Covid Vaccines and a little math
A brief glance at the numbers surrounding Covid Vaccines, risk of infection, and risk of death after becoming infected.
Covid vaccines and a bit of math.
Disclaimer: The data available surrounding Covid is incomplete. This document is an analysis limited to a comparison of the death rate between vaccinated and unvaccinated populations in a few discreet locations, and relies on publicly available information that is incomplete. The PA data set, for example, only includes slightly more than half of the hospitals in PA. The other data sets are similarly limited and incomplete. Please take time to evaluate the sources of data and the associated limitations of the data from each source for yourself. This document is not intended to be a guide for decision making at any level, nor is it intended to influence or suggest a course of action. I am not a medical expert, have no formal data analysis training, and am not associated with any group or organization tied to anything related to Covid, health care, or public policy in any capacity. Share or disseminate this document at your discretion. I take no responsibility for any consequences resulting from the use of this document or the included information.
Let’s start with some data from PA. (my analysis)
Vaccination impact on risk of death:
https://www.health.pa.gov/topics/disease/coronavirus/Pages/Post-Vaccination-Data.aspx
Pulling the relevant data:
Quote from link: “Among a total of 639,729 positive cases, there have been 35,389 identified post-vaccination cases”
Giving us 604,340 positive cases among unvaccinated and 35,389 positive cases among vaccinated.
Quote from link: “Among a total of 6,472 COVID-19-related deaths identified in Pennsylvania in 2021, there were at least 213 post-vaccination deaths identified”
Giving us 6259 deaths among unvaccinated and 213 deaths among vaccinated.
Crunching numbers:
604,340/6,259 = 96.5 (unvaccinated cases per death)
35,389/213 = 166.1 (vaccinated cases per death)
If you catch covid, you have a 1/96.5 chance of dying unvaccinated vs a 1/166.1 chance of dying vaccinated. (1.03% vs 0.6%) (42% reduced risk of death after catching covid if you got the jab)
And vaccination impact on infection in PA
https://www.health.pa.gov/topics/disease/coronavirus/Pages/Post-Vaccination-Data.aspx
Quote from link: “Cumulative case incidence among the unvaccinated and not fully vaccinated was 7.1 times as high as the case incidence among the fully vaccinated (5,840 vs. 819 per 100,000).”
Now for some data from Israel (my analysis)
Link to Israel’s Covid dashboard.
https://datadashboard.health.gov.il/COVID-19/general?utm_source=go.gov.il&utm_medium=referral
and the graphs from that site that I think are particularly valuable for this bit of analysis
Now my rough estimate is that less than 20% of the population (unvaccinated) is creating about 2/3rds of the total active patients. (eyeball averaged across ages) now for some math out loud… 100 people 80/20 vax/unvax split… 3 cases with a 1/2 vax/unvax split, 1 case per 80 vax’d vs 1 case per 10 unvax’d, so the vax group has a 1/8th rate of infection vs unvaxed. So… Israel, with a very high vaccination rate, is showing about 1/8th the rate of covid patients amongst the vaccinated vs the unvaccinated. (covid patients doesn’t mean people in the hospital, as there appear to be a little over 1000 in hospitals but 84k “patients”)
To look into this further, I pulled the total deaths of all ages (dropdown label in graph is wrong) from Israel’s dashboard. (below)
It looks like the total deaths between vaccinated and unvaccinated are about equal. If we consider that there are about twice as many unvaccinated cases as vaccinated cases, but the fatality case numbers are about equal, then breakthrough cases are about twice as deadly as normal cases.
Discussion of cases in Washington State. (Analysis by Evolve, a microbiology professor from UAB.)
OK, I pulled the case and vaccination numbers for Washington over the time period (1/27-8/27):
About 250,000 cases and 2,203 deaths, for an 0.88% mortality risk
About 26,000 breakthrough cases with 220 deaths, for an 0.85% mortality risk
So about 1/10 of total cases and deaths occurred in vaccinated people
The average number of vaccinated people over that time frame was about 4.2 million
Total Washington population is about 7.6 million, so the average number of unvaxxed over that time frame was 3.4 million
Thus, the risk to an unvaxxed person of contracting the virus was 6.6%, and the risk to a vaxxed person was 0.62%, corresponding to about 90% protection from infection, consistent with the original estimates.
