UPDATE: Wow, this got a lot of readers! Honestly, though, I wrote a response to common questions and comments about this essay and it is probably a better read.
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My spouse recently sent me a link to the article “Concerns with that Stanford study of coronavirus prevalence” by Andrew Gelman, a statistician at Columbia University. From reading this article, I got the impression that Gelman is a good mathematician. And he raises some legitimate concerns.
But I’ve noticed that many of the people criticizing the work coming out of the Ioannidis group – such as the study of how many people in Santa Clara county might have antibodies to Covid-19 – don’t seem to understand the biology underlying the numbers.
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First, some background: in case you haven’t noticed, most of the United States is operating under a half-assed lockdown. In theory, there are stay-at-home orders, but many people, such as grocery store clerks, janitors, health care workers, construction workers, restaurant chefs, delivery drivers, etc., are still going to work as normal. However, schools have been closed, and most people are trying to stand at least six feet away from strangers.
We’re doing this out of fear that Covid-19 is an extremely dangerous new viral disease. Our initial data suggested that as many as 10% of people infected with Covid-19 would die.
That’s terrifying! We would be looking at tens of millions of deaths in the United States alone! A virus like this will spread until a majority of people have immunity to it – a ballpark estimate is that 70% of the population needs immunity before the epidemic stops. And our early data suggested that one in ten would die.
My family was scared. We washed our hands compulsively. We changed into clean clothes as soon as we came into the house. The kids didn’t leave our home for a week. My spouse went to the grocery store and bought hundreds of dollars of canned beans and cleaning supplies.
And, to make matters worse, our president was on the news saying that Covid-19 was no big deal. His nonchalance made me freak out more. Our ass-hat-in-chief has been wrong about basically everything, in my opinion. His environmental policies are basically designed to make more people die. If he claimed we had nothing to worry about, then Covid-19 was probably more deadly than I expected.
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Five weeks have passed, and we now have much more data. It seems that Covid-19 is much less dangerous than we initially feared. For someone my age (37), Covid-19 is less dangerous than seasonal influenza.
Last year, seasonal influenza killed several thousand people between the ages of 18 and 49 in the United States – most likely 2,500 people, but perhaps as many as 5,800. People in this age demographic account for about 10% of total flu deaths in the United States, year after year.
Seasonal influenza also killed several hundred children last year – perhaps over a thousand.
There’s a vaccine against influenza, but most people don’t bother.
That’s shocking.
Seasonal influenza is more dangerous than Covid-19 for people between the ages of 18 and 49, but only 35% of them chose to be vaccinated in the most recently reported year (2018). And because the vaccination rate is so low, our society doesn’t have herd immunity. By choosing not to get the influenza vaccine, these people are endangering themselves and others.
Some people hope that the Covid-19 epidemic will end once a vaccine is released. I am extremely skeptical. The biggest problem, to my mind, isn’t that years might pass before there’s a vaccine. I just can’t imagine that a sufficient percentage of our population would choose to get a Covid-19 vaccine when most people’s personal risk is lower than their risk from influenza.
When I teach classes in jail, dudes often tell me about which vaccines they think are too dangerous for their kids to get. I launch into a tirade about how safe most vaccines are, and how deadly the diseases they prevent.
Seriously, get your kids vaccinated. You don’t want to watch your child die of measles.
And, seriously, dear reader – get a flu vaccine each year. Even if you’re too selfish to worry about the other people whom your mild case of influenza might kill, do it for yourself.
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We already know how dangerous seasonal influenza is. But what about Covid-19?
To answer that, we need data. And one set of data is unmistakable – many people have died. Hospitals around the world have experienced an influx of patients with a common set of symptoms. They struggle to breathe; their bodies weaken from oxygen deprivation; their lungs accumulate liquid; they die.
Many people have been put on ventilators, but that’s often the beginning of the end. Most people put on ventilators will die. Among patients over 70 years old, three quarters who are put on ventilators will die.
For each of these patients saved, three others are consigned to an agonizing death in the hospital, intubated among the flashing lights, the ceaseless blips and bleeps. At home, they’d die in a day; in the hospital, their deaths will take three weeks.
