVID-19 deaths, so they are independent of any testing practices or death attribution.

  • I will plot the all cause death rates, which are the total deaths in that week for the given age/vaccination status group divided by the population of that group during that week. Plotting the raw death numbers would be misleading since it would not adjust for the number vaccinated, a measure varying substantially over time and by age group. Using these death rates automatically adjust for this factor.

  • I will plot separately by age groups. Since both risk of death and vaccination rate vary strongly across age groups, failure to stratify by age under these circumstances can produce extremely distorted and misleading results as a result of Simpson's paradox, as previously shown in Israeli data. Stratification by time avoids this effect.

  • Further, we will plot the entire time curve, not overall summaries. Key pandemic factors including the overall SARS-CoV-2 infection levels, the predominant variant, the season of the year, and the mitigation strategies in place all change over time and could have a strong impact on death rates, and of course the vaccination rate has also changed substantially over time. Summaries that aggregate over time under these conditions can also produce a distorted and misleading picture of reality via a Simpson's paradox effect, as shown in a previous blog post. Plotting the entire time curves avoids this effect.

  • The population size of each age/vaccine status group changes greatly over time, with the vast majority of the population being unvaccinated at the beginning of the year, and becoming increasingly vaccinated as the year progresses, with the older groups vaccinated earlier and more extensively. To illustrate this effect, I will make the thickness of the line for each time plot proportional to the % of that age group with that vaccination status. By doing this, we can account for the population size for each vaccination status/age group over time, and can also see for a given age group when most received their vaccination, as indicated by the time of the year in which the thickness of the vaccinated lines is increasing rapidly.

To streamline the interpretation, I will separately analyze the fully vaccinated (2 dose) and partially vaccinated (1 dose) cohorts relative to the unvaccinated. This blog post will deal specifically with fully vaccinated, while part 3 of this 3-part blog post will deal with partially vaccinated.

For maximal transparency, here I share the script I used to download the data and produce these plots, so anyone can see the data for themselves and adapt the code to change the figures in any way they want. The plotting is done in the freely available statistical package R,

UK All Cause mortality 2 dose vs. unvaccinated.R
Download TXT • 3KB

Here is the plot for the oldest group, that is 80+ years old:

From this, the dominant feature is the huge spike of excess deaths in the winter that resulted from the massive Alpha COVID-19 surge, that impacted primarily the unvaccinated population. Some other observations:

  • Since vaccination started with this age group, many in this age group received their first dose in early January, and second dose by February to March, as indicated by the thickening of the lines for 2nd dose vaccinated and thinning of the line for unvaccinated during those times.

  • We don't see a major increase in death rate of this age group at time of second vaccination, although the death rate gradually increases over time from April through September, in the middle of which the UK Delta surge occurred.

  • The UK has experienced a massive Delta surge in the summer, and note the lack of high death rate from this surge, even in the unvaccinated group. The death rate is much lower than in the Alpha surge in the winter.

  • However, the death rate is considerably lower in the vaccinated group. For example, in week 30 for the 96% in this age group who are vaccinated with 2 doses, the death rate is 1575 per 1 million, while for the 2.8% unvaccinated, it is 2655 per 1 million, which is 1.7x higher. Thus, at that time, the all cause death rate in vaccinated is 1.7x lower than the unvaccinated.

Here is the data for the 70-79yr old group:

In this age group, we see the same massive surge of deaths in the winter Alpha surge, again focused primarily in the unvaccinated population. Some other observations:

  • We see the vaccination started slightly later in this age group, with first doses given a few weeks later in January, and second dose rates increasing in March.

  • Once again, we see no increase in deaths at the time when the second doses are given. The vaccinate groups deaths creep up between April and September, in the middle of which was the UK Delta surge.

  • Again, we see the Delta surge in the summer produced far fewer deaths than the winter Alpha surge, even in the unvaccinated.

  • Even though the vast majority of this age group is vaccinated with 2 doses (96.1% by week 30), there are still 3.1% unvaccinated.

  • The death rates during the Delta surge are higher in the unvaccinated (745 per 1 million) than the fully vaccinated group (397 per 1 million), with the fully vaccinated showing a 1.9x reduction in overall death rate in week 30.

Here is the data for the 60-69yr old group:

For this age group, we see the winter Alpha surge produced an uptick of deaths, but nearly as dramatic as we saw in the 70-79 and 80+ age groups. Also, the peak in deaths in this age group came a little later, in early March, than the older age groups for which it was in February. But once again, the death rates were higher in the unvaccinated than vaccinated cohorts during this time. Some other observations:

  • This group primarily received their first doses in February, and their second doses at the end of March and into April.

