For all my complaints about Substack, I was overjoyed to see Scott’s new post today.

Among many other things, he writes:

As I was trying to figure out how this was going to work financially, Substack convinced me that I could make decent money here.

I don’t know exactly what Scott’s calculus was, but it sounds like Substack’s monetization was part of it. If so, we owe them a huge debt of gratitude.

Having said that, it sucks that Substack enforces stylistic homogeneity. It sucks to see Slate Star Codex get sucked into the uniform aesthetic blob.

While the crypto people get to work on true decentralization, end-users already have tremendous control over at least one aspect of their online experience: CSS.

So I installed a Chrome Extension that makes editing CSS easy, copied over some styles from an archive.org page, and tada:

You don’t need to know anything about CSS to use these styles. Just follow a few steps:

• Install the Stylebot Chrome extension
• Navigate to https://astralcodexten.substack.com/
• Click the Stylebot icon in the Chrome bar, and click Open Stylebot
• Click Code in the bottom right
• Paste the following styles
• If you use Firefox, see this comment

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They also work on the main page:

As well as the comments section:

Of course, these won’t work in your email client, you have to actually be on the domain. And if Scott moves over to a custom domain, you’ll have to follow the steps again there.

Thanks to this comment on Hacker News for inspiring the idea.

–––

Edit 01/22: An earlier version of this post recommended more Chrome extensions I enjoy. I’ve since been told that one of them recently became malware. Sorry about that.

Warning: Speculative armchair epidemiology. All emphasis mine.
See also Youyang Gu’s projection.

Summary: In an article for Stat, Dr. Zach Nayer misrepresents research, makes indefensibly flawed assumptions, and fumbles basic arithmetic. Per CDC, actual US Covid cases are 4.6x higher than reported, and currently around 2.4x higher. Using improved parameters, our toy model finds that herd immunity may occur in less than 4 months, although neither estimate should be taken too seriously. It all depends on the transmissibility of the new strain, as well as our ability to ramp up vaccine production, distribution and acceptance.

1) Dr. Nayer Misrepresents the Evidence on Monthly Infection Rates

Last month, Dr. Zach Nayer [1] at Stat published an estimate of time to herd immunity, suggesting that without vaccines it may take as long as 55 months.

The model itself is straightforward. Assume we need to hit 75% immunity, then figure out when we’ll get there based on existing prevalence and monthly infection rate:

Unfortunately, Nayer’s parameters are totally off. Citing a study which found antibody prevalence of 9.3%, Nayer writes:

In late September, a Stanford study estimated that 9.3% of Americans have antibodies against SARS-CoV-2… If the base prevalence at the end of September — eight months from the onset of the epidemic in the United States on January 21, 2020 — was 9.3%, the coronavirus has an infection rate of approximately 1.2% of the population per month.

But take a closer look. Although the study was published in September, it was based on data collected in July. As the authors make explicit:

Our goal was to provide a nationwide estimate of exposure to SARS-CoV-2 during the first wave of COVID-19 in the USA, up to July, 2020

Instead of dividing 9.3% by an eight month range, Nayer should have used the 6 months from January through July. This yields an estimated monthly infection rate of 1.6% rather than 1.2%.

To his credit, Nayer attempts to confirm this result against another source of data, but fumbles the arithmetic. He writes:

one study [estimates] 52.9 million infections in the U.S. from February 27 to September 30, or an infection rate of 1.3% per month.

52.9 million infections is 16% of the US population. Over a 7 month time period, that’s a monthly infection rate of 2.3% per month, nearly double Nayer’s result.

Of course, the biggest problem with Nayer’s parameters is not even that he’s misinterpreted historical studies, it’s that he naively projects them into the future.

Nayer’s prediction isn’t based on linear growth or exponential growth, it’s based on 0 growth. He assumes that historical cases will be a good proxy for future cases, including the February base rate of 17 total confirmed monthly cases, and then uncritically takes this base rate as a future projection.

2) What is the Actual Monthly Infection Rate?