And the sheer quantity of deaths sounds scary – especially for people who don’t realize how many tens of thousands die from influenza in the United States each year.
Or, consider: cigarette smoking causes 480,000 deaths per year in the United States, including 41,000 people who die from second-hand smoke exposure. Those 41,000 aren’t even choosing to smoke! But cigarettes kill them anyway.
Indeed, when people die of Covid-19, it’s often because their lungs fail. Smoking is obviously a major risk factor for dying of Covid-19 – a significant portion of reported Covid-19 deaths could be considered cigarette deaths instead. Or as air pollution deaths – and yet, our current president is using this crisis as an opportunity to weaken EPA air quality regulations.
Air pollution is a huge problem for a lot of Black communities in the United States. Our racist housing policies have placed a lot of minority neighborhoods near heavily polluting factories. Now Covid-19 is turning what is already a lifelong struggle for breath into a death sentence.
I would enthusiastically support a shutdown motivated by the battle for clean air.
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So, Covid-19. We know how many people have died – already (CORRECTION AS OF APRIL 21) forty-two thousand in the United States.
But if we want to know how scary this virus is, we need to know how many people were infected. If that many people died after everyone in the country had it, then Covid-19 would be less dangerous than influenza. If that many people died after only a hundred thousand had been infected, then this would be terrifying, and far more dangerous than influenza.
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Initially, our data came from PCR testing.
These are good tests. Polymerase chain reaction is highly specific. If you want to amplify a certain genetic sequence, you can design short DNA primers that will bind only to that sequence. Put the whole mess in a thermocycler and you get a bunch of your target, as long as the gene is present in the test tube in the first place. If the gene isn’t there, you’ll get nothing.
PCR works great. Even our lovely but amnesiac lab tech never once screwed it up.
So, do the PCR test and you’ll know whether a certain gene is present in your test tube. Target a viral gene and you’ll know whether the virus is present in your test tube. Scoop out some nose glop from somebody to put into the test tube and you’ll know whether the virus is present in that nose glop.
The PCR test is a great test that measures whether someone is actively shedding virus. It answers, is there virus present in the nose glop?
This is not the same question as, has this person ever been infected with Covid-19?
It’s a similar question – most people infected with a coronavirus will have at least a brief period of viral shedding – but it’s a much more specific question. When a healthy person is infected with a coronavirus, the period of viral shedding can be as short as a single day.
A person can get infected with a coronavirus, and if you do the PCR test either before or after that single day, the PCR test will give a negative result. Nope, no viral RNA is in this nose glop!
And so we know that the PCR test will undercount the true number of infections.
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When we look at the age demographics for Covid-19 infections as measured by PCR test, the undercount becomes glaringly obvious.
Consider the PCR test data from the Diamond Princess cruise ship. To date, this is our most complete set of PCR data – everyone on board was tested multiple times. And from this data, it appears that very few children were exposed to the virus.
Friends, it is exceedingly unlikely that such a low percentage of children were exposed to this virus. Children are disgusting. I believe this is common knowledge. Parents of small children are pretty much always sick because children are so disgusting.
Seriously, my family has been doing the whole “social distancing” thing for over a month, and yet my nose is dripping while I type this.
Children are always touching everything, and then they rub their eyeballs or chew on their fingers. If you take them someplace, they grubble around on the floor. They pick up discarded tissues and ask, “What’s this?”
“That’s somebody’s gross kleenex, is what it is! Just, just drop it. I know it’s trash, I know we’re not supposed to leave trash on the ground, but just, just drop it, okay? Somebody will come throw it away later.”
The next day: “Dad, you said somebody would throw that kleenex away, but it’s still there!”
Bloody hell. Children are little monsters.
It seems fairly obvious that at least as high a percentage of children would be infected as any other age demographic.
But they’re not showing up from the PCR data. On the Diamond Princess cruise ship, the lockdown began on February 5th, but PCR testing didn’t begin until February 11th. Anyone who was infected but quickly recovered will be invisible to that PCR test. And even people who are actively shedding viral particles can feel totally well. People can get infected and recover without noticing a thing.
