DEEP DIVE: Should Naturally-Immune People Get Vaccinated?

President Biden’s new mandate, and the CDC, say: Even if you already had Covid, get vaccinated.

Is that based on science? Good science?

This is an important question! Many people, including myself, already had Covid before the vaccines came out, and wonder if vaccination would be helpful or not.

To find out, I spent a week carefully combing through the studies themselves.

The data paint a much more nuanced picture than the news headlines on either side. Here’s what I learned:

1) The data are clear that already-powerful natural immunity can be further increased by getting vaccinated. Two doses also provide more protection than one.

2) Getting vaccinated on top of natural immunity reduces the odds of getting Covid in a year by roughly 4 percentage points (more, if the person engages in riskier behavior than average). Having antibodies from a previous Covid infection, by itself, also means protection that’s comparable to vaccines in the short run, and better in the long run.

Side note: Israel’s data convincingly show that the Pfizer vaccine has a huge plunge in its ability to prevent infections around 6 months out!

3) Side effects for Pfizer/Moderna are not much worse for people who already had Covid.

4) Any vaccine should work, but Pfizer and AstraZeneca have the best data on people who already had Covid. AstraZeneca is weaker at the start but has better staying power.

But, I hope you’ll read the below data and make up your own mind!

1. Getting vaccinated makes you 1.5 - 2.5 times less likely to get Covid again

Let’s take the best study design first: Pfizer’s clinical experiment. Their study included 1,292 people who already had Covid antibodies. Of those, 626 were given 2 doses of Pfizer, and the rest got a placebo.

After 6 months, 3 people in the recovered+vaccinated group contracted Covid again, while 8 people in the recovered+placebo group got Covid again.

This suggests:

• 3 / 626 = 0.48% chance of reinfection for recovered+vaccinated

• 8 / 666 = 1.2% chance of reinfection for recovered+placebo

Other ways of putting that: people who were double-vaccinated on top of having antibodies from prior infection were just 40% as likely to get Covid. Also: they were 2.5 times less likely to get it.

The study has drawbacks: a big one is low sample size. Also, their observations finished before Delta took off in the US. But fortunately we have at least 3 other studies which, despite various flaws, help give confidence in a finding somewhere around this mark.

The other interesting studies: UK, Israel, CDC. Listed here from highest-quality to lowest, they find that for people who already had had antibodies from Covid:

1) UK study: 1 dose means you’re 71.7% as likely to get Covid compared to staying unvaccinated. Risk falls further to 45.7% with 2 doses.

• Cons: vax treatment not randomized, so risk-taking behavior may differ in vaccinated and unvaccinated, and be a confounding factor.

• Pros: done during Delta; randomized testing

2) Israeli study: 1 dose makes you 53% as likely to get Covid vs staying unvaccinated.

• Cons: confounding factor: risk-taking behavior. Also not quite statistically significant due to small sample¹ (20 infected in vaccine group and 37 in non-vaccine group).

• Pros: done during Delta; long interval between vaccine & re-infection (4 - 6.5 months))

3) CDC Kentucky study: one dose make you 64.1% as likely to get Covid; falls to 42.7% with full vaccination

• Cons: confounding factors: both risk-taking behavior and test-taking behavior; before Delta; one-dose stat not statistically significant

• Pros: better than nothing

Any one of these studies would hard to believe on its own, because of the methodological shortcomings, which are common in population-level studies.

But with all these lining up, and with them each having a different portfolio of weaknesses and strengths, it’s strong evidence.

Putting these results together, we’re looking at:

One dose makes you between 53% and 71.7% as likely to get Covid.

Two doses make you 40% - 45.7% as likely.

Put another way, the data indicate that you’re 1.4 - 2 times less likely to get Covid if you get partially vaccinated, and 2.2 - 2.5 times less likely to get Covid with 2 doses.

EDIT, Jan 7, 2022: After publication of this post, the CDC came out with a study claiming contrary findings the above studies. But it is an extremely weak study, with a bizarre methodology. It shouldn't be taken seriously in light of the well-done studies finding that natural-immunity-alone is much better than vaccine-alone. Click footnote for a detailed explanation of the new study’s flaws.²

It’s still possible to remain skeptical³ but the above studies are consistent enough to convince me.

But I still have 3 questions:

— How big is this gain in REAL, not just relative, terms?

— Will side effects be worse because I already had Covid?

— Which vaccine should I get?

I researched all those:

2. How big are these gains in real terms?

The gains above are only expressed in relative terms, and so are not inherently meaningful.

