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Lucy D'Agostino McGowan: The essential stats on breakthrough cases
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Lucy D'Agostino McGowan: The essential stats on breakthrough cases

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There are so many numbers floating around relating to breakthrough COVID-19 cases and vaccine effectiveness that it can be hard to keep them straight. In fact, a recent interview I did on this topic, despite best intentions, resulted in a headline that confused the message a bit (“Breakthrough cases rare, says WFU researcher,” Aug. 16). So let’s break it down. We’re going to talk about two numbers:

1. Vaccine effectiveness

2. The total number of breakthrough cases

Vaccine effectiveness tells us how protected you will be relative to an unvaccinated person. Even with the delta variant, this looks good for infections (and very good for severe illness).

When thinking about vaccine effectiveness, it is important to compare the correct numbers. In statistics, we do this using fractions. As most of us likely remember from grade school, fractions have numerators (top numbers) and denominators (bottom numbers) — to get a percentage, we divide the numerator by the denominator. Vaccine effectiveness is a comparison of two percentages — the risk of infection (or hospitalization or death) among the vaccinated compared to the risk among the unvaccinated. For this comparison to be correct we need the numbers we are comparing to be accurate.

For example, when thinking about how effective the vaccine is against hospitalization, instead of looking at the number of unvaccinated people hospitalized (the numerator) out of all people hospitalized (the denominator), as is commonly seen in headlines (i.e., 95% of all people in the hospital with COVID-19 are unvaccinated), you want to look at the number of unvaccinated people hospitalized (the numerator) out of all unvaccinated people exposed to coronavirus (the denominator) compared to the number of vaccinated people hospitalized out of all vaccinated people exposed to coronavirus. Why? The first way doesn’t tell us how effective the vaccine is because wrapped up in that number is the percent of people vaccinated. If the percent of people vaccinated increases, counterintuitively, this number will look worse. (Think about the extreme example when 100% of people are vaccinated; even if only one person is hospitalized, 100% of hospitalized people will have been vaccinated.) When looked at correctly, we see that vaccines are very effective.

We’ve established that the vaccines are very effective; that is, if I am deciding whether or not to get vaccinated, my outlook looks much better if I choose the vaccine. But how does this relative number, vaccine effectiveness, relate to the total number of breakthrough cases? Let’s look at two scenarios.

Scenario 1: If an unvaccinated person has a 10% chance of getting sick, and the vaccine effectiveness is 60%, a vaccinated person’s chance of getting sick is only 4%. But what if there is more virus around and fewer precautions in place?

Scenario 2: With more virus around and fewer precautions such as masking and social distancing, everyone’s risk increases. For example, let’s assume an unvaccinated person now has a 25% chance of getting sick. The vaccine effectiveness is still 60%. Now a vaccinated person’s chance of getting sick is 10%.

In these scenarios, the vaccine effectiveness didn’t change, but the risk for the vaccinated person increased because the overall risk increased. In fact, in Scenario 2, the risk to the vaccinated person was equal to the risk of the unvaccinated person in Scenario 1.

Why does this matter? Breakthrough cases are going to be more frequent for this exact reason. It doesn’t mean the vaccine isn’t effective, it means everyone’s baseline risk is increasing because COVID-19 is just more prevalent everywhere.

There is hope, though. There are many things we can do to bring that baseline risk back down, such as getting more people vaccinated, masking up, making ample use of testing (free tests are widely available in our community and you can buy at-home rapid tests, 2 for $20, at local pharmacies) and using caution when possible until things improve.

So what is the takeaway message?

If you are unvaccinated, the No. 1 thing (by a long shot!) that you can do to reduce your risk and the risk to those around you is to get vaccinated. These vaccines are highly effective and our best tool to help this pandemic end.

If you are vaccinated, even though your relative risk is dramatically reduced compared to your risk if you were not vaccinated, the overall high prevalence of COVID-19 in our community is increasing your overall risk. Adding some caution to your daily interactions is a good idea until we can get cases back down.

Lucy D’Agostino McGowan is an assistant professor of statistics for the Department of Mathematics and Statistics at Wake Forest University. She uses statistical tools to answer medical questions, often working with interdisciplinary teams of epidemiologists and clinicians to help answer important public health questions.

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