Evolutionary Just-So Stories About Viruses and Virulence

An evolutionary just-so story is a plausible sounding but unfalsifiable explanation for a trait or behavior of an organism. What follows will be one such.

The things that make you feel sick are a virus’s way of spreading to new bodies. A virus that multiplies inside you without causing any kind of effluvia will just sort of hang around until your immune system sees that something is up and snuffs it out. A virus that makes you sneeze, on the other hand, has a nice mechanism for jumping to the next body. Likewise for vomiting, diarrhea, sores, pustules, fever sweats, etc. Unfortunately, these things also make you really sick and can kill you if they’re bad enough. A virus that makes you over-produce mucus will make you sneeze, cough, wipe your nose and touch other surfaces, and so on. It might also give you a fatal pneumonia. A fever might make you sweat (do any viruses actually spread via sweat?), but too high a fever will kill you.

Viruses that kill their hosts quickly don’t do a very good job of multiplying. Even viruses that cause obvious symptoms of illness are bad at spreading, because they cause people to stay home and cause other people to keep their distance. This is particularly true if there is a deliberate effort to quarantine anyone with a specific set of symptoms. The virus that is best at spreading will find a sweet spot. “Don’t make my host so sick he’s bed-ridden or dead. Make him just sick enough that he smears his spittle on a few door-handles.”

Viruses mutate. Mutations will generally create variation in the virus' traits, including the severity of symptoms in its host. The mutations that make a virus less deadly will be better at spreading. Longer onset and lower severity of symptoms make for a more effectively spreading virus. If viral mutation is causing variation in the severity of symptoms, this will tend to make the virus less severe over time. (I don’t know if this generally takes place on the order of weeks or years or decades, but something like this happens with real viruses.) If you are a viral strain that gives people a few sniffles and the occasional sneeze, your hosts will be out and about spreading your offspring. Your “cousins” that leave people bed-ridden or kill their hosts will likely die off.

I recall a documentary about the introduction of the cane toad to Australia. It was introduced to control the population of cane beetles, another nasty pest. But it rapidly became an invasive species. It spread across the continent and is still spreading to this day. The interesting part of this story is that cane toads at the edge of its expanse tended to have longer legs than cane toads closer to the point of introduction (some sugar plantations north of Queensland). This makes sense. If cane toads are hopping around at random in search of habitat, the ones with the longest legs will have traveled the furthest. They will find other long-legged toads to mate with at the frontier and have long-legged offspring. The analogy here is that viruses with mild symptoms have “longer legs” than their more virulent strains.

Obviously I am hoping that something like this is happening with the coronavirus. I don’t know if that’s likely, or if it is how long it will take. It seems like the median case is mild or asymptomatic, and the reason it's so scary is that there is a small but non-trivial chance of a very bad outcome. The above story makes me skeptical that asymptomatic spread is a big deal. If you're not coughing or sneezing, the virus doesn't have as many avenues of escaping to the next body. (Unless it's like the infamously contagious measles, where an infected person can contaminate a room for hours just by breathing.)  It's still possible, just less likely. 

Valuing a Human Life

Some thoughtful commentators are trying to think seriously about the trade-offs between saving lives and all the other things we care about. Other less thoughtful commentators are demagoguing this issue, saying things like “You can’t put a price on a human life” or some other self-congratulatory nonsense. This is mostly with regard to the question of when the economy should “re-open” and how much illness and death are we willing to tolerate to get back to some semblance of a normal life. I want to tell this second group of commentators that they look childish. This is a really lame way to feel morally superior to your political opposites, and it doesn’t make you look good.

People place finite value on their own lives. We know this, because people don’t spend every last dollar of disposable income on safety. Also observe that people go out of the house for movies, plays, concerts, parties, and other reasons that are pure entertainment. Each venture outdoors entails a small chance of death, a car accident for example, but we deem the risk worth while. We even haul our beloved children along with us. We visit our elderly relatives during the peak of flu season without even thinking about it. We risk our own lives and those of our loved ones when the benefit exceeds the cost according to some arcane formula deep in our minds. The difference here is one of degree, not of principle. If it sounds cold and calculating to place a dollar value on a human life, recognize that we all implicitly do so all the time. It is hypocritical in the extreme to blast moral outrage at people who bring the topic into the light of day for an open discussion.