We now know it halves our odds of getting Covid — but what exactly were our odds of getting Covid again, considering we were already immune? Not so high, as we learn below.

Pfizer, in their clinical trial, estimated that:

COVID-19 was less frequent among placebo recipients with positive N-binding antibodies at study entry (7/542; ~1.3% attack rate) than among [placebo recipients] without evidence of infection at study entry (1015/21,521; ~4.7% attack rate), indicating ~72.6% protection by previous infection

So there’s one clear answer: natural immunity provides 72.6% protection. That’s around what J&J (66%) and Astra (76%) say they give, but lower than the short-run protection from Pfizer/Moderna.

It may also be an underestimate, because people who got Covid before vaccination probably tend to be risk-takers, and that could account for some of their re-infection rate. It’s also based on just a handful of people who got Covid.

Let’s check the other datasets.

The Israeli study also considered: how does natural immunity (without vaccination) compare to vaccine-only immunity?

On this, they find:

… vaccinees had a 13.06-fold (95% CI, 8.08 to 21.11) increased risk for breakthrough infection with the Delta variant compared to those previously infected …

Whoa! That’s a crazy stat. You may have seen it in headlines already. Israeli researchers find vaccine-alone is 13 times less effective than having had Covid?

What’s going on?

Turns out, Israel just recently discovered that the Pfizer vaccine alone, without natural immunity, falls off a cliff around 4 - 6.5 months out in terms of effectiveness.

In other words, the study does not find that natural immunity is insanely great; it finds that the vaccine alone degrades dramatically after several months.

Their study is pretty well-done; it compares people who were initially infected/vaccinated at the same time, so it’s comparing apples to apples.

The Israeli government has released other data that line up with that: during June - mid July, they say the vaccine had just a 16% efficacy for people who got vaccinated in January and 44% for those who got it in February. Note, though, that they still find a high 75% for those who got the vaccine recently, in April, which roughly lines up with what we know and is nice to see as a sanity check. Furthermore their data also show that the vaccine remains 80-90% effective at preventing hospitalization and death.

Quite the decay.

This data is behind Israel’s recent decision to offer booster shots to everyone. It’s even behind some of the headlines you’ve read about US boosters. As Politico reports:

Biden … suggested that boosters could be administered just five months after the initial regimen, rather than the eight his administration had just proposed. Those remarks, coming after a meeting with Israeli Prime Minister Naftali Bennett …

Clearly, the Israeli PM told him about their data.

But can their data be right? Haven’t we seen conflicting data?

No. UK data appear on first glance to suggest dramatically higher efficacy, but there’s a big problem: Their data only go up to 3 months out. So they can’t address Israel’s findings. Pfizer’s controlled study goes up to 6 months, but it has a different critical problem: Its testing period ends in mid-June, just before Delta spiked in the US.

Each Delta virus particle is better at binding to human cells than previous strains, and so greater immunity is needed to prevent infection.

Early data from Minnesota that cover the Delta period confirm the Israeli data, showing Pfizer was down to 42% efficacy against cases in July, considering a population whose vaccinations were mostly done 2 - 4 months prior. Moderna, which uses higher doses, retained 76% efficacy.

Looking closely, it makes sense that Israel is the only one to already see the 5-6 month Delta efficacy cliff because they led the world by a lot in vaccinations. By the end of February, Israel had 45% of it population vaccinated; at that time, the UK had just 15% covered and the US just 11%.

I predict, based on this: The Northern Hemisphere is going to be in big trouble in terms of Covid breakthrough cases when winter comes. (Less trouble regarding hospitalizations and death; maybe society needs to just accept high cases? But that’s a whole question in itself.) I suspect Booster shots will be offered for everyone, just like Israel is doing now.

Right now, Israel has higher case rates than during the non-Delta winter wave, despite having 80% of the population vaccinated. Hospitalizations and deaths still remain about half of the last pre-Delta wave, thanks to the vaccines.

Now, back to the main subject of this post… estimating the impact of the gains to naturally immune people getting a vaccine.

I needed to go through the above to get Israel’s estimate of vaccine effectiveness for the period of their study. They show an average of 30% vaccine effectiveness for people who got vaccinated in Jan/Feb, the observation period of their study.⁴ And we also know from the study that:

… vaccinees had a 13.06-fold (95% CI, 8.08 to 21.11) increased risk for breakthrough infection with the Delta variant compared to those previously infected …

Solving for the missing variable (natural immunity effectiveness)⁵ we get:

Natural immunity effectiveness = 94.65%

This puts it right in line with the best vaccines, when new. Note that this applies to natural immunity 4 - 6.5 months out, and regards Delta.

