Dr. Ron Brown – Opinion Editorial
October 8, 2021
Reuters published a “fact check” article several months ago: Why Relative Risk Reduction, not Absolute Risk Reduction, is most often used in calculating vaccine efficacy. In presenting their arguments, the authors of this article minimized the importance of reporting the absolute risk reduction (ARR) and defended the use of the relative risk reduction (RRR) to represent vaccine efficacy. Yet, the article also mentioned that the ARR is more dependent on group infection rates in a clinical trial, implying that the ARR is a more sensitive and relevant measure for vaccine efficacy than the RRR. For example, the larger the groups in a clinical trial, and the smaller the rate of infected people in the groups, the smaller the absolute risk reduction (ARR), even if the relative risk reduction (RRR) remains the same. This is why both the ARR and RRR of a clinical trial must be reported. The following examples illustrate this effect based on formulas for calculating the ARR, RRR, and the relative risk (RR)—a method that an epidemiologist might use to calculate these measures.
First, we have to define three terms.
ARR = Placebo infection rate – (minus) Vaccine infection rate.
This is the absolute risk reduction, or the simple mathematical difference in the infection rates between the Placebo and Vaccine groups, assuming a higher rate in the Placebo group.
RR = Vaccine infection rate / (divided by) Placebo infection rate.
This is the relative risk, or the proportion of the Vaccine infection rate (the numerator) relative to the Placebo group (the denominator).
RRR = 1 – RR.
This measures the relative risk reduction assuming that the relative risk is less than 1. In other words, the RRR assumes that the Vaccine infection rate (the RR numerator) is lower than the Placebo infection rate (the RR denominator).
Let’s say we have three infected people out of four people in our mini trial. That is, we have one infected person out of two people in the Vaccine group, and two infected people in the Placebo group.
Vaccine infection rate = 1 infected person out of 2 people = 50%
Placebo infection rate = 2 infected people out of 2 people = 100%
ARR = 100% – 50% = 50%
RR = 50% / 100% (same as .5 / 1) = 50%
RRR = 1 – 50% = 50%
The ARR and RRR both start off evenly with each other at 50%. But our sample is too small to give us accurate estimates, so, let’s see what happens if we place the three infected people in larger groups of 100 people. Notice that the RRR stays the same, but the absolute risk reduction drops by 49 percentage points to 1%.
Vaccine infection rate = 1 infected person out of 100 people = 1%
Placebo infection rate = 2 infected people out of 100 people = 2%
ARR = 2% – 1%= 1%
RR = 1% / 2% = 50%
RRR = 1 – 50% = 50%
The examples show that the absolute risk reduction is dependent on the increasing number of people in the groups and the dropping group infection rate, while the relative risk reduction is not. In the RRR, as long as the proportion of the group rates don’t change, the RRR doesn’t change regardless how many people are in the groups.
This explains why the ARR can be used to determine the number of people needed to be vaccinated to prevent one infection. The Number Needed to Vaccinate (NNV) is the reciprocal of the ARR (1/ARR). In other words, one reduced infection (the numerator) relative to the difference in the group infection rates (the ARR in the denominator).
Let’s put our three infected people into even larger groups of 1000 people.
Vaccine infection rate = 1 infected person out of 1000 people = 0.1%
Placebo infection rate = 2 infected people out of 1000 people = 0.2%
ARR = 0.2% – 0.1%= 0.1%
RR = 0.1% / 0.2% = 50%
RRR = 1 – 50% = 50%
The absolute risk reduction further drops by 10-fold to one tenth of one percent, while the RRR continues to remain the same. This proves that the absolute risk reduction is the more sensitive and relevant measure for vaccine efficacy depending on the group size and infection rate.
Population studies versus clinical studies
Still, noting that the RRR remains consistent regardless of the setting, the Reuters article quoted an assistant professor of biostatistics from the University of Florida, who said of the RRR, “It is more meaningful.”
Meaningful, perhaps, for epidemiological analysis of various sized populations, based on the RR or risk ratio used by epidemiologists. As long as the proportion of the populations exposed and unexposed to the risk remains the same, larger population sizes in different settings do not matter. But, as demonstrated in the examples above, the RRR is less meaningful for clinical research involving smaller groups of individuals where the size and infection rate of the group matters, even if the proportion of the group infections (the RRR) remain the same.
A similar distinction between population and clinical studies occurs in the Body Mass Index (BMI), used to categorize weight and height. Originally intended to measure entire populations, BMI is not sensitive to an individual’s body composition such as body fat and lean body mass levels, and BMI often miscategorises people by weight class.
Summing up, vaccine efficacy in clinical trials, based solely on RRR normally used by epidemiologists for larger population studies, ignores absolute risk differences in smaller group sizes and misrepresents vaccine efficacy in clinical trials. At the least, both ARR and RRR should be reported in clinical trials to prevent information bias.
Furthermore, I see no reason why clinicians shouldn’t drop the RRR altogether and leave its use exclusively for larger population studies. If clinicians want to compare treatment efficacies from different trials, the NNT or number needed to treat (or the NNV for vaccine trials) are more informative than the RRR.
Unfortunately, our current dysfunctional public health system continues to ignore this important issue, and with the assistance of media outlets like Reuters, the public remains largely unaware of the COVID-19 mRNA vaccines’ true efficacy.