  • Once again, there is not a large increase in deaths at times second vaccination, but the vaccinated death rates increased from May through September, coinciding with the timing the summer UK Delta surge.

  • By summertime, the vast majority of this cohort have been fully vaccinated, with 93.3% given 2 doses and only 5.2% unvaccinated by week 30.

  • The death rates in the summer Delta surge are much higher for the unvaccinated population (322 per 1m) than the fully vaccinated (138 per 1m), with the fully vaccinated showing all cause death rate 2.3x lower than the unvaccinated.

Finally, here is the youngest cohort 10-59.

Whoa!!! For this age cohort, we see that initially, the small number of fully vaccinated had lower death rates than unvaccinated during the winter Alpha surge. however, by April, we see a sharp increase in the death rate for the fully vaccinated relative to the unvaccinated in April, around the same time most of the vaccination occurred in this age group and has remained higher since then. The all cause death rate in fully vaccinated in this age group at 30 weeks is 28.7 per 1 million, while the death rate in unvaccinated in this age group at 30 weeks is 15.7 per 1 million. Thus, we see the death rate is 1.8x higher in fully vaccinated than unvaccinated. Could this be evidence that the vaccines are "killing more than they save", that they cause serious adverse events in the young that lead to fatal complications. Alex Berenson sure thinks so, blogging on this late last week and suggesting this was a sure sign of vaccine-induced mortality

This has been widely circulated on social media (and especially on the alternative social media platforms populated by the most ardent vaccine skeptics).

This is disturbing at first glance, and warrants investigation. What is different about the 10-59yr age group from the other older age groups? Is there some explanation for this?

It is possible that these results are an artifact of Simpson's paradox, since the age range is too broad and the older end of the age range having much higher vaccination rates and with inherently higher risk of death than the younger ages in the range. These are the precise conditions in which we saw Simpson's artifact produce misleading results in Israeli data and UK Case Mortality Rate data before.

Using publicly available UK population, vaccination, and background mortality data broken out by 5-year age groups, we can compute the expected background mortality rate for the vaccinated and unvaccinated 10-59yr groups based on their disparate age distributions to see if we expect them to differ by a ratio of 2.0x or so. To do this we will use the following data sources:

  1. Annual UK population & mortality data for each age 0-105+ from 1961-2019 from ONS.

  2. UK vaccination rates over time for age groups split in 5-year groups.

First, from the 2019 annual death counts in the UK for each age, we compute the annual death rate per 100k for each 5 year semi-decade group between 10-59yr:

Note how the older end of this age group has background death rates orders of magnitude greater than the younger end of this age group, e.g. with 55-59yr having an annual death rate that is >50x greater than the 10-14yr.

Looking at the UK vaccination rates over time,

we also see that the older end of this age group has much higher vaccination rates than the younger end, and was vaccinated much sooner in the year.

To account for the different population sizes, we computed the proportion of the total UK population comprised by each 5-year semi-decade age group.

These 5-year groups are not too disparate, with all of them between 5.5% and 7.0% of the population, but should be accounted for in our calculations.

After interpolating the vaccination rate data into the 5-year semi-decade groups, we put these data together in a common spreadsheet:

We can see that the overall annual mortality rate in the 10-59yr age group is 149.5 deaths per 100k, but it ranges from 8.8 deaths per 100k in the 10-14yrup to 478.2 deaths per 100k in the 55-59 range.

Since we are focusing on the 10-59yr age group only, I normalize the population size to get the age distribution of each 5yr semi-decade group within the 10-59yr old population.

Next, but multiplying the % vaccinated by the relative population size for each 5-year age semi-decade, we get the proportion of 10-59yr population that are (1) vaccinated and (2) within each 5-year age semi-decade:

By subtracting from the total age distribution, we can compute the proportion of 10-59yr population that are 1. unvaccinated and (2) within each age group

Next, we will normalize each of those two columns by dividing by the respective sums (61.9% and 38.1%) to get the age distribution within the vaccinated and unvaccinated cohorts in the 10-59yr cohort.

For easy visualization, here is the age distribution in the vaccinated and unvaccinated subpopulations within the 10-59yr age group:

As you can see, the vaccinated subset of the 10-59yr are MUCH older, not at all comparable to the unvaccinated 10-59, and I include the annual background mortality rate for each 5-year age semi-decade from which you can see the major disparities.

To compute the annual background mortality death rate per 100k in the vaccinated and unvaccinated subsets of the 10-59yr age groups based on their respective age distributions, we use a weighted average: multiplying the age-specific annual death rate and the % of the respective (vaccinated or unvaccinated) cohort in that age group.

