How well have our vaccines protected the oldest members of our society against COVID?

Last update: Saturday 6/11/22 

Throughout the pandemic the coronavirus has killed a far higher percentage of the oldest members of our society than any of the younger age groups. Using CDC data, this blog note compares the death rates for vaccinated persons with the death rates for unvaccinated persons within each age group

Hypothesis
To be specific, the following pair of ratios will be calculated for each age group: 

-- In a population of 100,000 vaccinated persons, the vaxRatio would be the number of vaccinated persons who became infected and died.

-- In a population of 100,000 unvaccinated persons, the unVaxRatio would be the number of unvaccinated persons who became infected and died.

If the vaccines have any effectiveness, the vaxRatio should be smaller than the unVaxRatio. The hypothesis underlying this analysis is that the human body loses its capacity to fully respond to vaccines as we grow older.  We define the ratsRats as the ratio of these ratios = unVaxRatio / vaxRatio for each age group

• If our vaccines have any effectiveness for an age group, then fewer vaccinated persons will die per 100,000 than unvaccinated persons, i.e., the unVaxRatio will be greater than the vaxRatio, so the ratsRats will be greater than 1.
  
  
• The ratsRats for each age group tells us how many unvaccinated persons died for each vaccinated person who died. For example, if the ratsRats for persons in the 50 to 64 age group was 5, that would mean that five unvaccinated person out of 100,000 unvaccinated persons died for each vaccinated person who died out of 100,000 vaccinated persons. In other words, unvaccinated persons were five times as likely to die as vaccinated persons.
  
  
• Our hypothesis predicts that the ratsRats for older age groups would be smaller than the ratsRats for younger age groups because we assume that vaccines lose their effectiveness as people grow older, i.e., more vaccinated persons become infected and die in older age groups; so the vaxRatio in the denominator of the ratsRats ratio will get larger.
  
  
• If vaccines were to lose all effectiveness for an age group, then vaccinated persons would be as likely to die as unvaccinated persons, i.e., the vaxRatio and unVaxRatio would have the same value, so the ratsRats would equal 1.

Data from the CDC's National Center for Health Statistics (NCHS)

When the editor of this blog visited the NCHS page via data.CDC.gov on Thursday 6/9/22, he entered the following keywords into the search box: "covid" "age" "deaths" "vaccinations". The search engine returned links to 258 results. The file that best provided the data the editor needed was called "Rates of COVID-19 Cases or Deaths by Age Group and Vaccination Status" and had been updated on 5/20/22

• The file provided weekly outcomes (infections or deaths) in the U.S. since early 2021 for Age Groups  = 5-11 years; 12-17 years; 18-29 years; 30-49 years; 50-64 years; 65-79 years; and 80+ years
  
  
• For each week, the table provided the number of deaths among fully vaccinated persons, deaths among unvaccinated persons, estimates of the number of unvaccinated persons in the U.S., and the number of vaccinated person in the U.S.
  
  
• The editor downloaded the csv file to his Mac, then wrote a few "tidyverse" scripts in the R language to extract the data required to construct the three ratios that appear in the three tables in the next section of this blog note
  
  
• The tables present the ratios for three weeks: (1) one in April 2021, around the time that deaths from the original variant had peaked, (2) one in August 2021 during high deaths from the Delta variant, and (3) one in February 2022, during high deaths from Omicron.

Three tables of ratios

Table 1. Ratios of Unvaxed Deaths per 100,000 

month	MMWR week	5-11	12-17	18-29	30-49	50-64	65-79	80+
APR 2021	202114	NA	0.01	0.08	0.55	2.97	10.09	23.42
AUG 2021	202134	NA	0.15	0.75	5.73	22.92	70.13	80.18
FEB 2022	202206	0.04	0.09	0.16	0.89	7.48	47.93	86.14

Table 2. Ratios of Vaxed Deaths per 100,000 

month	MMWR week	5-11	12-17	18-29	30-49	50-64	65-79	80+
APR 2021	202114	NA	0.00	0.00	0.03	0.13	0.42	1.48
AUG 2021	202134	NA	0.00	0.01	0.13	0.81	3.30	12.57
FEB 2022	202206	0	0.01	0.03	0.12	0.58	2.61	10.32

Some comments about the tables of unVaxRatios and vaxRatios

• The most significant difference between the death rates per 100,000 shown in the two tables is that the death rates in the unvaxxed table are at least ten to twenty times larger than the death rates in the vaxxed table, providing conclusive evidence of the power of our vaccines
  
  
• Within each row of each table, the death rates tend to increase as we move from the rates in one age group to the rates in the next group. In other words, this virus tends to kill older people, the older the age group, the more people within at group are killed; and the rates in the oldest age groups are 100 times higher than in the youngest age groups.
  
  
• Technical note: The "NA" entries denote missing values. Vaccines were not authorized for 5 to 11 year olds until the late fall of 2021; that's why these values were missing in April 2021 and August 2021.
  
  

Table 3. Unvaxed to Vaxed Death Ratios

	5-11	12-17	18-29	30-49	50-64	65-79	80+
APR 2021	NA	Inf	Inf	18	23	24	16
AUG 2021	NA	Inf	75	44	28	21	6
FEB 2022	Inf	9	5	7	13	18	8

Some comments about the ratsRats table

• Once again "NA" denotes a missing value; but the "inf" entries are interesting. They occur in weeks in which there were no deaths among the vaccinated:  so the vaxRatios in the denominator of the ratsRats is zero, which gives the fraction an infinite value, designated as "Inf"
  
  There were no breakthroughs under the original variant, i.e., no breakthrough infections, so zero deaths among persons who were vaccinated. But breakthroughs occurred under Delta in August 2021 and Omicron in February 2022.
  
  
• Delta was the most lethal of the three major variants, an attribute that is consistent with the large ratsRats values that occur in the second row of the table for August 2021 when Delta was dominant. Omicron was the least lethal variant, a fact consistent with the smallest ratsRrats values are in the table's third row for February 2022  when Omicron was dominant.
  
  
• Finally, the ratsRats values in the last column of the table for persons 80 and over are substantially lower than all of the other values in the first and second rows, and lower than the two preceding values in the third row. This pattern is consistent with the possibility that our vaccines provide far less effective protection for our nation's oldest residents than for others ... Nevertheless, our vaccines are still worth taking today under the Omicron variants because the last entry in the last row of the table shows that unvaccinated seniors may be 8 times more likely to die from COVID than seniors who are vaccinated.

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Links to related notes on this blog:  

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