However, the numbers seem to argue against the hypothesis that the vaccines protect against hospitalization and death, which appear to occur at similar rates for both vaxxed and unvaxxed once infection occurs.
Conclusion: data is supportive of COVID-naive people getting vaccinated, but also the need for therapeutics since everyone will still eventually catch the thing, even if the vaxxed take 10 times as long as the unvaxxed to finally catch a bullet. Also, worth considering that you’ll never be younger than you are today, so your risk of death from infection will increase forever – there is never a better time than today to catch the virus from that perspective…
Discussion of cases in Vermont (analysis by a friend)
Main board: Data Summary | Vermont Department of Health
Most recent report (it’s cumulative, so you really only need this one):
COVID19-Weekly-Data-Summary-9-10-2021.pdf 1
584.87 KB
Slide 36 of the PDF (also imaged below) shows that the breakthrough cases really started rising near the end of July, and in the last 5 weeks or so have been between 30-40% of the positive cases. But VT reports that hospitalizations and deaths among this cohort are “just a small portion”. Ahem. On the other hand, I note that 18 deaths among 1906 cases (0.94%) is about the same as the state’s total (284 deaths among 29588 = 0.96%). Hmm. But maybe this 18 deaths of 1906 cases is too small of a universe, statistically, to try to draw comparisons.
Slide 23 (not imaged below) gives population-wide covid hospitalization data and it turns out the hospitalization rate over the course of the whole pandemic is 2.8% of cases.
Meanwhile breakthrough cases requiring hospitalization, as shown in slide 36 below, are 51/1906 = 2.7%. Hmm. Ahem. Same caveat though regarding “small universe” and how much reliance one can put on these comparison hospitalization numbers being very similar.
Looking at these only on a week-by-week case basis, it seems the risk of catching it vaxxed/naive in VT for the last 4 or 5 weeks is closer to 3.5 to 10.
So, perhaps this isn’t enough data. Too bad the larger, heavily vaccinated states don’t have nice “breakthrough breakdowns” the way VT does. But I question how well this “pandemic only of the unvaxxed” meme holds water.
I should add that as more and more Vermonters become vaccinated, the “general population” numbers vs. the “breakthrough” numbers of course have to converge as everyone becomes vaccinated. As of now, though, they’re at 68% of total residents, and that’s ~ 85% of the eligible (over 12) residents.
Discussion of cases nationwide
https://www.cdc.gov/mmwr/volumes/70/wr/mm7037e1.htm?s_cid=mm7037e1_w
From June 20-July 17 (Delta variant prevalent), 6,089 out of 101,633 total not fully vaccinated cases required hospitalization = 6%, and there were 1,006/101,633 deaths = 1%. For fully vaccinated people, 951 hospitalizations out of 22,809 total cases = 4%, and 188/22,809 deaths = 0.8%.
Note: the CDC stopped monitoring breakthrough cases on 1 May 2021. The following link provides a good starting point to look into this further. https://www.kff.org/policy-watch/covid-19-vaccine-breakthrough-cases-data-from-the-states/
Summary:
In Israel, a Vaccinated person is 1/8th as likely to catch Covid, but if they do catch Covid, they are twice as likely to die.
In Pennsylvania, a Vaccinated person is 1/7th as likely to catch Covid, but if they do catch Covid, they are half as likely to die.
In Washington, a Vaccinated person is 1/10th as likely to catch Covid, but if they do catch Covid, they are equally likely to die.
In Vermont, a Vaccinated person is 1/3rd as likely to catch Covid, but if they do catch Covid, they are equally likely to die.
In the US overall, a Vaccinated person is much less likely to catch Covid, but if they do catch Covid, they are almost (80%) as likely to die.
Overall, without getting into the weeds of what qualifies as vaccinated, what qualifies as a covid case, what qualifies as a covid death, what impact time has on the efficacy of the vaccines, and a few dozen other significant issues… We have two clear results:
First: getting vaccinated reduces transmission rates significantly (this is not the same thing as preventing any given person for catching or transmitting covid)
Second: the vaccine does not clearly improve survival rates in breakthrough cases
Bottom line: the vaccine reduces the R value of covid within a population but may not impact survival rates of those who become infected