Rather than start in January, we can consider the monthly infection rate for December, the month Nayer’s article was published. That month, cumulative confirmed cases rose from 13.8 million, up to 20 million, for 6.2 million new cases, or a monthly infection rate of 1.9%.

But remember, confirmed cases are not a good proxy for actual infections. Nayer’s cited research reported 9.3% antibody prevalence in July, equivalent to 31 million total cases. Meanwhile, only 4.56 million cases had actually been confirmed by July 31st, suggesting a confirmed-to-actual multiple of 6.8x. Using this multiple, December’s 6.2 million confirmed cases represent 42.16 million actual cases, for a 12.8% monthly infection rate.

But again, that data is from July, and testing may have improved since such that a greater number of actual cases are correctly reported.

In late November, CDC researchers set out to estimate cumulative incidence by correcting for undercounting. They report 52.9 million total infections through the end of September, even though only " 6.9 million laboratory-confirmed cases of domestically acquired infections were detected and reported". That implies a multiple of 7.67x, or as the authors write:

This indicates that 1 in 7.7, or 13% of total infections were identified and reported… Our preliminary estimates indicate approximately 1 in 8, or 13%, of total SARS-CoV-2 infections were recognized and reported through the end of September

If this multiple held true in December, it would imply 47.7 million new infections, or 14.5% of the population.

Most recently, the CDC reports 83.1 million total infections through December. Since there were 20 million confirmed cases, that’s a multiple of 4.2x, and an actual monthly infection rate for December of 7.8%. [2] They also report a 4.6x multiple for total COVID–19 infections reported.

Having said that, if we were undercounting by 7.7x through September, and by 4.2x overall, that implies we were undercounting by less than 4.2x after September. With 52.9 million actual cumulative cases as of 9/30 and 83.1 as of 12/31, we can infer 30.2 million actual new cases in between. By comparison, confirmed cumulative cases rose from 7.27 million to 20.03 million in the same period, for 12.76 million confirmed new cases. Using this estimate, the confirmed-to-actual multiple since September is 2.4x.

Here’s a table of monthly infection rates, depending on how you measure it:

(Note that “source” does not indicate that the literal claim about monthly infection rate was made, merely that it’s the source of the relevant data used for the estimate.)

Of these, I think 4.6% is the best estimate, though note that there is a lot of uncertainty as to which multiple applies best for December, as well as underlying uncertainty in the original studies. [3]

In any case, Nayer’s 1.3% estimate was substantially off. It was the result of flawed arithmetic, a misreading of his cited study, and the incredibly naive assumption that the January - July average would project into the future with no growth.

3) Conclusion: How Long to Herd Immunity?

Using the CDC’s estimate of 25% base prevalence, a monthly infection rate of 4.6% and Nayer’s original model, we’ll achieve 70% immunity in 8 months.

Incorporating further information about vaccinations, antibody loss and a more pessimistic 80% threshold, my best guess is herd immunity by July 3rd. You can find detailed explanations for these parameters in the appendix.

You should not interpret these estimate too seriously.

Here’s an abbreviated table of results based on vaccine acceleration rate (how many more vaccinations today than yesterday), and herd immunity threshold:

Edit: After talking to Alvaro again, I am less confident about antibody loss. See footnote 6 for a revised table.

I hope this is of interest, but do not let the table of results fool you into thinking this is a rigorous model with well tested assumptions. It assumes, in decreasing order of certainty:

• Vaccines last several years
• Antibodies last 8 months [6]
• One administered dose is “worth” 50% as much as a full infection
• There is a 2.4x multiple between December’s confirmed cases and actual infections
• No one who already has antibodies receives a vaccine
• We administer 50,000 more vaccines each day than the day before [7]
• Confirmed cases remain at 200,000 / day

In particular, the last two are totally up in the air.

There is a new strain, soon to be a new administration, and we can still do dramatically better than we have done so far. Predictions are helpful, but the important thing is to actually create the future we want.

Even stupid models can be useful. In this case, I hope the findings illustrate how sensitive our timeline is to an accelerated vaccination schedule, and highlight the urgency of ramping up distribution.