We add these numbers to our figure to include the expected annual number of deaths per 100k in each age group. They are not too different from the 10yr-39yr age groups, but note the major differences in the 40-59yr groups driven by higher vaccination rates and mortality risk.

If we sum across all age groups, from the weighted average, we obtain the annual background (expected) mortality rate for the vaccinated and unvaccinated subsets of the 10-59yr cohort based on their disparate age distributions:

To clarify and avoid confusion, nothing in this table has any data about actual deaths from vaccinated or unvaccinated cohorts.

It is presented to derive the expected death rates in the recently vaccinated and unvaccinated cohorts based solely on their differential age distributions.

  • The bar plot in the figure shows the age distribution in vaccinated (blue) and unvaccinated (orange) cohorts, that shows the recently vaccinated group is systematically older than the unvaccinated.

  • The black numbers at the top are the mortality rates by age from 2019, showing older people, unsurprisingly, inherently have a much higher risk of death.

  • The bottom numbers are obtained by multiplying the mortality rate (black at top) and % for that age group (bar plot), which when summed across all age groups yields the expected death rate for vaccinated and unvaccinated cohorts based on their differential age distribution.

From these calculations, note that the original annual mortality rate for the 10-59yr cohort was 149.5 per 100k, but the older age demographic of the vaccinated subset makes their annual background mortality rate 192.3, and the younger age demographic for the unvaccinated subset makes their annual background mortality rate 79.7.

Thus, even if the vaccines had NO impact, either beneficial or deleterious, on all-cause mortality, because of their disparate age distributions, we would expect the ratio of deaths in the vaccinated:unvaccinated subsets to be 192.3/79.7=2.41.

Thus, the results we see in the actual UK all-cause deaths for fully vaccinated and unvaccinated is not unexpected, and can be fully explained by the Simpson's paradox artifact since the observed ratio of vaccinated:unvaccinated all cause death rates, 1.82x in week 30, is less than the expected background ratio of 2.41x based on their disparate age distributions.

This suggests Berenson and other's conclusions that these data are evidence of vaccine-caused deaths is unfounded.

Unfortunately, the ONS did not list all-cause death data on a finer age grid within 10-59yr -- if they did, we could see whether, like the 60-69, 70-79, and 80+ age groups, there was also evidence of a reduction of all-cause deaths, and thus strong clinical benefit of the vaccination program, within the various decade groups in that range. The data is not inconsistent with that result, but we can't know until/unless they post the data on a finer grid.


In this blog post, I have plotted and interpreted all-cause death rates over time split out by vaccination status for the various age groups. The carefully chosen plotting techniques enable parsing out some of the confounding effects of time, age, vaccination rate, infection rate, and variant and get a fair assessment of how the UK vaccination program is affecting all cause deaths. In the 60-69yr, 70-79yr, and 80yr+ age groups, we clearly see the vaccinated groups having lower risk of all-cause death, and this is especially evident during the winter Alpha surge and summer Delta surges. with all-cause death rates MUCH lower in vaccinated than unvaccinated during the Alpha surge, and between 1.7x and 2.3x lower during the Delta surge, during a time when the vaccine effectiveness has started to wane.

Conversely, starting April, the 10-59yr age group showed about 1.5-2x higher all cause death rates in vaccinated than unvaccinated groups. However, I demonstrated that we would expect the vaccinated cohort to have 2.4x higher all cause death rate than the unvaccinated cohort based on their disparate age distributions, with the vaccinated subset much older and having a background annual mortality rate of 192.3 per 100k and the much younger unvaccinated subset much younger and with background annual mortality rate of 79.7 per 100k, in comparison with the overall 149.5 per 100k mortality rate of the full 10-59yr cohort.

This suggests this effect is an artifact caused by Simpson's paradox, and not an indication of vaccine-caused deaths.

This does not tell the whole story, since in this blog post we have focused only on the fully (2 dose) vaccinated, and left out the partially (1 dose) vaccinated.

Although this group is relatively small (1.2% for 80yr+, 0.8% for 70-79yr, 1.4% for 60-69yr, and 16.0% of 10-59yr during week 30), it is important to investigate this group, especially to look for any signal of potential harm caused by vaccination. The ONS data base splits this group out by <21 days since 1st dose, and >21 days after 1st dose.

In the 3rd and 4th part of this 4-part blog series, I will present and interpret these single-dose data focusing first on recently vaccinated (<21 days since 1st dose) and then partially vaccinated (>21 days since 1st dose.

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