Economists have clever ways of computing the “statistical value of a human life.” They can figure out how much consumers are willing to pay, or forego paying, for a given safety feature on vehicles. If the safety feature costs X, and it has a probability p of saving your life, then, crudely, the statistical value of a human life is X/p. Similarly, if there are two approximately similar jobs, but one has a higher hazard of death, the difference in pay reflects the value that the workers place on their lives. If the pay differential, the “hazard pay”, is X and the difference in probability of death is p, then again the statistical value of a human life is X/p. Typically this comes out to about $10 million in the United States, although of course it depends on age, occupation and other demographics. In a portfolio sense, the auto consumers are willing to pay about $10 million per life saved, and the workers are willing to accept about $10 million in compensation for each on-the-job death (or input whatever figure you prefer for $10 million). 

If the government is going to use society’s resources and impose costs on us to save lives, it had damn well better be respecting our preferences. A government that tells us, “We’re going to spend $50 million per life saved” is declining to respect our true wishes, because that is way more than we're willing to pay as revealed by our own choices. A politician or government epidemiologist is of course free to idly wish we would make different choices. They are free to think we should make different trade-offs or to believe our actions are irrational. But they should not have a free hand to overrule us and make for us the choices that they think we should make. “I see you’re only willing to pay up to $50 for this safety feature, while the true cost is $100. Sorry, overruled. I’m going to make it mandatory anyway for all new vehicles.” Their role is to help us solve collective action problems and to realize our preferences as they are, not to change our preferences through social engineering and coercion.

I don’t know if various government imposed shut-downs are worth the cost. I do know that some commentators are making it impossible to have that conversation, and I wish they would stop their moral grand-standing. They are making it sound as though “the economy” is just the stock market or a big pile of money, categorically and infinitely less valuable than a human life. No. “The economy” is just a short-hand for “all the other things we care about and all the things we enjoy doing.” It's not mere crass materialism that we enjoy human contact.

I also want to push back against the overuse of the “precautionary principle”. There is no such thing as the precautionary principle when mistakes in all directions are costly. There is no safe harbor. You must confront the trade-offs with eyes wide open. I think some people are imagining that we can simply “buy” safety by spending mere dollars. There is some insurance broker into which we can just pump unlimited amounts of money and out of which comes safety and lengthened lives. No. To the extent that we use our resources to purchase other kinds of safety, we eventually hit a limit in which buying more insurance against the coronavirus means getting less overall safety. There are other potentially deadly effects, too. I dread the mental health effects of the lock-down. I am a well adjusted adult with a rewarding family life including small, delightful, loving children in the home, and even I am going a little stir crazy. Some people don’t have anyone right now. Some people have gone over a month with no human contact. Young, single people. Old divorced or widowed people. Some without even the companionship of a pet. There is a limit to how much isolation they will tolerate. (A Zoom call is not the same.) They might eventually decide it’s worth getting sick to see other human beings. The mental health consequences of unemployment are also looming large. We shouldn’t be making that decision for these vulnerable people. We shouldn’t even be telling them what they should want. I think there is a serious risk here that we exhaust everyone’s patience before the virus has truly gotten started. What if we’re using up all our ammo now, before a significant fraction of the population has immunity? Suppose there are no more levers to pull when the virus roars back? It does no good to claim that policy X or Y was done “out of an abundance of caution.” We need to take seriously the possibility that excessive caution makes people worse off and even causes more deaths.  

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Here is an excellent post by Bryan Caplan. He amusingly points out:

Economists are widely-seen as heartless.  Their use of the phrase “value of life” is often seen as damning confirmation of this heartlessness.  Nice people say, “You can’t put a value on a human life” and change the subject!
What’s striking, though, is that when you successfully cajole non-economists to put a dollar value on a human life, their numbers are vastly below the economic consensus.  Economists’ standard estimate is around $7,000,000.  Non-economists’ usually say under $1,000,000.

So what’s up, you heartless non-economists? Why do you put such a low value on human life? You might say, “I wasn’t asked, that’s not the answer I would have given.” But, c’mon. The $1 million answer comes from people basically similar to yourself, having the same visceral reaction to the question and using the same kind of rhetoric. But, sure, maybe you’re more sophisticated.

And because Bryan Caplan and Zach Weinersmith make such an excellent pairing, I find this SMBC appropriate right now.