Sources

Original Article
Models in Google Sheets
Data from Our World in Data on cases and vaccines
Multiples:

• 6.8x: Anand et al.
• 7.7x: Reese et al.
• 4.6x: CDC
• 4.2x: CDC, computed based on 83 million actual vs 20 confirmed
• 2.4x: Computed, “With 52.9 million actual cumulative cases as of 9/30 and 83.1 as of 12/31, we can infer 30.2 million actual new cases in between. By comparison, confirmed cumulative cases rose from 7.27 million to 20.03 million in the same period, for 12.76 million confirmed new cases. Using this estimate, the confirmed-to-actual multiple since September is 2.4x.” The 52.9 is from Reese et al, 83.1 from CDC. Confirmed cases from Our World in Data.

Appendix: Details on Parameter Values and Questionable Assumptions

So far, out model has relied on a number of untenable assumptions:

1. Cases will remain at December levels
2. Antibodies last indefinitely
3. There are no vaccinations

Forecasting cases
Cumulative cases have been rising exponentially at a fairly consistent rate since April, so it might feel easy to project into the future.

Having said that, I am not very confident that the trend will hold. Given that we are ramping up vaccine distribution, facing a more transmisible strain, and launching a new administration, there is much more uncertainty to come. [4]

I’ll continue to use December’s estimated rate of 4.6%, and accept that I am making the same mistake as Nayer in assuming no growth, with the hope that I am at least doing so with better reason. Let this be an additional warning that this model is purely for illustrative purposes, and should not be taken too literally.

Antibodies
With regards to antibodies, there appears to be some ongoing controversy. A recent study from Science Immunology found “infection generates long-lasting B cell memory up to 8 months post-infection”; however, another second study suggests it might be shorter. Discussion of the conflict here.

In 8 months, we will start to see more and more re-infections as time goes on. There were 1.5 million confirmed cases 8 months ago, which is 11.6 million using the 7.7x multiple. It is possible all of their antibodies have now “expired”.

If we have to wait another 6.2 months, everyone infected until November 25th could lose their antibodies as well. That’s 12.9 million confirmed cases, or 59.3 million actual cases using the CDC’s 4.6x multiple.

As a first approximation, that’s another 5 month delay, but note that it cascades. As we wait to “make up” for the 59.3 million lost antibodies, more and more people’s antibodies will “expire”.

At a monthly infection rate of 4.6% and 8 month “shelf-life” for antibodies", we will never be able to hit more than 36.8% immunity at any time. Under this model, we never achieve herd immunity at current infection rates, even for conservative estimates.

In absolute numbers, 70% herd immunity would mean 231 million people with antibodies simultaneously. If antibodies last 8 months, that means we would need to hit 29 million cases per month, and sustain that continuously for 8 months. That’s all assuming that everything immediately clears up on the day we achieve herd immunity.

Given out current growth rate, and the increased transmissibility of a new strain, those numbers might be more achievable than they sound. Our recent high of 0.25 million cases in a single day (7-day rolling average) extrapolates to 7.6 million cases per month. With the 2.4x multiple, that’s 18.2 million cases.

Although I say “achievable”, this would not actually be a good thing. We would defeat the virus, but only through immense human sacrifice.

Vaccines
Okay, so it’s looking quite bad, can vaccines save us? You may have heard that vaccines are 90% or 95% effective, but that’s for preventing symptoms, not preventing transmission through asymptomatic infection.

A Moderna report to the FDA writes:

Amongst baseline negative participants, 14 in the vaccine group and 38 in the placebo group had evidence of SARS-CoV-2 infection at the second dose without evidence of COVID-19 symptoms. There were approximately 2/3 fewer swabs that were positive in the vaccine group as compared to the placebo group at the pre-dose 2 timepoint, suggesting that some asymptomatic infections start to be prevented after the first dose.

More recently, Tyler Cowen cites this article claiming that Pfizer vaccine is very effective in preventing transmission. The author writes “Data from 102 subjects shows 98% of them developed significant presence of antibodies; survey’s editor says participants most likely won’t spread the disease further” I am not sure what “most likely” means, but I’ll take it at face value.

