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+).

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.

The vast majority of the 80yr+ age cohort received their 2nd shots between wk8 and wk14, with the percent fully vaccinated increasing from 12.8% to 75.8%, while during the same period of time the percent partially vaccinated decreased from 81.7% down to 20.4%.

Thus, the partially vaccinated group prior to wk14 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 wk14 is a very small group, comprising just 2-11% of the 70-79yr age cohort between wk15 and wk20 and only 1-2% between wk21-38. This group includes some ** stragglers **who received their first doses later than the rest of the 80yr+ age cohort as well as a

**who never received 2nd doses.**

*remnant*Summing all-cause deaths between wk15-38, we find a total of 10,678 deaths in the partially vaccinated (>21 days after 1st dose) group, which is 0.42% of the total 80yr+ age cohort size of 2,516,133, and 3.82% of the total 80yr+ partially vaccinated population of 279,470 as of wk15.

Here is a plot of weekly deaths along with the "expected deaths" computed by multiplying the weekly death rate in the unvaccinated 80yr+ cohort by the corresponding weekly population size of the partially vaccinated (>21 days after 1st dose) cohort.

Again, we see that up until wk14, the partially vaccinated group had a much lower number of all-cause deaths than would be "expected" if it had the same weekly death rates as the unvaccinated, with a total of 106,623 "prevented deaths," representing the areas between the red and blue lines between wk0-14, which is 4.2% of the 80yr+ age cohort population of 2,516,133.

Here is a plot on the log scale to make the magnitude of weekly deaths after wk14 more visible.

Summing the area between the blue and red curves between wk14-38, we find a total of 6,562 "excess deaths" in the partially vaccinated, which is 0.26% of the 80yr+ age cohort and 2.35% of the 279,470 in the 80yr+ partially vaccinated (>21d after 1st dose) cohort in wk15.

**Conclusions for the 60-69yr, 70-79yr, 80yr+ analyses:**

In all three age groups, we observed the same pattern:

The death rate for partially vaccinated individuals was much lower than the unvaccinated up until the point when most in the age cohort had received their second doses, which are weeks 15, 18, and 22 in the 60-69yr, 70-79yr, and 80yr+ cohorts, respectively.

The individuals remaining in the partially vaccinated cohorts after week 20 or so represent a very small and select group, 1-2% of the total age cohort, but a very important and potentially distinct one including

who did not get their 2nd dose on schedule, including a*stragglers*who never received second doses.*remnant*At this point, the death rate for these remaining partially vaccinated individuals turned sharply upward and spike around the time that the second dosing is complete in this cohort.

After coming down from this spike, the levels plateau to a level higher than unvaccinated for the remaining time.

The spikes in death rate for the partially vaccinated around the time most had become fully vaccinated is very unusual, and given that we saw them in all 3 age groups, it is worth some additional thought. Given its occurrence corresponds precisely with the time at which nearly all of the cohort completed 2nd dose vaccination, outside of a small number of stragglers, it is possible that this could be a numerical artifact related to death reporting delays.

In a recent blog post, Prof. Norman Fenton demonstrates that delays of even just 1 week in death reporting can cause a large spurious spike of deaths in the unvaccinated cohort just at the time the vaccination levels near 100%, as the unvaccinated get very small. Here is a plot of this phenomenon from his__ blog post__, from a simulation of a fictional "placebo vaccine" with equal death rates as unvaccinated.

If you plot % 2nd vaccination, partially vaccinated (>21 days after 1st dose) death rate, and fully vaccinated (2 dose) death rate together, we see the same picture, with "% given second dose" playing the role of "% Vaccinated", "partially vaccinated" playing the role of "unvaccinated" and "fully vaccinated" playing the role of "vaccinated" in the simulation. The coincidence of this spike with the precise time at which the % given 2nd dose asymptotes makes this a plausible explanation for the spike.

However, it does not fully explain the higher death rate in these** stragglers**, since even after the spike, the death rate plateaus at a level higher than unvaccinated death rates. Thus, it appears there are factors in this group of

**that makes it a select group with higher risk of death than the corresponding unvaccinated or fully vaccinated cohorts.**

*stragglers*To quantify the magnitude of the number of potential excess deaths in this select group, we computed the **expected deaths **for the partially vaccinated in each week/age cohort under the assumption their death rate was the same as the unvaccinated in the corresponding week/age cohort. This was done by multiplying the unvaccinated death rate by the corresponding partially vaccinated population for each respective week/age group.

From that, we subtracted these expected deaths from the actual deaths to compute **"excess deaths"**, which when negative could be called** "prevented deaths"** for lack of a better term, since it would indicate the partially vaccinated group had few deaths than expected based on the unvaccinated control group.

Plots of the actual and "expected" deaths for each of the age groups are presented above. To summarize, here a table presenting actual, "expected", and "excess" deaths for each age cohort, aggregating over 5-week intervals..