Asymmetric Outrage Over Changing Prices

Isn’t it outrageous that gasoline prices are so [low] due to this recent pandemic? Greedy gas companies are charging [less] for gas just because demand has changed! They shouldn’t be changing their posted prices just because gas consumers are willing to pay [less] for a given quantity of gas.

If that sounds bizarre, now you know how I feel about the spittle-infused outrage spewed at so-called “price gougers.” Change the product from gasoline to toilet paper or hand sanitizer or face masks, and change the words in parentheses to “high” and “more”, and you get a perfect symmetry. You simply cannot have it both ways. If the decline in gas prices seems perfectly reasonable and banal, then the increase in prices for these other scarce goods makes just as much logical sense.

Like Alex Tabarrok says, prices are information wrapped in an incentive. When demand for a given product increases, the price should go up. The higher price discourages hording. (No one would be grabbing multiple mega-packs of toilet paper if you just charged a few extra bucks for each one.) It also encourages production. Supposing we need more disposable gowns and face masks, the suppliers need to see a higher market price before they’ll be willing to ramp up production. Manufacturers tend to optimize their cost structure for a given level of supply. They’ll use the most efficient factory and the most proficient workers and the cheapest available inputs. Expanding production implies using the second and third most efficient factories, hiring and training new workers, bidding more for existing inputs and using less efficient inputs, and so on. Naturally this will raise the price. That’s fine, assuming the scarce goods really are more valuable and more of them are needed.

We need to stop moralizing about prices. At the very least, we need to be consistent. If there’s nothing wrong with low gas prices, then there’s nothing wrong with high prices for face masks.

If someone could show me that the higher prices for, say, hand sanitizer or toilet paper were a significant portion of anyone’s household budget, I would backtrack slightly on this argument. (I would not end up endorsing anti “price-gouging” laws, but I’d have a little more sympathy for the people grousing about high prices.) But I don’t think that’s likely. Even at higher prices, I’m guessing that these scarce goods are a puny fraction of a household’s budget, even a low-income household.

Getting this right is deadly serious. Insisting on a bunch of new ventilators at the pre-crisis price means not getting any new ventilators. Moral outrage is not serving us well.

Cause of Death Misidentification is a Big Deal, But Probably Not for COVID-19

I've written on this topic a number of times regarding drug poisoning deaths, and I see it is re-emerging in light of the recent pandemic. Some people are claiming that reported COVID-19 deaths are exaggerated because they're simply coding anyone who had the virus at the time as a "COVID-19 death". It could be incidental but did not kill the person in a "but for" sense, like someone who happens to have a cold having a fatal heart-attack. Or it could be one of several contributing causes. Possibly someone in poor health whose remaining life expectancy was in months or weeks was finished off by the coronavirus. In a "but for" sense, the virus killed them, but it didn't really remove much time from their life. Thought of another way, it's just as valid to call it a "chronic lung condition death" or a "cancer death" or a "complications of immuno-suppressive drugs death." That is the claim, anyway. I don't know if this is a big deal for COVID-19. We can say that cause of death misattribution is generally a big deal, even if it's not a big deal in the specific case of COVID-19.

I think some people have been too quick to dismiss this as "not even a thing." To be sure, some have latched onto this as a conspiracy theory or a slam-dunk "debunking" of the epidemic. Maybe what I'm seeing is an over-correction by reasonable people of less reasonable people? I want to do my part with this post to tone down some of the snark and the smugness.

See this study, a retrospective study of 601 death certificates:

A total of 580 (93%) death certificates had a change in ICD-10 codes between the original and mock certificates, of which 348 (60%) had a change in the underlying cause-of-death code.

Also see this one, a study on the quality of the information contained on death certificates:

Of the 290 properly completed CODs, 141 (49%) contained disagreements: 73 (52%) on underlying CODs; 44 (31%) on immediate CODs; and 47 (33%) on other significant conditions (part II).

Both studies are very short and quite readable. Both of these studies were cited in a Cato paper by Jeff Miron, Overdosing on Regulation. (I was involved in the writing and editing of this paper.) Rather than implying poor information quality or sloppiness  on the part of medical examiners, I think they speak to how inherently difficult it is properly assign a cause of death in general. Specifically with respect to drug overdoses...

Witness France and Germany having a 3-fold difference in drug overdose deaths without any obvious explanation, other than France being more reluctant to classify a death as a drug overdose. (See the quote from Drug War Heresies.) Reporting bias is real.