Also informative is that the Israelis do a separate analysis on natural infection going farther back, finding that, for natural immunity with an average Israeli duration of 8 months (and ranging from 4 and 12 months):

SARS-CoV-2 naïve vaccinees had a 5.96-fold (95% CI, 4.85 to 7.33) increased risk for breakthrough infection …

Do the conversion math again, and we’re looking at 87% effectiveness. Again that’s if your natural immunity is 8 months old, which was the actual average age of immunity in Israel this summer. We can see that natural immunity declines gradually.

In our estimates, let’s use this range for natural immunity effectiveness: 72.6% as a lower bound, and 87% as an upper bound. This is for people who had Covid and aren’t vaccinated.

That range is better than many vaccines, even before they start wearing off. It also protects well against hospitalization and death.

But we also know from part 1 that adding vaccines could further prevent infection. Let’s adjust it per the research in part 1, to see how it changes with a vaccine added:

Two doses make you 40% - 45.7% as likely to get Covid

Doing the math⁶ and working that into the range, we get:

Efficacy if you had Covid, and got a 2-dose vaccination: 88.3% - 94.3%

That’s good! That’s even with Delta.

So — Is it worth it to get vaccinated to go from 72.6% - 87% effectiveness, to 88.3% - 94.3%?

Let’s put it in further context. A study finds that a third of Americans got Covid in 2020. Let’s go with that estimate, and keep in mind the 2021 is looks like it’ll have just as many cases.

Doing the math based on that, a naturally immune person’s odds of getting Covid in a year:

4.3% - 9%⁷ (average 6.65)

Naturally immune PLUS fully vaccinated:

1.9% - 3.9%⁸ (average 2.9)

So overall, if you’re a typical person, you’ll be about 4 percentage points less likely to get Covid in a year if you do get vaccinated. Meaning that out of 25 naturally-immune unvaccinated people taking average risks, roughly 2 would normally get it. If the same group were vaccinated, roughly 1 would get it.

Note: that gain will be higher that 4 percentage points to the extent that one continues to take the risks that perhaps led to getting Covid to begin with.

Is this gain worth it?

Far from obvious — if considered from an individual’s perspective in isolation.

For what it’s worth, here’s Mikhaila Peterson’s experience with getting mild/moderate Covid twice, while unvaccinated. For her, Delta was worse than her first time.

And of course, we’re not in isolation.

Especially if we like to travel and engage in risky behavior, it seems extra ethical to get the vaccine and top-up immunity — so that one doesn’t get it and spread it to others.

5% may not be such a big gain for one person, but if one person, on average, spreads it to 2 people, and each of them spreads it to 2 people — and so on, until the virus runs out of people whose immunity has waned… that can be a big harm.

If the individual case is already borderline, that suggests the social case is pretty clear.

But what about…

3. What about the side effects? Are they worse for naturally-immune people?

I’d heard this notion a lot, and also had two acquaintances with natural immunity who said they got 104-degree fevers after a first shot (but both lasted just a day.)

So I was surprised to find that the Pfizer study says:

… there was minimal observed difference in the overall reactogenicity [inflammatory side effect] based on baseline infection status …

The find it’s because while the first dose is harder on naturally-immune people, the second is easier. Moderna’s data also show little difference in side effects between naturally-immune and others, when both shots are considered.⁹

Side effects remain a real cost. Most people have some side effects.

Pfizer also reports half-a-percent chance of having a “severe” side-effect, beyond placebo (it happened to 0.7% of the placebo group, and 1.2% of the vaccine group.)

Moderna reports that 6.4% of naturally-immune subjects experienced “severe” side effects on first dose, compared to 3.3% who got a placebo.

The good news is, side effects when considered across both doses appear not significantly worse for people had Covid. So our the experiences of our friends and relatives who didn’t have Covid are representative.

4. Which vaccine should we get?

Let’s break this down into two categories:

1. Efficacy for naturally-immune people

Almost all of the above numbers focus on Pfizer, which clearly works in the short run.

The UK study also looked at AstraZeneca. Check out the beautiful graph of theirs below. “BNT162b2” is Pfizer. “ChadOx1” is Astra.

Lower means more protected. So this shows, A) Naturally-immune people are much better off no matter which they get. B) Astra is less good to start out, but seems to have much better staying power.

This graph only goes up to 3 months after vaccination; that’s a big limitation of the UK data. Israeli data should give us great cause for alarm that Pfizer will continue its exponential-looking decline in effectiveness.