We see the same thing when we look at the PCR data from Italy. If we mistakenly assumed that the PCR data was measuring the number of infections, and not measuring the number of people who were given a PCR test while shedding viral particles, we’d conclude that elderly people went out and socialized widely, getting each other sick, and only occasionally infected their great-grandchildren at home.
Here in the United States, children are disgusting little monsters. I bet kids are disgusting in Italy, too. They’re disgusting all over the world.
A much more likely scenario is that children spread this virus at school. Many probably felt totally fine; some might’ve had a bad fever or the sniffles for a few days. But then they recovered.
When they got their great-grandparents sick – which can happen easily since so many Italian families live in multigenerational homes – elderly people began to die.
So we know that the PCR test is undercounting the true number of infections. Unless you’re testing every person, every day, regardless of whether or not they have symptoms, you’re going to undercount the number of infections.
In a moment, we can work through a way to get a more accurate count. But perhaps it’s worth mentioning that, for someone my age, Covid-19 would seem to be about as dangerous as influenza even if we assumed that the PCR data matched the true number of infections.
If you’re a healthy middle-aged or young person, you should not feel personally afraid.
That alone would not be an excuse to go out and start dancing in the street, though. Your actions might cause other people to die.
(NOTE & CORRECTION: After this post went up, my father recommended that I add something more about personal risk. No one has collected enough data on this yet, but he suspects that the next most important risk factor, after smoking and age, will be type 2 diabetes. And he reminded me that many people in their 30s & 40s in this country are diabetic or prediabetic and don’t even realize it yet. Everyone in this category probably has elevated risk of complications from Covid-19.)
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After you’ve been infected with a virus, your body will start making antibodies. These protect you from being infected again.
Have you read Shel Silverstein’s Missing Piece book? Antibodies work kind of like that. They have a particular shape, and so they’ll glom onto a virus only if that virus has outcroppings that match the antibody’s shape. Then your body sees the antibodies hanging out on a virus like a GPS tracker and proceeds to destroy the virus.
So to make an antibody test, you take some stuff that looks like the outcroppings on the virus and you put it on a chip. Wash somebody’s blood over it, and if that blood contains antibodies that have the right shape to glom onto the virus, they’ll stick to the chip. All your other antibodies, the ones that recognize different viruses, will float away.
An antibody test is going to be worse than a PCR test. It’s easier to get a false positive result – antibodies are made of proteins, and they can unfold if you treat them roughly, and then they’ll stick to anything. Then you’ll think that somebody has the right antibodies, but they don’t. That’s bad.
You have to be much more careful when you’re doing an antibody test. I wouldn’t have asked our lab tech to do them for me.
An antibody test is also going to have false negatives. A viral particle is a big honking thing, and there are lots of places on its surface where an antibody might bind. If your antibodies recognize some aspect of the virus that’s different from what the test manufacturers included on their chip, your antibodies will float away. Even though they’d protect you from the actual virus if you happened to be exposed to it.
If you’re a cautious person, though – and I consider myself to be pretty cautious – you’d much rather have an antibody test with a bunch of false negatives than false positives. If you’re actually immune to Covid-19 but keep being cautious, well, so what? You’re safe either way. But if you think you’re immune when you’re not, then you might get sick. That’s bad.
Because antibody tests are designed to give more false negatives than false positives, you should know that it’d be really foolish to use them to track an infection. Like, if you’re testing people to see who is safe to work as a delivery person today, use the PCR test! The antibody test has a bunch of false negatives, and there’s a time lag between the onset of infection and when your body will start making antibodies.
It can be dangerous to use antibody tests to address the wrong questions.
If you use the antibody test on a bunch of people, though, you can tell how many were infected. And that’s useful information, too.
In the town of Robbio in Italy (pop. 6,000), the PCR test showed that only 23 people had been infected with Covid-19. But then the mayor implored everyone to get an antibody test, and 10% of people had actually been infected with – and had recovered from – Covid-19. Most of them couldn’t even recall having been sick.
The PCR test measured 23 cases. The antibody test suggested there’d been at least 600. And antibody tests, by design, will generally have a bunch of false negatives. When a team at Stanford assessed the antibody tests manufactured by Premier Biotech in Minneapolis, they found that for every 3 people who’d been infected with Covid-19, the tests registered only 2 positives.