Witness the comorbidities of drug overdose deaths. Chronic illnesses are often listed on the death certificate (~1/3 of the time or more). This seems to imply that whoever filled out the certificate thought that the condition contributed to the death. It's worth asking if some of these are drug poisonings at all.

Note the language in the medical textbook The Pathology of Drug Abuse by Stephen Karch. I excerpted it at length here and here. It feels like every other sentence is warning the reader to be skeptical about the true cause of death. An apparent drug overdose might not be one. Given that he's writing a medical textbook, he must think that this is a problem to be corrected, or at least that it is something that's easy to mishandle. Karch writes:

When a doctor “certifies” a cause of death, his certification is based upon his evaluation of the evidence available to him, but it is still just his opinion and does not set a precedent for similar cases.

Like I said, I don't know if misattribution is a big deal regarding COVID-19. If COVID-19 is everywhere, say 10% of the population having been infected, I would say we need to worry about the misattribution problem. If it's much less prevalent, then it's probably small enough to ignore. And keep in mind that errors can happen in two directions. Misattribution is just as likely to lead to under-counting as over-counting, especially given the lack of adequate tests for the virus.

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A quick back-of-the-envelop calculation. There are about 2.8 million deaths a year in the U.S.. There is some mild seasonality, but ignoring that let's divide by 12 and call it 233 thousand each month. So we should get about 466 thousand total deaths from all causes in March and April. Supposing 1% of the population has been infected, we should have gotten about 1% * 466 thousand = 4.66 thousand deaths in two months from people who happened to be infected with COVID-19. Compare this to the ~50 thousand deaths reported to date (with seven days left in the month of April), and it looks like over-counting is not a big deal. (I have been using this source for total deaths; if there's another I should be using instead, let me know.) If you think the true prevalence is more than 1%, say in the 5% to 10% range, then over-counting might be a really big deal. The amount of likely over-counting depends critically on how many people actually have had the virus. If it turns out that's a large fraction of the population, we have to start talking about how many of those people would have died anyway over the relevant time period. The above is only a very crude estimate, and perhaps we'll have finer-grained understanding of "excess deaths" in the coming weeks and months. If there are enough such excess deaths, it will rule out over-counting as a significant effect. (Maybe this can already be done for New York city and other hard-hit places?)

Some mechanics of the cause-of-death attribution process. [Edit. I do not know if COVID-19 death counts are coming from the process described below. I am describing the normal process of filling out and reporting death certificates. I suspect that there is some ad hoc reporting with the coronavirus numbers.]

A death certificate contains a section that looks like this.

The person filling it out is supposed to fill in a cause, or a sequence of causally related conditions, in Part I. The immediate or proximate cause is supposed to go at the top. The conditions or incidents that initiated the sequence go toward the bottom. So "auto accident" might go in Part I line b, while "blunt force trauma to the head" might go in Part I line a. Part II allows the examiner to mention contributing factors that aren't directly part of the sequence.

When the CDC intakes this death certificate, it assigns an underlying cause of death. The way it does so is elaborate and kind of cool. It actually parses the raw text of the certificate, converts these from free-form text to a finite set (thousands) of causes of death, each with an ICD-10 code, and puts all this into one big data file, marking which part of the death certificate each cause came from. I have made a ritual of pulling this data file once a year and analyzing it. Up to 20 contributing causes of death are listed on the CDC's death record for that individual (though it's rare to see more than 10 or so). There is then a sequence of rules for how to assign the underlying cause of death:

General Principle: Select the condition on the lowest line of Part I only if it could cause all the above conditions.
Rule #1: If General Principle does not apply, select the cause of the first-mentioned sequence.
Rule #2: If there is no sequence, select the first-mentioned condition.
Rule #3: If previous rules lead to a condition that is obviously caused by something else on the certificate, report that instead.
Other useful rules: Time intervals will always be obeyed, a linkage in part I will always be preferred over Part II, The most specific chain will always be chosen.

There are some arcane and hard-to-parse decision rules which attempt to automatically code the underlying cause of death. A very patient employee at the CDC once helped walk me through an example to arrive at the correct cause of death. But she also told me that these records  have to be checked by a human being. Apparently these rules leave a lot to interpretation, and there is room for error. (I believe the text parsing software is called MICAR or superMICAR, and the decision rules are called ACME and TRANSAX, if you want to look these up.) In other words, there are a lot of checks in the process, because misattribution is a big deal. It's easy to make mistakes when assigning a cause of death, just like it's easy to make mistakes when it's assigning a cause to anything.