Note that while already-infected people have much more protection overall, the same shape in waning effectiveness is in both green and red lines.

So Astra vs. Pfizer is a close call. Do you want super high protection for 4 months, or something that’ll probably last longer?

But anyway, those of us with natural immunity already have a lot of protection; we’ll be doing much better than most people, regardless of which of these we pick.

Astra isn’t available in the US, due to overregulation, but is available overseas.

J&J seems an intriguing option, as it only requires one shot for “full” administration. But looking at their clinical trial, while they DO have more than 4,000 subjects who had antibodies going in, they obnoxiously fail to report the raw outcome data for such people — it’s not even reported in their supplementary tables.

J&J seems a weak option in efficacy because of their lack of data transparency on that.

Also, none of the studies in part 1 seriously looked at J&J, and it also has much lower efficacy for the general population: their clinical trial reports 66%.

However, it does have one thing going for it: its design is similar to Astra, and *IF* it has a similar efficacy profile for naturally-immune patients, it’d be a decent option.

Moderna has longer effectiveness in the general population than Pfizer. But it’s much less common around the world, and so is less-studied. Their own clinical study, unlike Pfizer, also does not have enough people with prior infection to estimate efficacy for that subgroup.

2. Side effects

The Minnesota study suggests that (for people who didn’t have Covid) Moderna has both greater efficacy and side effects, due to its higher dose:

Assuming similar sized constructs … each [Moderna] dose provides three times more mRNA copies of the Spike protein than [Pfizer], …

Certain adverse effects, such as myalgia [muscle pain] and arthralgia [joint stiffness], were observed more frequently after vaccination with [Moderna] …

So, Moderna is plausible choice if one willing to deal with worse side effects for extra-extra protection. Pfizer reports somewhat lower severe side effects, as discussed above.

J&J hasn’t published safety data with results broken out for people with antibodies.

AstraZeneca also does not give such a breakdown; their sample of antibody-positive people is too small anyway.

We know that all these vaccines have common side effects but are pretty safe.

4. Conclusion

It seems clear that getting a vaccine, even if one already had Covid, helps society. It may be in certain individuals’ own interest as well.

Hope this data is useful to you, or people you know.

Please subscribe to see future data deep dives! It’s free, and all my posts will always be free. Paid subscriptions also encourage me to do more of them. This is the first analysis of many.

DISCLAIMER: Above is not medical advice, just my best attempt to lay out the most important data using my statistics knowledge, so you can make your own call. Also, if you see any NEW important data, or anything I missed, or any mistakes, please let me know in the comments.

Next up: Does Covid really cause significant harm to the brain, as some headlines claim? I’ll do another critical analysis of the studies on that.

1. Intriguingly, the Israeli researchers also have an additional subset of people who got vaccinated and THEN got Covid, and they find that these people are just as immune as the people who did it the other way around.
Also, when they add this reverse-order subset to the group, then the sample size is just large enough that the results are statistically significant.

2. The CDC authors admit, "The findings in this report are subject to at least seven limitations," and the biggest issue that I see is the bizarre choice of study method. Instead of trying to follow people with natural-vs-vax immunity and compare their results, the study strangely did this:

First - looked at hospitalizations for COVID-19-LIKE illnesses, and checked how many were natural-immune-only vs vax-only.

Second - looked at what % of those people actually tested positive as Covid in the hospital.

Third - act as if that % -- the proportion of people with confirmed-Covid to Covid-LIKE-symptoms in a hospital -- shows effectiveness of natural-vs-vax.

It doesn't make much sense. This is an EXTREMELY weaks metric to look at. Covid-19 hospital testing is fickle, in that it has to be done right in the window where the virus is active. Many people have Covid, and are hospitalized, but a test isn't done right in the window where the virus is active. 

On that note, the low %s are extremely suspicious. In the study, a mere 5 to 9% of people hospitalized for Covid-like symptoms were confirmed positive with a test in the hospital!

They note:

Laboratory-confirmed SARS-CoV-2 infection was identified among 324 (5.1%) of 6,328 fully vaccinated persons and among 89 of 1,020 (8.7%) unvaccinated, previously infected persons.

Does that sound right? A mere 5 to 9% of people hospitalized for Covid-LIKE symptoms actually had Covid?

No.

I can certainly believe that these small %s makes up all the people who they tested in the short active-virus window. But it's not plausible that it's reflective of how many actually had Covid -- which would be necessary for the study method to be valid. 

