Vaccination is highly protective against Covid-19

As in Europe, the US is currently experiencing a surge in Covid-19 cases and hospitalizations driven by transmission among the unvaccinated.  Two days ago, health officials in Vermont noted that 90% of Covid cases in Intensive Care Units are unvaccinated. Currently 74% of the Vermont population is fully vaccinated. This information allows us to do a simple calculation using only high school algebra to estimate the difference in risk of severe Covid infection among vaccinated compared to unvaccinated.

Let us say the infection rate among the unvaccinated is I and the relative risk of severe infection in vaccinated versus unvaccinated is R. So the infection rate among the vaccinated is R*I.

Let us assume a population of 100 in which 74 are vaccinated and 26 are unvaccinated. Then the number of severe infections requiring admission to ICU is 26*I unvaccinated and  74*R*I vaccinated. So the proportion of ICU cases who are unvaccinated is 26*I /( 26* I + 74 *R*I), and we know that this ratio is 0.9. So we can write:

                26*I / ( 26* I + 74 *R*I)  = 0.9    

Solving this equation for R:

                                        26* I       =  0.9 * (26*I + 74 *R*I)  

or                                         26      =  23.4  +  66.6*R

so                                      R       =   (26-23.4)/66.6    = 0.039

Thus the vaccinated have a risk of severe Covid infection that is 3.9% of that for the unvaccinated.  Inverting this, we can say that the unvaccinated have 1/0.039  = 25.6 times the risk of severe infection as the vaccinated.  The actual risk will vary somewhat in populations with the mix of Covid variants and the overall time since vaccination, but the figures from Vermont graphically illustrate the huge protection that full vaccination provides.  And the evidence is that this protection is definitely enhanced by getting a third booster shot.

A previous post I made on the importance of boosters attracted a couple of anti-vax comments claiming ^ that I was admitting the vaccine did not prevent Covid. I hope the simple analysis above of readily accessible data is adequate to clarify to anyone who thinks like this that the vaccine offers a huge level of risk reduction. And if you were vaccinated more than five or six months ago, get a booster! It improves the level of protection further.

2 thoughts on “Vaccination is highly protective against Covid-19

  1. Sadly, fake news is everywhere these days.

    European Journal of Epidemiology
    “Increases in COVID-19 are unrelated to levels of vaccination across 68 countries and 2947 counties in the United States”

    The Lancet!
    “The epidemiological relevance of the COVID-19-vaccinated population is increasing”

    Lies, damned lies and statistics …

    • I initially took the “fake news” comment to be referring to my post about vaccine effectiveness, and decided not to post the comment until I had read the two references given. When I read these, I became unsure whether in fact the comment was in fact agreeing with me and presenting the papers as examples of “lies, damned lies and statistics”.
      The first of these presents a cross-sectional statistical analysis which is not an incorrect analysis of the actual data, but is inadequate to draw the implied conclusion that vaccines are not effective at reducing infection rates. In fact, the authors actually draw the conclusion that “The sole reliance on vaccination as a primary strategy to mitigate COVID-19 and its adverse consequences needs to be re-examined, especially considering the Delta (B.1.617.2) variant and the likelihood of future variants.”

      As far as I know no countries have solely relied on vaccination. To varying degrees, countries have implemented various forms of social distancing and mask wearing, ranging from full lockdowns and other travel restrictions through to unenforced recommendations to wear masks in limited situations. All of these measures impact Covid transmission rates, and undoubtedly analysing the correlation of any one of them on its own against Covid infection rates at a point in time would almost certainly find no correlation either.

      In addition, the title of the article claims that “increases in Covid-19 are unrelated to vaccinations across 68 countries” whereas in fact no analysis is done of the rate of increase of Covid infections or equivalently the effective reproduction rate Re.

      Apart from not controlling for other determinants of the level or rate of increase, the analysis does not mention what is perhaps the most important factor in influencing cross-country variation in infection rates at a given point in time. The authors analysed new Covid case rates for the 7 days leading up to 3 September 2021. This was right in the middle of the period when the delta variant was becoming dominant in many countries. The delta wave resulted in rapidly increasing case numbers in many countries due to the transmissibility of delta, but these waves started and peaked at different times for different countries. This can easily be seen by examing new case rates on Our World in Data for the period June 10 2021 to October 1. The delta wave peaked in July for some countries (eg. Spain, Netherlands, UK), in August for France and Iceland and in September for other countries (eg. Israel, USA and Switzerland).

      Many countries had achieved vaccination rates in the range 50% to 70% by September 2021, so there were still many unvaccinated to drive the delta cases upwards, and infect vaccinated people also (at a lower rate). Depending on the start of the delta wave, it is entirely possible for a country with higher vaccination rate in September 2021 to have higher new case rates than another country with somewhat lower vaccination rate where the delta wave started later. An analysis capable of detecting the real impact of vaccination rate on delta transmission would need to either control for the start time of delta transmission (and the average time since second vaccine shot) or to properly examine the effective reproduction rate as outcome variable.

      So this article is not “fake analysis” or “lies” but it is an analysis from which it is impossible to draw conclusions about the impact of vaccination rates, and where the implied conclusions of the analysis are invalid.

      The second reference presents data s that the numbers of Covid cases among vaccinated people is increasing and that the numbers of secondary infections are essentially the same for a Covid case in a vaccinated and in an unvaccinated person. All good so far, and completely consistent with the evidence that vaccination reduces the risk of catching Covid and more importantly reduces considerably the risk of serious illness or death.

      My post showed how the observation being widely reported that hospitalized Covid cases are predominantly in unvaccinated people can easily be used to estimate the relative risk of catching Covid for unvaccinated versus vaccinated people (for the source population of the cases with all the varying additional social distancing measures that were in place in the previous few weeks). In fact, Dr Fauci summarized these risks in a hearing in Congress yesterday saying that unvaccinated people were 10 times more likely to test positive for Covid-19, 17 times more likely to be hospitalised and 20 times more likely to die.

      I assume these would be US-based averages for the recent period when omicron is becoming dominant. Not dissimilar to the figures I came up with from a back of the envelope calculation for data from one State hospital system.
      I am perfectly happy for people to comment on my posts with reasoned arguments. For example, to explain why they consider a particular analysis or the conclusions drawn from it to be flawed or inadequate. Or why they consider the conclusions to be inconsistent with other evidence. But when slogans like “fake news” or “lies” are just thrown out, without justification, or even enough context to know what the commenter was referring to, I’ve decided not to approve such comments in future. Base reasoned arguments on an understanding of the available data and the issues involved in its interpretation, and I’ll post the comment.

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