Insurance Deductibles and Covid-19 Counts

I was thinking about the boring topic of insurance deductible pricing. The deductible is the part of the claim that the insured customer is responsible for. E.g. if you select a $1,000 deductible and you make a claim on $5,000 worth of damage to your house, you cover $1,000 and the insurance company covers $4,000. (Insurers like deductibles because they discourage small, frivolous claims. Insurance customers like them because they make the premiums more affordable. Win-win!)

We actuaries have to be careful about the “unseen claims.” If everyone has a $1,000 deductible, we don’t know how many claims there would have been between 0 and 1,000. Those would-be claims don’t enter our data sets. They are censored from our view, because the customers don’t bother to make them. (The term for these losses that don’t show up at all is “truncated”; “censored” is reserved for a policy limit, in which you know about the claim but don’t know how big it would have been if not for the limit.) But it’s okay, because we have an approach that mathematically “re-inserts” these claims. It’s an application of basic probability theory. We have to make some assumptions about the shape of the severity curve below the deductible. This takes the form of assuming the distribution type: is it gamma, log-normal, Pareto? But you have to do this if you want to offer, say, a $500 deductible or full coverage. You can’t just assume those unseen claims don’t exist. You make various assumptions about those would-be claims that never come to your attention, and mathematically they reenter your data set. Perhaps you test the sensitivity of the result to those assumptions, but you still have to adjust. 

I was very disappointed to realize that epidemiologists either don’t have these methods or don’t take them seriously. I still see people reporting the “case fatality rate”, or CFR, as if it’s a meaningful metric of the disease’s deadliness. It’s not. The CFR divides known deaths by known cases. A case only becomes known if it comes to the attention of healthcare workers. We disproportionately find out about severe cases that lead to an office visit, hospitalization, or death. The mild and (apparently common) asymptomatic cases are censored from our view and don’t enter the CFR’s denominator. (Unless we did extensive random testing, which we’re not yet doing.) I have seen some attempts to adjust the raw CFR downward, but still ending up with a fatality rate that’s way too high. I’m seeing that some epidemiologists are building in the assumption that 1% or 2% of people who get infected eventually die. I think this is way too pessimistic. It is more alarmist still to report the raw CFR.

Time will tell how big a deal this is. My reading of the Princess Diamond cruise ship and the data from Iceland (which has done extensive random testing) is that there is a broad distribution of disease severities, including lots of mild and even asymptomatic cases. The true mortality could be in the range of the seasonal flu, or it might be a few times higher. There is still a lot of uncertainty. Still, I think it’s just needlessly alarmist to exaggerate the true risk by taking raw data, with all it's well understood flaws, at face value. I can't tell if people actually find the high estimates of Covid-19's mortality to be credible, or if they're trying to achieve some kind of "consistent messaging" to get across to a public with a short attention span. If anyone is consciously taking this approach, I want to gently suggest that such deceptions are likely to backfire. The noble lie gets found out. Look at the backlash against the messaging about face masks being ineffective. "Don't buy them, because they're ineffective. Also, medical staff need them more than you." People will start to resent it if their public health bureaucracy is making value judgments and trade-offs for them and "juking the stats" to back into their desired policy recommendations.

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I know that Covid-19 could be worse than the flu even if it has a similar fatality rate. Maybe it's worse because a lot more people get it, or because the lingering damage to the lungs is worse than any lasting effects of a bad case of the flu. None of that justifies exaggerating the mortality risk.

Suppose insurance losses follow a distribution, a "density function", f(x). The density function tells you the relative likelihood of observing a claim at a given dollar value. The cumulative distribution function, called F(x), is the integral of f(x). F(x) is the probability of a claim being x or less.  To find the shape of f(x), you would gather a bunch of observed losses, x1, x2, x3, and so on. The likelihood of observing a loss at x1 is f(x1). Assuming the losses are independent, the likelihood of the observed set of losses is the product f(x1)*f(x2)*...*f(xn). You can use this likelihood function to estimate the parameters of your distribution and find out the shape of f(x).

