# UK data: Impact of vaccines on deaths. Part 4: Partially vaccinated (>21 days after 1st dose)

Updated: Dec 2, 2021

This is part 4 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.

__Part 2 __focused on all-cause deaths, comparing unvaccinated vs. fully vaccinated (2 dose),

__Part 3__ focused on all-cause deaths, comparing unvaccinated vs. recently vaccinated (<21 days since 1st dose), demonstrating that these data provide no indication of excess vaccine-caused deaths within 21 days of first dose, the time period most cited in concerns about vaccine-induced deaths, primarily based on anecdotal reports on social media and VAERs-based analyses.

This blog post, part 4 of the series, will compare the all-cause deaths in unvaccinated vs. partially vaccinated, defined as >21 days after 1st dose but not yet receiving second dose.

It is important to look at the partially vaccinated data, not just because the vaccine benefit takes a few weeks to kick in and the vaccine effectiveness of single dose vaccination is demonstrably lower than full (2 dose) vaccination, but also to assess whether there is any evidence of a "safety signal" suggesting excess deaths after vaccination. If an individual has a serious adverse events or major complication after the first dose of vaccine, it is unlikely that they would receive a 2nd dose, making any safety analysis restricted to 2nd dose subject to serious ** selection bias**, as rightly pointed out by many vaccine skeptics.

While the intended schedule for Pfizer and AstraZeneca vaccines was 21 days between 1st and 2nd doses, in early 2021 the __UK decided to delay the second dose__ for up to 12 weeks (84 days) to maximize the number of people in the population getting partial protection in a setting of vaccine scarcity, partially supported by preliminary data for the AstraZeneca vaccine suggesting a 12 week interval led to better immune protection than the intended 3-4 week interval.

Thus, many of the "partially vaccinated" during the winter and spring of 2021 were those awaiting their 2nd dose on the prescribed delayed schedule, but some are ** stragglers **who have delayed their 2nd dose, including

**a**

**that appear to have foregone the 2nd dose entirely. It is this subset that requires the most careful study to assess for a potential "safety signal."**

*remnant*A complete population-based data source containing weekly all-cause deaths separated out by vaccination status and age like these UK ONS data is a treasure trove of information beyond what has been publicly available to date. It is far superior for detecting any potential "safety signal" for death than an open reporting system like the USA's VAERs, with lack of verification, lack of a control group, reporting bias, and underreporting among its substantial documented __ limitations____.__

The UK ONS data are verified, should be completely reported, and contain a natural control in unvaccinated deaths for the same week and age group against which to compare to see there are excess deaths that might suggest a "safety signal" is present.

In this blog post, I will plot and evaluate the __UK death data posted by the ONS on November 1__, comparing the weekly all cause death rates from January 2, 2021 through September 24, 2021 between those partially vaccinated (>21 days after 1st dose) and unvaccinated, split out separately by the age groups in the ONS report (10-59yr, 60-69yr, 70-79yr, and 80yr+).

__Here is a link to the Excel spreadsheet containing the data____.__

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

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.

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 percentage of the corresponding age group with that vaccination status. By doing this, the underlying sample size of each group at a given point in time will be immediately and visually apparent.

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. As pointed out in__part 2__of this series, the 10-59yr age group is far too wide given the major variability in vaccination rate and death risk in this age group, so this subset is still subject to distortion by Simpson's paradox and needs to be interpreted with this in mind.Further, we will plot the entire time curve, not aggregated summaries over time. 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 using weekly summaries avoids this effects.In addition to plotting the all-cause death rates over time split out by vaccination status, I will also construct plots of proportion partially and fully vaccination over time to reveal the time at which most partially vaccinated individuals received their second dose, and to help characterize the nature of the group remaining only partially vaccinated many months after the rest of their cohort has received second doses.

I will also use the corresponding unvaccinated deaths in the same week/age group as a control to compute "expected death" numbers under the assumption that partially vaccinated have the same death rate as unvaccinated, which can be used to give us a sense of magnitude of any prevented or excess deaths.

For maximal transparency, here I share the scripts I used to download the data and produce these plots, tables, and analyses, 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__,

**Results:**

As we saw in the unvaccinated vs. fully and recently vaccinated analyses done in the previous blog posts, the 10-59yr old age group is too broad to since the older end of this cohort is much more vaccinated and has >50x higher background mortality rate than the younger end of the cohort. As a result, here I will first present data and interpret the results for the 60-69yr, 70-79yr, and 80yr+ age cohorts, which share similar patterns, and later return to interpret the 10-59yr old cohort while computing and adjusting for the actual age distribution disparity in partially vaccinated and unvaccinated subsets and their respective inherently different mortality rates.