I don’t know who made the tests used in Robbio – maybe they were a little better, maybe they were a little worse. Based on my experience, I wouldn’t be so surprised if the true infection rate with Covid-19 in that town was really just 10% – nor would I be surprised to hear that the chips had a high false-negative rate and that the infection rate was 20% or more.
If you calculate the fatality rate of Covid-19 in Italy by assuming that the PCR tests caught every infection, you’d get a terrifying 10%.
If you instead assume that many other towns had a similar infection rate to Robbio, you’ll instead calculate that the fatality rate was well under one percent.
Italy has higher risk than the United States due to age demographics, smoking rates, and multigenerational households – and even in Italy, the fatality rate was probably well under one percent.
When researchers in Germany randomly chose people to take a Covid-19 PCR test (many of whom had no symptoms), they found that 2% of the population was actively shedding virus – a much higher number of cases than they would have found if they tested only sick people. And when they randomly chose people to take an antibody test, they found that 15% had already recovered from the infection (again, many of whom had never felt sick). According to these numbers – which are expected to be an undercount, due to false negatives and the time lag before antibody production – they calculated a case fatality rate of 0.37%.
That would be about three-fold more dangerous than seasonal influenza.
In the United States, our bungling president gutted the CDC, leaving us without the expertise needed to address Covid-19 (or myriad other problems that might arise). During the first few months of this epidemic, very few people managed to get a PCR test. That’s why our data from the PCR tests is likely to be a dramatic undercount – indeed, when we finally started producing accurate tests, the apparent growth in Covid-19 caseload superimposed with the growth in test availability.
In the absence of good PCR data, we have to rely on antibody data to track infections after the fact. Which is why a town in Colorado with zero reported infections, as measured by PCR, had sufficiently widespread exposure that 2% of the population had already recovered from Covid-19.
And it’s why the data from the Stanford Santa Clara county study is so unsurprising.
Yes, there were problems with the Stanford study’s data collection – they displayed advertisements to a random selection of people, but then a self-selected subset responded. The pool of respondents were enriched for white women, but Santa Clara’s outbreak probably began among Asian-Americans. And we all know that random sampling doesn’t always give you an accurate depiction of the population at large – after all, random polling predicted that a competent president would be elected in 2016.
Now look at us.
It’s also likely that people with a poor understanding of the biology could misinterpret the result of the Stanford study. They found that PCR tests had undercounted the infection rate in Santa Clara county, at the time of this study, by 85-fold.
It would be absurd to assume that you could simply multiply all PCR results by 85 to determine the true infection rate, but some people did. And then pointed out the absurdity of their own bad math.
In places where more people are being tested by PCR, and they’re being tested more often, the PCR results will be closer to the true infection rate. If you gave everyone in the United States a PCR test, and did it every day, then the PCR data would be exactly equal to the true infection rate.
If we had data like that from the beginning, we wouldn’t have been scared. We would’ve known the true case fatality rate early on, and, also, at-risk people could’ve been treated as soon as they got infected. We’d be able to save many more lives.
If access to health care were considered a basic right in the United States, we might’ve done something like this.
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In Italy, it seems like Covid-19 is three- or four-fold more dangerous than seasonal influenza. My guess is that Italy might have had about 50,000 deaths if they hadn’t enacted the lockdown.
In the United States, on a population level, Covid-19 is probably also more dangerous than seasonal influenza. But there’s a big difference in terms of the distribution of risk.
The New York Times is running a series with short biographies of people who’ve died of Covid-19. As of noon on April 17, about 10% of the people profiled were younger than 35.
10% is roughly the proportion of young people who die of seasonal influenza. But only 1% of Covid-19 deaths are people younger than 35. The news reports don’t always make clear how much the risk of Covid-19 is clustered in a small segment of the population.
This has serious implications for what we should do next. If we were dealing with a virus that was about three-fold more dangerous than seasonal influenza for everyone, we might just return to life as normal. (Indeed, we carried on as normal during the bad years when seasonal influenza killed 90,000 people instead of last year’s 30,000.)