With no deductible, f(x) just means "I observe a claim of x dollars." If there is a deductible, say $1,000, and the total cost of the damage is x (insurer's share plus the insured's $1,000 share), the observation enters the likelihood function as f(x) / [1 - F($1,000)]. Which is like saying, "I observe a claim of x dollars given that it's greater than $1,000 dollars."

Early-stage epidemiology could benefit from this kind of thinking. Stop thinking of the known case counts as "I observe a case of Covid-19." It is rather "I observe a case of Covid-19, given that it is above a severity threshold that brings a patient to the hospital." Granted there is uncertainty initially about the distribution of severities, some intelligent guesswork can convert "known cases" to a (possibly wide) range of true cases. 

Some Thoughts About Covid-19

I thought I'd share some of my thoughts on the pandemic. My overall outlook is optimistic. It seems to be far less fatal than early reports would have indicated.

Reported Mortality Rates Are Biased High

There are varying estimates of the deadliness of the virus. One that's almost certainly biased high is the "case fatality rate", the CFR. This is literally the number of confirmed cases divided by the number of confirmed deaths. (See this piece for a useful discussion of "case fatality rate" versus "infection fatality rate"; the latter is the true measure of deadliness of the disease.) This number can be alarmingly high. See the CFR by country here. A 12% CFR for Italy? Does this mean you have a 12% chance of dying if you catch the virus? No, of course not. It is only the most severe cases of illness that are typically brought to our attention. This is particularly true in the early stages of a pandemic. The denominator in the CFR is biased low. In my opinion, this bias is extreme and dramatically overstates the true mortality rate. Some irresponsible journalists have reported the CFR as if it's the true fatality rate for the virus, and some (in my opinion, equally irresponsible) public health officials have under-corrected this number and gotten a still-too-high number. What bothers me is that everyone knows that the number of official cases is an under-count, and I hear daily reminders of all the reasons why. How much grousing (very much justified grousing, I should say) do we hear about how there isn't adequate testing? How many complaints have your heard from frustrated local hospitals and public health officials that they can't test patients even when they have symptoms that match the profile of Covid-19? How many (possibly alarmist) stories have you seen about how quickly the virus spreads, how long it lives on surfaces, how long the incubation period is (during which you may be asymptomatic but still contagious), how "exponential growth" implies that the virus has already expanded beyond our ability to contain it? The CFR might be a useful benchmark at the onset of an outbreak, a basis for extrapolating to what the true mortality will eventually turn out to be. (The fatality rate per infected individuals is called the infection fatality rate, or IFR; see the link above.) But unless you test every single individual in the entire population with a reasonably reliable test (one with low rates of false positives and false negatives), we won't know about the mild or asymptomatic cases of the disease.

Like other viruses, and like almost any phenomenon we're interested in, the severity of illness follows some sort of distribution. There are mild cases, there are severe cases requiring hospitalization and ICU attention, there are permanent injuries and ongoing conditions following recovery, and there are deaths. Extrapolating from the CFR to get the IFR requires some assumptions about what that distribution looks like, but it seems clear that there are a lot of asymptomatic and mild cases of Covid-19. See John Ioannidis' discussion of the virus here.

The one situation where an entire, closed population was tested was the Diamond Princess cruise ship and its quarantine passengers. The case fatality rate there was 1.0%, but this was a largely elderly population, in which the death rate from Covid-19 is much higher.
 Projecting the Diamond Princess mortality rate onto the age structure of the U.S. population, the death rate among people infected with Covid-19 would be 0.125%. But since this estimate is based on extremely thin data — there were just seven deaths among the 700 infected passengers and crew — the real death rate could stretch from five times lower (0.025%) to five times higher (0.625%). It is also possible that some of the passengers who were infected might die later, and that tourists may have different frequencies of chronic diseases — a risk factor for worse outcomes with SARS-CoV-2 infection — than the general population. Adding these extra sources of uncertainty, reasonable estimates for the case fatality ratio in the general U.S. population vary from 0.05% to 1%.

The IFR of the seasonal flu is about 0.1%. So if we took the central estimate of 0.125% to be about right, Covid-19 is only slightly deadlier than the flu. I have read that there were ultimately 9 deaths from this population, so scale his numbers up by an appropriate factor to correct for this. (That would place the central estimate at about 0.16 rather than 0.125.) On the other hand, this puts some kind of limitation on claims that "asymptomatic people just haven't had a bad outcome yet". Based on the Diamond Princess experience, we can rule out that everyone who is infected eventually gets horrifically sick.