**Results for the the 60-69yr age cohort.**

Here are plots of the all-cause death rates for the partially vaccinated (>21 days after1st dose) and unvaccinated over time for the 60-69yr age cohort.

We see that the partially vaccinated had considerably lower rates of all-cause deaths for the first 21 weeks up until late May (~5.0x lower in wk12, late March) at which point the lines cross, and the death rate sharply increased from weeks 20-25 (late June) to levels greater than the unvaccinated (~3.0x higher in wk27) with a sharp spike around week 25, and then coming down a bit but remaining higher than unvaccinated for the remaining 2.5 months. As we will see later, a similar pattern is seen in all of the age cohorts, and does not appear driven by a Simpson's paradox like artifact. It is important to investigate this pattern in detail.

The change point at which the lines cross occurs around weeks 20-22, mid to late May, coinciding with the emergence and rise to dominance of the Delta variant in England.

It is well documented that a single dose of Pfizer or AstraZeneca is __much less effective than two doses for Delta__, and was shown to produce __negligible levels of neutralizing antibodies__, which could explain why those given only one dose would have higher death rates from COVID-19 than those given two doses.
However, as we showed in __part 1 of this series__, there were very few COVID-19 deaths in the partially vaccinated cohort between weeks 18 and 25 (early May to late June), a time period coinciding with the lull of confirmed cases between the winter Alpha surge and the summer Delta surge.

Thus, the pattern we are seeing and the crossing of the lines does not appear to be driven by a transition to Delta.

Another element of this effect's timing is that it coincides with the time at which nearly all vaccinated people in the age cohort had received their 2nd dose.

Here is a plot of the percentage of the 60-69yr age cohort in each vaccination status over time, in which we see that the percentage partially vaccinated (>21d after 1st dose) is largest around wk15 and sharply decreases to very small numbers by wk22.

Focusing on the partially vaccinated (>21 days after 1st dose) and fully vaccinated (2 doses), here is the plot on the log scale to make it easier to see the percentages in the later weeks:

The vast majority of the 60-69yr age cohort received their 2nd shots between wk12 and wk22, with the percent fully vaccinated increasing from 3.5% to 88.1%, while during the same time period the percent partially vaccinated decreased from 88.2% down to 3.6%.

Thus, the partially vaccinated group prior to wk22 is a very large group comprising a high proportion of the 60-65yr old UK population, dominated by those who were waiting for their 2nd dose on the prescribed delayed schedule of up to 12 weeks.

Conversely, the partially vaccinated group after wk22 is a very small group, comprising just 1-2% of the 60-69yr age group between wk23 and wk38. This group contains * stragglers *who did not get their second dose on schedule, including any

*of the 60-69yr age cohort that for one reason or another did not receive their second dose at all.*

**remnant**Thus, although it is small, this group is important to study more carefully, since it includes any

individuals who experienced health complications after dose 1 that prevented them from receiving dose 2, including some whose health complications may have been vaccine-related. As I conclude at the end of this blog post, I think a deep dive into this subset is crucial as a responsible effort to discover any additional risks the vaccines might pose beyond those that have already been established.

To put this group into perspective, I will consider the total number of deaths we are talking about here, and compute how many of them could be considered "excess deaths" over and above what we'd expect if they had the same death rate as the unvaccinated during this time period.

Summing every all-cause death in those partially vaccinated (>21 days after 1st dose) between wk22-38, we find a total of 1,486 deaths, which is 0.028% of the total 60-69yr age cohort size of 5,272,561, and 0.46% of the total 60-69yr partially vaccinated population of 320,208 as of wk22.

It is useful to compare this number with the number of deaths that would have occurred in this group of partially vaccinated individuals had their death rate been the same as the unvaccinated 60-69yr during this same time interval. We could call these "expected deaths," easily computed by multiplying the weekly death rate in the unvaccinated 60-69yr cohort by the corresponding weekly population size of the partially vaccinated (>21 days after 1st dose) 60-69yr cohort.

Here we plot the number of "expected deaths" along side the actual partially vaccinated deaths over time.

First, we see that up until wk21 when the lines cross, the partially vaccinated group had MUCH lower all-cause deaths than the number "expected" if this group had the same weekly death rates as the unvaccinated. For lack of a better term, we could refer to the space between the red and green lines from weeks 0-21 as "prevented deaths."

Summing over weeks 0-21, we find a total of 12,811 "prevented deaths" in the partially vaccinated group, which is 0.24% of the 60-69yr age cohort population of 5,237,013.