Okay, so we have data on sterilizing immunity and vaccine administration, the problem is we don’t know how much of the latter is first vs. second doses. I also don’t know if being “66% immune” is worth 66% as much as full immunity. So a few simplifying assumptions:

• Each vaccine dose is “worth” 50% of full immunity
• No one who already has antibodies receives a vaccination
• We administer 50,000 more vaccines each day than the day before [5]

Using this model (available here), I estimate 70% immunity on April 2nd, and 90% immunity on April 24th.

With sufficiently high vaccination, it turns out lost antibodies are just not that big a deal. 8 months before April 24th was August 24th, at which point we had 5.73 million confirmed cases. Using the CDC’s 7.7 multiple, that’s 44.1 million actual.

But even if 27 million people lose their antibodies, our model has vaccinations at nearly 6 million / day by April 24th, so the delay isn’t that costly. Incorporating antibody loss, we only get pushed back to April 17th for 70% immunity, and May 6th for 90%.

There is also a cascading loss of antibodies between April 24th and May 6th, but this only pushes out estimates by another day or so.

What if 50,000 more vaccines per day is too optimistic? Alvaro mentions this Metaculus estimate giving 82.5 million by May 13th. Note that the 82.5 million refers not to administered doses, but to people who have completed both vaccinations, so this is 165 million doses total. That’s consistent with around 10,000 more vaccines per day, rather than the 50,000 I suggest.

Frequently Asked Questions

Why do you care? Stat isn’t an academic publication and it’s not peer reviewed.
No, but they are widely acclaimed, and often cited on Marginal Revolution. Until now, I would have felt confident taking their word at face value.

How poorly does this reflect on Stat?
To Stat’s credit, Dr. Nayer is not a regular contributor. His forecast was also not presented as a serious prediction, but was mostly intended to illustrate the importance of vaccines. Even there, it is bad that he made these basic errors, and it is bad that Stat did not fact check his writing.

Anyone can make mistakes. If you’re emboldened by my findings, you should go and run checks against more articles and try to find additional errors. Perhaps this is a one-off mistake, or perhaps there is a more systematic problem.

Why do you use different multiples at different points?
The CDC estimates a 4.6x multiple overall, but previously reported a 7.7x multiple for data up to September. Based on those numbers, I inferred a 2.4x multiple for data after September.

In section 4, I use a 7.7x multiple for cases before September to estimate antibody loss. I also use a but a 2.4x multiple for December’s cases which I’m using as our monthly infection rate. I also use the overall 4.6x multiple in one paragraph referring to data across a broad range of time:

If we have to wait another 6.2 months, everyone infected until November 25th could lose their antibodies as well. That’s 12.9 million confirmed, or 59.3 million actual using the CDC’s 4.6x multiple.

Okay, but really, when can I go outside?
I have no idea. If you put a gun to my head, I would say cases rise more than expected, and vaccinations go worse than expected, but I don’t know how those factors balance out. Maybe early summer, but it is still in our collective power to do better.

This isn’t a question, I just need a reason to feel optimistic.
I have been using a flat rate of infections, but they have been growing quite rapidly historically. If this remains true, the timeline would be greatly accelerated. A new strain might increase infections as well. That’s all bad news for America, but if you’re a cautious introvert taking appropriate precautions, it might be good news for you.

There is also hope on the vaccine side. Biden claims the Trump administration is to blame for distribution delays. I don’t know if this is true, but it could be, and it could mean improved distribution starting today! So far we have seen vaccines administered per day increase rapidly, but there may be a 2nd degree acceleration as well (i.e. the daily increase is itself increasing).

Also note that if you live in a hot spot, your region may achieve herd immunity before the nation as a whole.

Footnotes

[1] I am not an epidemiologist, but for the record, neither is he. As per his bio on StatNews: “Zach Nayer is a transitional year resident physician at Riverside Regional Medical Center in Newport News, Va., and an incoming ophthalmology resident at Harkness Eye Institute at Columbia University in New York City.”

