### Abstract

*Every 30 to 50 days, the Vaccin Effectiveness decreases with 10%-points.*

### Introduction

In several studies around the world, waning is seen for Vaccin Effectiveness (VE) for infection, hospital admission or death. The waning effect for infection is investigated.

NotesMultiple research shows that the VE for severe disease, hospitalization and death remains high!This analysis has been done with very simple methods and are only meant as a rough indication.

### Method

Data from the RIVM is used. Every week they publish for a timeframe of 6 weeks (probably to smoothen out the data and/or privacy reasons) the amount of people infected and whether they are vaccinated or not(fully) [1]

The data is given like this

The groups “not vaccinated” and “not fully vaccinated” are combined in one group. For the positive tested people with an unknown vaccination status, it is assumed that they were (not) vaccinated with the ratio of the known people.

This weekly data, from 22nd of August 2021 until nowadays, with exception of 12/09/2021 is retrieved (when needed with the help of webarchive.org).

The cumulative number of fully vaccinated people (“*Cumulatieve vaccinatiegraad voor volledige COVID-19-vaccinatie naar geboortejaar en week”) *[2] is retrieved. Age groups are combined and slightly changed to match the other data as much as possible. The vaccination-% of the two 5-year groups are averaged to represent the 10 year group. Vaccination-% of 11–17 is linked to the cases of the age group 10–19, the vaccination-% of 18–30 is linked to the number of cases of the age group 20–29. The percentage has been multiplied by the total number of people in that age group.

Also the date on which 50% of the age group is fully vaccinated is calculated and/or estimated.

The VE is calculated for each age group for every week:

V = number of people tested positive|vaccinated / number of people vaccinated * 100000

N = number of people tested positive| not vaccinated / number of people not vaccinated * 100000

VE = (1- V/N)*100%

It is also possible to use odds but for the ease of understanding VE is chosen.

Also the number of days between the outcome and the date of which 50% of the age group is fully vaccinated is calculated.

The data is aggregated in a Google sheet [3] Python in combination with Streamlit is used. The source code is linked at the end [4].

### Results

The latest results can be found here [5].

VE in time is shown in % and as an index:

VE is plotted in relation to the date on which 50% of an age group is vaccinated

10–19 and 80+ seem to be outliers, so these groups can be excluded from the graph:

The slope for the various age group is calculated, and the number of days in which all the effected has waned. The 10–19 age group has an increasing VE. Their vaccins are relatively “new” and the vaccin “starts to work”. Also in theory, the intercept should be 100 in all cases (starting with VE =100%)

Also the VE for the total population (with and without the group ‘0–9’ – excluded in the other calculations because they haven’t had a vaccination yet- indicated as ‘kids’)in time has been plotted. It is remarkable that the last two weeks decreased more than proportional. (NB. this graph contains one week more than the others)

### Conclusion

In general every 30 to 50 days there is a reduction of around 10%-point of VE for infection, though it differs per age group. These results have consequences for the uses of permissions in society based on (not) being vaccinated and/or the use of booster vaccins.

### Discussion

- This is an analysis with the use of very easy methods (just a simple calculation of correlation) without taking in account confounding, morbidities, sex, vaccine taken etc. so the conclusions have to be taken with a lot of precaution.
- There is a bias of testing behavior of vaccinated (“I don’t test because I am vaccinated”) and not vaccinated (“I don’t test because I don’t believe in the problem”) people. Same for differences in risk behavior of both groups. These bias/differences play also a role in time, in combination with measurements of the government.
- Confidence intervals are not taken into account
- These results don’t say anything about VE for severe disease, hospital admission and death.
- The number of people with an unknown vaccination status is a big factor and might lead to a bias.
- Should the line start with a VE of 100% or is it possible that the VE already starts with a value lower than 100%?
- Immunity by natural infection is not taken in account
- It is arbitrary which percentage of fully vaccinated (here 50%) is chosen to take the date of reference .
- It is possible that people who have a break through infection are less susceptible or transmittable, thus the Secondary Attack Rate is what really matters. RIVM calculates the VE (also) with the help of Secondary Attack Rate (SAR). https://www.medrxiv.org/content/10.1101/2021.10.14.21264959v1.full.pdf
- Waning is probably a sigmoïdal function instead of a lineair decrease

### Ideas for exploration

- Use of logistic regression and other methods. (RIVM seems to use a ‘negatief binomiaal regressiemodel met log-linkfunctie’ [6]. For other methods see remarks in [7].)
- Repeat this calculation for severe disease, hospital admission and/or death. However, data is lacking
- Comparing these results with results from other countries

### Remarks / edits

- The graphs show a shift in dates of three weeks compared to the enddate in the RIVM table. Because the statistics are about 6 weeks it is probably better to use a date in the center of that period.
- Other studies seems to follow the VE = 0.33x+100 (exc. Quatar, which is an outlier starting with 72.1%). See [3] (sheet “Other studies”)

- Graphs have been updated on the 2nd of November 2021

### Resources

- [1] Number of infected people with vaccination status https://www.rivm.nl/coronavirus-covid-19/grafieken
- [2] Vaccination data https://www.rivm.nl/covid-19-vaccinatie/cijfers-vaccinatieprogramma
- [3] Google sheet with data : https://docs.google.com/spreadsheets/d/12pLaItlz1Lw1BM-f1Zu66rq6nnXcw0qSOO64o3xuWco/edit#gid=1548858810
- [4] Python script : https://github.com/rcsmit/COVIDcases/blob/main/VE_nederland.py
- [5] Streamlit page https://share.streamlit.io/rcsmit/covidcases/main/covid_menu_streamlit.py?choice=25
- [6]Studie Effectiviteit van COVID-19 vaccinatie tegen ziekenhuis- en intensive-care-opname in Nederland https://www.rivm.nl/documenten/studie-effectiviteit-van-covid-19-vaccinatie-tegen-ziekenhuis-en-intensive-care-opname
- [7] Some experiments https://github.com/rcsmit/COVIDcases/blob/main/VE_nederland.py