If those super-low numbers WERE reflective of the proportion who actually were hospitalized for Covid, then Covid would be dramatically overhyped. But we know that's not the case from all-cause mortality data, which shows many more deaths during Covid. So it's the study's method that's garbage. 

Their result is almost certainly the result of randomness in whether people were tested at the hospital within the often-narrow window where the virus is active.

Oddly, the authors don't even seem to consider this issue in their paper. They do identify seven other flaw in their method -- but to me, the already-outlined problem is big enough to sink the study. 

It would have been much smarter to take a population-based approach. 

For example, the study found that, among people hospitalized with confirmed Covid, 89 people had natural-immunity-alone and 324 people had vax-alone. So among hospitalized people who definitely had Covid, 3.6 times as many were vaxxed.

And among people who were hospitalized for Covid-LIKE symptoms, 6.3 times as many were vaxxed-alone as had natural immunity alone.

To make good use of those numbers, we would need an estimate of the prevalence in the general population of natural-immunity-alone vs vax-alone. Had the authors attempted to collect that info, they would have an interesting study. They did not.

As the CDC paper admits, 

"These findings differ from those of a retrospective records-based cohort study in Israel, which did not find higher protection for vaccinated adults compared with those with previous infection."

They're guilty of using weasel-words there, which, on top of the crazy methodology, makes one wonder about their objectivity.

Technically, yes, the Israeli study "did not find higher protection for vaccinated adults" as they say -- but it would be much more accurate to say: "The Israeli study found about 13 times LESS protection for vaccinated-only adults, due to waning immunity after several months."

See here for more on the Israeli study, and others that touch on the issue: https://maximumtruth.substack.com/p/deep-dive-should-naturally-immune

Thanks to Patrick Rusk in the comments for first noting the basic issue here. 
Thanks also to Philip in the comments for noting yet an additional study finding natural immunity is much better and lasts over a year: https://academic.oup.com/cid/advance-article/doi/10.1093/cid/ciab999/6448857

3. For instance, you could throw out the clinical trial due to its small sample size. Then all the remaining studies have the problem of not being able to randomize behavior, which means their results could also occur even if the vaccine did not help you, merely if those who got the vaccine also engage in less Covid-risky behavior. In such a case, the behavioral difference would create “spurious correlation”. However, it’s not even obvious which direction behavioral differences would move things in. Vaccinated people might tend to be more cautious types of people. Yet, some might also feel more free to engage in risky activities thanks to vaccines; also, unvaccinated people are not allowed to engage in risky indoor activities in many places.

4. The two relevant months for that study are people who got vaccines in Jan and Feb, which now have a 16% and 44% effectiveness in Israel, respectively. About an equal number so subjects are from each month, so we can take the average of 30%.

5. Vaccine non-effectiveness = 1 - .3 = .7 = 70%

Natural immunity non-effectiveness = 70% / 13.06 = 5.35 %

Therefore, natural immunity effectiveness = 1 - .0535 = 94.65%

6. Let’s take the midpoint at 42.8.

Starting with the higher end. 87% efficacy. So 13% inefficacy. We need to erase (1 - 42.8%) of that. So lose .13 * .572 = 7.44%. So now inefficacy is 13%-7.44% = 5.66%. So efficacy is 1 - .0566 = 94.33%.

For the other end, same deal: 27.4% inefficacy… lose .274 * .572 = 15.7%. So now inefficacy is 27.4%-15.7% = 11.7%. Efficacy is then 88.3%.

7. Lower bound: .33 * 13 = 4.3% … upper bound: .33 * 27.4% = 9%

8. Lower: .33 * .057 = 1.9% Upper: .33 * .117 = 3.9%

9. Here’s Pfizer’s exact data on this:

“BNT162b2 recipients with evidence of prior infection reported systemic events more often post-dose 1, and those without evidence reported systemic events more often post-dose 2. For example, 12% of recipients with evidence of prior SARS-CoV-2 infection and 3% of those without reported fever post-dose1; 8% of those with evidence of prior infection and 15% of those without reported fever post-dose 2.”

Moderna provides raw data (table S6) that has equivalent numbers. For their vax it would be:

9% of already-had-Covid people got fever after 1st dose, compared to 0.5% who never had Covid.… 13.5% of already-had-Covid people got a fever after the 2nd dose, compared to 15.7% who never had Covid.

Hmm. The first and second dose chances are somehow flipped, for fever… but total probability remains about the same. And for “systemic events” as a whole Moderna is not “flipped”; 1st dose is worse for naturally-immune people and 2nd dose is worse for others.