That's the RRR. What about the ARR!?

In my frequent outreach efforts on social media about vaccine efficacy, it never fails that after I mention that vaccines reduce the risk of Covid-illness from between 76% to 95% and death by at least 99%, someone will inevitably post:

Yeah, but, what's the ARR? Just saying.

Social Media posts have used the ARR numbers to make it look like the vaccines don't work. They cite the 90+% efficacies as frauds. They think the ARR shows that vaccines don't work. This is incorrect. In other posts, it is argued that the ARR shows that the risk of getting Covid is so low that we don't need to get vaccinated.

What is the ARR?

The ARR is the Absolute Risk Reduction. It's literally in the name. What is the reduction in risk? So, right away, this means that we are going to compare groups and determine a difference between them. We can look at any treatment group to determine this. Let's say that we wished to see how useful Wet Floor signs are in preventing falls on wet floors. We would compare the percentages of falls before and after treatment and look at the difference between the two. This is the ARR(1).

With Covid-19, we can look at many risk factors such as Sars-Cov-2 variants, population density, improvements in medical treatments, mask-wearing, age, etc. These can all influence the impact of vaccines. So the ARR for infections, deaths, transmissibility, hospitalizations, and recovery can all be different per vaccine. Let's say we have a study that is looking for hospitalization rates after getting a vaccine and not deaths. 0 out of 40,000 people get Covid-19 and are hospitalized after having a vaccine while the unvaccinated group could have 400 out of 40,000 get Covid and end up hospitalized. The ARR would be 1% even though NONE of the vaccinated group developed Covid-19 and were hospitalized.

A popular figure on social media reflects a Lancet's Comment paper showing that the ARR reflects exactly such a low number(2). Instagram disinformation posts show ARRs between 1.2 to 1.4%. Yes, indeed, these are lower numbers than the higher percentages that "the Media" and "Fauci" discuss. Where's that 99%? There must be something nefarious going on right? No. Not at all. The problem is that most people have no idea what an ARR is. They see drastically lower numbers than expected so it's conspiracy time.

The ARR can be calculated as follows: Treatment AR Minus Untreated AR = ARR. So,

(0/40,000 - (400/40,000)= 1% ARR).

So, what does this mean? Basically, we each have our own absolute risk(AR). Let's say I was part of an experimental group (n=100) that was vaccinated. No one in my group died. That's 100% efficacy. My own absolute risk will not change, so my absolute risk is 0/100 or 0%. This doesn't mean that the vaccine is 0% effective. Now, in the control group, let's say that 3 out 100 got Covid and died. Let's say Karen Carlson is part of that group. Karen's AR in that population would be 3%. Now, let's determine the ARR. (0% - (3/100)= 3%). So, the ARR would be 3%. So, without intervention (not getting vaccinated), there is a 3% risk reduction of dying from Covid. Again, notice that the vaccine was 100% effective.

Let's investigate another population. Let's say that 1 person in a vaccinated group (n=500,000) died from the Delta strain of Covid-19. Now, let's look at the unvaccinated. Let's say that the unvaccinated group has 25 out of 500,000 that died from the Delta variant. That's 1/500,000 and 25/500,000 AR respectively. Let's do the math. Let's use the larger number first because we wish to see the reduction (0.005% - .0002%)= 0.0048% ARR). That's a 0.0048% risk reduction from dying if they get vaccinated.

This number seems small, but what it's actually showing is that vaccines work. If they didn't you'd get an equivalent value between the control and experimental. Let's see: 2/500,000 of vaccinated and 2/500,000 unvaccinated. (0.00004% - 0.00004%)= 0.00% ARR). This would mean that there is an equal risk reduction of zero. No Treatment effect.

To state this clearly, there are 95 million adults over 40 in the US. A risk reduction of 0.0048% could potentially save over 400,000 lives if those 95 million got Covid. Keep in mind that we are just talking about deaths. If avoiding severe illness the ARR would be more profound.

Now, look again at that 0.0048% percentage. What's interesting is that the ARR in the Lancet comment were from between 0.9% to 1.9%. Much higher than my scenarios. That's even more lives saved. An ARR of 1.9% shows that a vaccine is actually working.

The ARR doesn't show what some vaccine skeptics think it shows. More importantly, I think it prudent to remind the public that 158 million Americans have been vaccinated as of this post(4). 99% of all new Covid-19 hospitalizations are from unvaccinated people(5).

Thanks for reading.