How To Estimate the Efficacy of The Vaccine

18 May 2021

(Updated 14 June 2021:  Added UK Data)

 

If you receive this piece of news, what would you think?

The news is about Seychelles,  a small island country somewhere in Indian Ocean. The paper said this small nation has 37% of the infected people fully vaccinated.

 

https://www.reuters.com/business/healthcare-pharmaceuticals/who-reviewing-seychelles-covid-19-data-after-fully-vaccinated-people-test-2021-05-11/

To some,  this is really a shocking piece of news.  To others,  they might "brush it off" claiming it is just another fake news.  Unless the vaccine is useless, it is hard to believe. How come one can get infected so easily when one already has the  full 2 doses of vaccine. 

 

Now, what exactly does that News report really mean?

Vaccine Efficacy 

“Vaccine efficacy” is a familiar term nowadays.  It simply tell how effective is a vaccine in reducing the virus infection.   If we say Seychelles' vaccines have a combined efficacy of 60%,  one will quickly understand that the vaccines are actually working.  Just that the vaccines are not having very high efficacy.  It is as claimed by some countries. We have also an infectious African variant,  B1351,  "roaming" around.  This efficacy is still above the threshold of 50% set by WHO for approval under emergency usage.  The question now is how to roughly work out this 60% efficacy without all those laboratory tests and trials ?

 

Efficacy Measurement

The vaccine efficacy is always worked out by carrying out the tests in a laboratory or otherwise under controlled environment. This is to ensure the variables that will affect accuracy are kept to a minimum. In the real World, it is unlikely to accurately measure the efficacy vaccine.  This is because one will know how many people have been infect and there is no way to tell how many were exposed to the virus. But there is nothing to stop us from estimating the "Vaccine Efficacy" or usually termed as "Vaccine Effectiveness" for the purpose of knowing if the vaccines we have taken are in order.  

 

How to Estimate the Effectiveness?

Take the case in Seychelles for example, in the news report, we can gather the following information:-

1.  37% of those infected people were fully dosed 

2.  The seven day rolling average of positive cases increased from 120 on April 30 to 314 on May 8

3.  Nearly 60% of the population have had two doses. (about 66% in other news report) 

From some other websites, we can also find the following information

1. The total population of Seychelles is 97,625

2. This Reuters news report is on 12 May 2021

We can also gather these information from this page or alternatively,  from graphics.reuters.com & www.worldometers.info.

1. The total number of infection between Jan 12 and May 11 2021 is 7,571;

2. Seychelles’ vaccine roll out date is 12 Jan 2021

Equipped with these information, we can now roughly work out the attack rates of those vaccinated (ARV) and unvaccinated (ARU) .  

Finally, using the standard Efficacy rate of the Vaccine formula, we can work out the rough effectiveness for the vaccines used in Seychelles.  This is roughly 60.70% as shown in this example sheet

 

Similarly,  we can also work out the vaccine effectiveness roughly for other countries and a copy of which is shown in this table

Interactive Template

One can use the follow template to estimate the rough effectiveness in your country if you also have the required information 

(Note:  Please doubleclick the following image to be re-directed to the calculation template or Just click this link )

UK Example  Updated (11 Jun 2021) 

UK Public Health released a report on the effect of Covid-19 Variants.  It has this table 6 on page 15 reported about infection &  deaths of Delta (Indian Variant) confirmed cases from 1 February 2021 to 7 June 2021. 

The report said 9,344 vaccinated people were infected,  among them 1,785 has full 2-doses.    Using this information,  we could roughly estimated the UK's vaccine efficacy to be about 74% for all vaccinated,  93% for those having full doses only & 68% if we were to include only the vaccinated & unvaccinated. 

Note: This is the efficacy estimate only against Delta variants

About the Method

This is a simple example.  The aim is to give users a reference to  work out roughly and compare the combined vaccine effectiveness.   The example uses the "window" between rollout date and the breakthrough date.   Users can always choose other "windows" if the information are available. 

In the  real World,  there is always a difficulty getting the numbers for the people exposing to the disease,  especially for those unvaccinated. This information are required to work out the attack rates. 

It is a common knowledge that in the real World,  the vaccinated and unvaccinated are not living & working together . Their risk of exposure to the virus are much different.  Any attempt to estimate the vaccine efficacy over a short period &  over a sudden spike can be misleading.

Take the case that happened in Singapore in recent weeks. 78 people with full doses among some 400 others were found infected. Attempt to use these information to work out the vaccine efficacy will yield misleading result. This is because most of the 78 vaccinated were front-line staff.  Their exposure to virus will be much higher than those unvaccinated whom they were serving.

 https://tinyurl.com/u2ts2hfn