In the later time periods, we see a a substantial number of **"excess deaths"**, with 902, 2626, and 6561 more deaths than expected in the partially vaccinated group in the 60-69yr, 70-79yr, and 80yr+ age cohorts, respectively, summing the red counts over weeks 21-38 for the 60-69yr age cohort and weeks 16-38 for the 70-79yr and 80yr+ age cohorts. These sum up to a total of 10,089 deaths in the UK from January 2 through September 24, 2021.

Those remaining in the partially vaccinated cohorts after week 16-20 or so are clearly a select group, and characterization of this group demographically and clinically is crucial to understanding how to interpret these deaths. There are a number of key questions to answer:

What proportion of these eventually received their first dose, but at a time much later than the vast majority in their age cohort? Is there something about them clinically or demographically that gives them a higher (or lower) mortality risk than the others in their age cohort?

What proportion of these are a

of individuals who received their first dose but never received their second dose, even long after the scheduled time by UK guidelines? Why did they forego the second dose? Was it due to a medical complication that arose after the first dose? If so, was it plausibly or possibly vaccine-related? Or was it a choice driven by vaccine skepticism, perhaps emerging after concerns about vaccine safety were increasingly prominent on social media? Or did they forego second dose for some other reason? Based on these reasons, is there something about these groups demographically or clinically that gives them higher (or lower) mortality risk than others in their age cohort?*remnant*

It should be a priority to dig deeper into this select group of individuals who either received their first doses late or never received their second doses and answer these questions.

This group potentially contains some individuals who may have had vaccine-related medical complications that were serious enough to forego the second dose, and eventually died from these complications. If there are some additional risks of minority harm from the vaccines beyond the established rare but dangerous anaphylaxis, myocarditis/pericarditis, VITT, and Guillain-Barre Syndrome risks, it is important to discover, validate, and characterize these risks so they can be taken into account, and these data, this select subgroup in particular, could be valuable in this venture.
However, it would be unreasonable to assume that all of these ~10,000 so-called "excess deaths" are vaccine-induced, since there are numerous potential medical issues unrelated to the actual vaccination that could arise in an individual and cause them to either delay first dose or forego second dose, and increase their mortality risk over the others in their age cohort. Such factors would produce ** selection bias** in this group, even aside from any vaccine-induced factors. That is, this small select group of those remaining only partially vaccinated in these age cohorts after wk16-20 may have inherently higher mortality risk because of the factors putting them in this group. A careful study of this select group could sort out these questions.

Even if there are some vaccine-related deaths in this select group, any evaluation of the UK vaccination strategy must consider the entire picture, including the substantially lower death rates in the partially vaccinated in wk0-20 of the pandemic.

We see a large number of **"prevented deaths" i**n the early weeks, with 12,708, 30,670, and 88,797 fewer deaths than expected in the partially vaccinated group in the 60-69yr, 70-79yr, and 80yr+ age cohorts, respectively, by summing the green counts across wk0-19 in the 60-69yr age cohort and wk0-14 in the 70-79yr and 80yr+ age cohorts, for a total of 132,175 fewer deaths than expected over these three age groups.. Had the vaccination program not commenced, we expect many of these deaths would have occurred, and given the results of the fully vaccinated vs. unvaccinated analysis in __part 2__ we also expect many more "prevented deaths" from that analysis would have occurred.

Summing over all time periods, the partially vaccinated had far fewer deaths than expected, with 11,806, 28,044, and 82,236 fewer deaths than expected in the partially vaccinated group in the 60-69yr, 70-79yr, and 80yr+ age groups, respectively, summing up to 122,086 indicating even in the partial vaccination group, the net societal benefit of the vaccination program was the prevention of >120k deaths.

I have purposely provided all data and code used to construct these plots, tables, and analyses for full transparency, and I welcome anyone to download and do their own analysis, and am glad to hear any criticisms of my analysis or interpretation, and consider any alternative analyses people think provide additional information or are more appropriate.

**Note on Analysis of 10-59yr old data**

As previously discussed, the 10-59yr old cohort is so wide, there are major systematic differences in the vaccination rate and inherent mortality rate for the vaccinated and unvaccinated cohorts. This makes the unvaccinated cohort an invalid control against which to compare the partially vaccinated cohort, and doing so will lead to erroneous conclusions based on Simpson's paradox based distortions. Thus, it is necessary to age-adjust the partially vaccinated and unvaccinated cohorts based on the known differential vaccination rates and inherent mortality risks (pre-pandemic) before doing this comparison. That will require additional time that I do not have right now, so I will post this article now with just the 60yr+ analysis, and append the 10-59yr old analysis here when it is complete.

At that point, I will also append my general conclusions looking across the results from all parts of this 4-part analysis of the UK ONS mortality data.

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