[2] 4.2 is the multiple I get by dividing 83.1 million by 20 million reported cases, but the CDC states a multiple of 4.6 for “total COVID–19 infections were reported”. I don’t know how to explain the discrepancy.

[3] The CDC’s 95% UI for “total COVID–19 infections were reported” is a multiple of 4.0 – 5.4. Anand et al. report 9.3% with a 95% CI of 8.8%–9.9%. Reese et al. does not provide a CI for the 7.7x, but gives an related 7.1x multiple a 95% UI of 5.8-9.0.

[4] If you’re curious, you can look at Zvi’s toy models.

[5] This is really just guesswork. 50,000 is based on the rate of increase from January 5th to January 15th. If you started counting 1/1 you would get 35,000, and if you started 12/21 you would get 30,000. Using 10,000 gets us consistent with the Metaculus estimate.

[6] I expressed confidence after seeing “8 months” cited in multiple reports, but this may be limited by the data we have available. It seems the studies may actually be saying “at least 8 months”. From Dan et al.:

Overall, at 5 to 8 months PSO, almost all individuals were positive for SARS-CoV-2 Spike and RBD IgG… Notably, memory B cells specific for the Spike protein or RBD were detected in almost all COVID-19 cases, with no apparent half-life at 5 to 8 months post-infection… These data suggest that T cell memory might reach a more stable plateau, or slower decay phase, beyond the first 8 months post-infection.

Thanks to Alvaro for pointing this out. Here’s a revised table of results, removing antibody loss considerations from the model:

[7] I do worry that there’s some kind of logistical maximum rate of vaccinations, and it is not realistic to think we could ever be at 6 million / day. You may have heard that NYC alone did 400,000 vaccines / day in 1947, but that was a very different problem. Note also that this depends on vaccines actually being accepted! As I wrote in the appendix here, trust is still low, though it depends on who you ask, and may increase as more people get the vaccine.

This is a part of a series explaining the background, stakes and future of Progress Studies as I understand it. The previous post was A Question in Search of a Discipline. Fair warning: This post is not exactly my beliefs, but it is an earnest attempt to summarize the context of an ideological movement.

In the last year, bloggers have mastered the art of the post-covid rant [1]:

• The elites have failed us
• We need new institutions
• This is a serious matter of life and death

Though it post-dates the coining of the term, this writing is fundamental to my understanding of Progress Studies. Until 2020, the easy rebuttal “why isn’t this just economic history” still had force. Today, it feels irrelevant. Whatever failed us in 2020 will fail us again tomorrow.

Collectively, these posts walk us through the last 12 months, viewed through the lens of crisis management.

As Milton Friedman put it, the promise of liberal capitalism is to put “freedom before equality”, and still “get a high degree of both”. And yet, throughout Covid, we’ve had neither liberty nor prosperity. Instead, liberalism has resulted in twin failures:

• Authoritarian lockdowns and coercive quarantines dramatically outperformed voluntary social distancing. [2]
• Our leading institutions failed, first to take Covid seriously, then to promote the use of masks, then to enable distribution of the vaccine. In fact, they worked actively against these causes. [3]

Perhaps worst of all, the US did not even perform well with regards to individual liberties. Though we were able to avoid truly coercive quarantines, we did deploy numerous lockdowns, shutdowns and curfews. And yet, as our Covid cases continue to rise, it appears that we’ve gotten the worst of both worlds.

These points present a serious crisis for the US. More broadly, they threaten the continued dominance of liberalism as our default political ideology.

As in all crises, these weaknesses have not been a discovery, so much as as the revelation of open secrets. In 1992, Fukuyama’s The End of History claimed:

with the ascendancy of Western liberal democracy… humanity has reached “not just … the passing of a particular period of post-war history, but the end of history as such: That is, the end-point of mankind’s ideological evolution and the universalization of Western liberal democracy as the final form of human government.” [emphasis mine]

Of course, that is not what happened.