Because the risk from Covid-19 is so concentrated, though, we can come up with a plan that will save a lot of lives.
Healthy people under retirement age should resume most parts of their lives as normal. Schools should re-open: for students, Covid-19 is much less dangerous than seasonal influenza. I think that people should still try to work from home when possible, because it’s the right thing to do to fight climate change.
At-risk people should continue to isolate themselves as much as possible.
This sounds crummy, but at-risk people would just continue to do the thing that everyone is doing currently. And the plan would save many lives because the epidemic would end in about 3 months, after the virus had spread to saturation among our nation’s low-risk cohort.
Indeed, when a team of researchers from Harvard’s School of Public Health modeled the Covid-19 epidemic, they found that social distancing was generally unhelpful. That’s what their data show, at least – but in their abstract, they instead recommend that we continue social distancing for the better part of two years.
Their data are easy enough to understand. In each of these graphs, they show a blue box for how long social distancing would last, and then four colored lines to represent how many infections we’d see if we did no social distancing (black), medium quality social distancing (red), good social distancing (blue), or excellent social distancing (green).
So, from top to bottom, you’re looking at the graphs of what happens if we do a month of social distancing … or two months … or three, or four … or forever.
And you can see the outcomes in the panels on the right-hand side. The black line shows what would happen if we did nothing. Infections rise fast, then level off after the virus has reached saturation. There are two important features of this graph – the final height that it reaches, which is the total number of severe cases (and so a good proxy for the number of deaths), and the slope of the line, which is how fast the severe cases appear. A steeper hill means many people getting sick at the same time, which means hospitals might be overwhelmed.
So, okay. Looking at their graphs, we see that social distancing saves lives … if we do it forever. If you never leave your house again, you won’t die of Covid-19.
But if social distancing ends, it doesn’t help. The slopes are nearly as steep as if we’d done nothing, and the final height – the total number of people who die – is higher.
(Often, one of their curves will have a gentler slope than the others — usually the good-but-not-excellent social distancing seems best. So you’d have to pray that you were doing a precisely mediocre job of not infecting strangers. Do it a little better or a little worse and you cause people to die. This isn’t an artifact — it’s based on the density of uninfected people when social distancing ends — but let’s just say “mathematical models are wonky” and leave it at that.)
In a subsequent figure, the Harvard team tried to model what might happen if we occasionally resumed our lives for a month or so at a time, but then had another shutdown. This is the only scenario in which their model predicts that social distancing would be helpful.
But, unfortunately, there’s a problem. Research done with other coronaviruses shows that immunity fades within a year. Because the Harvard model would cause the epidemic to last longer than a year, people would have time to lose their immunity and get infected again.
Even in the extreme case that we mostly stayed in our homes for the better part of two years, social distancing would case more deaths from Covid-19 than if we had done nothing.
That’s not even accounting for all the people who would die from a greater risk of domestic violence, hunger, drug addiction, suicide, and sedentary behavior during the shutdown.
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When our data was limited, the shutdown seemed reasonable. We wouldn’t be able to undo the damage we’d done by waiting.
Except, whoops, we waited anyway. We didn’t quarantine travelers in January. The shutdown didn’t begin March, when the epidemic was well underway in many places.
Now that we have more data, we should re-open schools, though. For most people, Covid-19 is no more dangerous than seasonal influenza. We already have enough data from antibody testing to be pretty confident about this, and even if we want to be extremely cautious, we should continue the shutdown for a matter of weeks while we conduct a few more antibody studies. Not months, and certainly not years.
At the same time, we need to do a better job of protecting at-risk people. This means providing health care for everyone. This means cleaning our air, staunching the pollution that plagues low-income neighborhoods. This might mean daily medical checkups and PCR tests for people who work closely with at-risk populations.
Our country will have to be different in the future, but mostly because we, as a people, have done such a shitty job of creating justice and liberty for all. We need to focus on addressing the inequities that we’ve let fester for generations. That’ll help far more than using a bandanna to cover up your smile.
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UPDATE: Wow, this got a lot of readers! Thanks if you made it this far. I’ve also written a response to common questions and comments about this essay.
Frank Brown Cloud 