However, after week 21, the number of weekly all-cause deaths in the partially vaccinated group is greater than the "expected" number. We could refer to the space between the green and red lines from weeks 22-38 as "excess deaths"

To make the magnitude of these deaths after week 21 more visible, here is the same plot on the log scale:

Summing over weeks 22-38, we find a total of 1,067 "excess deaths" in the partially vaccinated after wk22, which is 0.02% of the 60-69yr age cohort, and 0.31% of the 320,208 in the 60-69yr partially vaccinated (>21 days after 1st dose) cohort in wk22.

The explanation of these "excess deaths" depends on the particular characteristics that make this group of ** stragglers** (late in receiving first dose) and

**(never receiving 2nd dose) a select group. This includes individuals with health complications arising after receiving the first dose, some (but not all) of which may have been vaccine-related, but could also involve other factors, i.e. people who were previously too sick to receive their first dose on schedule. A deep dive to characterize this group is important to identify which may comprise vaccine-related deaths.**

*remnant***Results for the the 70-79yr age cohort.**

Here are plots of the all-cause death rates for the partially vaccinated (>21 days after 1st dose) and unvaccinated over time for the 70-79yr age cohort.

We see a similar pattern here as in the 60-69yr cohort: that the death rates for the partially vaccinated were much lower for the first number of weeks, but at some point the lines cross and the death rate increased to become substantially greater than for the unvaccinated group. Again, this change point corresponds precisely to the time at which the vast majority of those in that age cohort had received their second doses, which is ~wk17 for the 70-79 age cohort, about 4 weeks sooner than for the 60-69yr age cohort.

This can be seen in this plot of the percentage in each vaccination group over time.

We see the proportion partially vaccinated (>21 days after 1st dose) is largest around wk10 (early March) and sharply decreases to very small numbers by wk17 (late April).

Here is the plot on the log scale so we can more easily visualize the percentages after wk17.

The vast majority of the 70-79yr age cohort received their 2nd shots between wk11 and wk18, with the percent fully vaccinated increasing from 2.1% to 91.7%, while during the same time period the percent partially vaccinated decreased from 90.4% down to 4.9%.

Thus, the partially vaccinated group prior to wk18 is a very large group, dominated by those who were waiting for their 2nd dose on the prescribed delayed schedule of up to 12 weeks.

Conversely, the partially vaccinated group after wk18 is a very small group, comprising just 0.7-2.9% of the 70-79yr age cohort between wk19 and wk38. This group includes some ** stragglers **who received their first doses later than the rest of the 70-79yr age cohort as well as a

**who never received 2nd doses.**

*remnant*Summing all cause deaths between wk18-38, we find a total of 3,782 deaths, which is 0.09% of the total 70-79yr age cohort size of 4,305,940, and 1.85% of the total 70-79yr partially vaccinated (>21 days after 1st dose) population of 204,533 as of wk18.

Here is a plot of weekly deaths along with the "expected deaths" computed by multiplying the weekly death rate in the unvaccinated 70-79yr cohort by the corresponding weekly population size of the partially vaccinated (>21 days after 1st dose) cohort.

Again, we see that up until wk17 during which the lines cross, the partially vaccinated group had a much lower number of all-cause deaths than "expected" if it had the same death rate as the unvaccinated, with a total of 30,819 "prevented deaths," representing the areas between the red and blue lines between wk0-17, which is 0.72% of the 70-79yr age cohort population of 4,305,940.

Here is a plot on the log scale to make the magnitude of weekly deaths after wk17 more visible.

Summing the area between the blue and red curves between wk18-38, we find a total of 2,774 "excess deaths" in the partially vaccinated after wk18, which is 0.06% of the 70-79yr age cohort and 1.36% of the 204,533 in the 70-79yr partially vaccinated (>21d after 1st dose) cohort in wk18.

**Results for the the 80yr+ age cohort.**

Here are plots of the all-cause death rates for the partially vaccinated (>21 days after 1st dose) and unvaccinated over time for the 80yr+ age cohort.

We see a similar pattern here as for the 60-69yr and 70-79yr age cohorts: the death rates for the partially vaccinated were much lower for the first number of weeks, but at some point the lines crossed and the death rate increased to become substantially greater than for the unvaccinated group. As before, this change point corresponds precisely to the time at which the vast majority of those in that age cohort had received their second doses, which is ~wk14 for the 80yr+ age cohort, about 3 weeks sooner than the 70-79yr age cohort and 6 weeks sooner than the 60-69yr age cohort, respectively.

This can be seen in this plot of the percentage in each vaccination group over time.

We see the proportion partially vaccinated (>21 days after 1st dose) is largest around wk8 (late February) and sharply decreases to very small numbers by wk15 (mid April).

Here is the plot on the log scale so we can more easily visualize the percentages after wk15.