Since 1992, China’s (reported) GDP has grown 35x, from 0.4 trillion, up to 14 trillion today. During this same period, the US grew less than tenth as much (6.5 trillion to 21 trillion). China is now within spitting distance [4], yet rather than confront our impending slip into second place, we seem to be in denial. From Thiel:

I do think it’s interesting that the questions about China are being asked less often in the US today than they were a decade ago. In 2005, it was a very widespread question, in what year will China overtake the US? A decade later, it’s reasonable to think that it’s a decade closer to when this will happen. It’s a much less commonly asked question.

Meanwhile, the US has undertaken what Ben Thompson’s post calls “China-lite without any of the upside”. We won’t take authoritarian action to prevent a pandemic, but we will censor your speech [5]. It is not a coincidence that cultural limitations on free speech co-occur with broader institutional failures. If we were not so deeply in denial, we could at least properly acknowledge and take action against the latter.

Instead, we’ve gone through years of cancel culture by mob, now enshrined by our largest media companies as opaque, unilateral deplatforming. You could probably justify the coordinated ban of the US President, it is not so easy to justify Youtube’s ban on content that contradicts the WHO.

On one hand, the WHO is still ostensibly the world’s leading health organization. On the other hand, their highlights over the last 12 months include leading the charge against face masks, refusing to acknowledge the efficacy of Taiwan’s success, refusing to acknowledge Taiwan’s existence, and issuing the now regrettable claim:

"DON’T - talk about people “transmitting COVID-19” “infecting others” or “spreading the virus” as it implies intentional transmission & assigns blame [6]

Which alone might not sound so bad, had the Director-General not doubled down with:

The stigma, to be honest, is more dangerous than the virus itself. And let’s really underline that. Stigma is the most dangerous enemy. [emphasis mine]

Viewed in this light, our institutional failures and culture wars are intertwined. While the US was busy arguing about whether to vaccinate by age or occupation and how seriously to weigh racial equity, Israel went ahead and vaccinated 7 times as many people.

Note that this goes both ways! If the US were capable of vaccinating that many people in the first place, we would not have felt the need to waste time fighting for crumbs.

This all ends up presenting a serious ideological challenge, not just to our current crop of leaders, but to the institutions that put them there. As Alvaro writes:

if Carlsen is fake that also implicates every player who has played against him, every tournament organizer, and so on. The entire hierarchy comes into question. Even worse, imagine if it was revealed that Carlsen was a fake, but he still continued to be ranked #1 afterwards. So when I observe extreme credential-competence disparities in science or government bureaucracies, I begin to suspect the entire system.

How deep does the rot go? Is the problem the Director-General of the WHO? The entire organization? The liberal international order that legitimized them?

Progress Studies aims to find out, and cannot do so by relying on existing methods. Though its lack of established disciplinary base is a weakness, it is also a necessity.

In the next posts, I’ll look into what’s required to build a discipline from scratch, what we’ve tried so far, and where we ought to go next.

[1] Most recent in the series is Ben Thompson’s New Defaults. For the best of this genre, see Mark Lutter’s COVID Radicalized Me, Alvaro’s Are Experts Real? and Tanner Greer’s On Cultures that Build.

[2] China’s authoritarian lockdowns worked miraculously, even thought it was the epicenter of the pandemic and didn’t benefit from advance warning. The only sizable countries to perform similarly are either islands, South Korea (effectively an island), or Singapore (tiny city-state), both of which used coercive lockdowns.

[3] Failures on mask usage were not merely a matter of prioritizing supply for healthcare workers. US Surgeon General “STOP BUYING MASKS! They are NOT effective in preventing general public from catching #Coronavirus” and WHO: “There is no specific evidence to suggest that the wearing of masks by the mass population has any potential benefit. In fact, there’s some evidence to suggest the opposite in the misuse of wearing a mask properly or fitting it properly”. I am not sure how badly and unnecessarily FDA delayed vaccine rollout, but it was not 0 days. More details here.

[4] If you look at those numbers and take solace in the fact that we’re still 50% larger, Covid has not yet instilled in you a proper appreciation for exponential growth.

[5] I understand that the former is up to the federal government, while the latter is a question for private actors. Like I said, these are not really my views, but I don’t disavow them either.

[6] Surfaced via Mark Lutter’s aforementioned post.