See also the data from Iceland, which has done some large-scale testing of its population (apparently not fully random testing, but the data is still useful). Jacob Sullum explains here:

The deCODE sample is self-selected, so it may not be nationally representative. But assuming the sample's infection rate applies to the general population, it means that something like 3,400 Icelanders already have been infected, implying a current CFR (including mild and asymptomatic cases) of around 0.1 percent, which would make COVID-19 in Iceland about as deadly as the seasonal flu. Even assuming that Iceland in a month has as many COVID-19 deaths, as a proportion of its population, as the United States does now, the CFR would still be remarkably low.

I hesitate to conclude definitively that the true fatality rate is close to 0.1% based on either the Diamond Princess or the Iceland experience. One is a small sample of people, the other is a small island whose experience may not be generalizable. Also, note the younger population of Iceland, which Sullum points out in his piece. Any crude mortality estimate must be age adjusted or, better yet, broken out by age groups to be meaningfully informative. Granting those caveats, we should take these data points seriously. Iceland's testing is much closer to a random sampling of the population than the (extremely) biased sampling that yields Covid-19 counts for various nations and states reporting. And the Diamond Princess is a little petri dish where we know 1) who was infected and 2) who has died, basically down to a person.

See also the example of Gangelt, Germany, which is getting a fatality rate of around 0.37% after doing extensive testing of the population. (Keep in mind that age distributions are a big deal because of the very steep age-mortality curve for Covid-19, as well as for everything else. Germany has an average age of 46 years, while Iceland has an average age of 36.5 years. It's hard to tell without detailed demographic data, but it's possible that the data from Gangelt is consistent with the data coming out of Iceland w.r.t. mortality rates.) It would be nice to see more of this done, say for an entire US state or large European country. If testing the entire population isn't feasible, then representative sampling would be extremely informative right now.

Comparisons to the Seasonal Flu

I have seen attempts to compare Covid-19 to the seasonal flu. I have also seen some of these comparisons met with apoplectic outrage or sneering sarcasm. I want to argue that comparisons to the flu are totally appropriate, even if it's to say something like "Covid-19's fatality rate is X times higher than the seasonal flu" or "Covid-19 is only slightly deadlier than a typical seasonal flu, but it's worse because so many more people get it." Or "It would be terrible if five times as many people got the seasonal flu, all within a compressed flu season, because our hospitals would be overrun." The seasonal flu is a useful baseline, because it's something we're all used to. It's something that kills tens of thousands of people a year, but we're inured to it because the risk is somewhat inevitable. It's inadequate to say we can't compare Covid-19 to the flu because it's different in some dimension. It's more helpful to point out in what ways it's different so we can think clearly about how we should respond. Hell, maybe this kind of reflection will lead us to treating the seasonal flu more seriously. Maybe our default rule is wrong and we just don't bother to think about it. That's the kind of thought we'd never get to explore if we reflexively shout down anyone who brings up the topic.

It's possible that the fatality rate of Covid-19 is much higher than the seasonal flu. (Note the confidence intervals given by Ioannidis above.) In fact, it is probably prudent at this point to act as if it is deadlier, say a true IFR of 0.3% or 0.5%. But there are limits on what's reasonable here. There is no "precautionary principle", no "safe" default rule, when mistakes in any direction are costly.

See this page by the CDC on recent flu seasons. The worst season in the past decade was 2017-2018, where about 61,000 people died of the flu. Every death is a tragedy, but it is worth reflecting on how we mostly accept this as a fact of life. People die of the flu. We don't shut down society because of a bad flu season. In fact, you probably don't even read a single news story about it. Did you know that 2017-2018 was a ten-year high for flu deaths? I hadn't.

Another thing I hadn't realized is this: a "bad" flu season isn't one where the disease itself is particularly deadly in terms of having a high IFR. A bad flu season is one where a lot more people get it. Spot-checking for a few years, it looks like almost all flu seasons have an IFR of around 0.1-0.2%. But in years where a lot more people get it, a lot more people die. (Exceptions are the Spanish flu and the 1957-58 flu season, where the IFR was exceptionally high.)

So maybe it's no deadlier on a per-infection basis, but a lot more people get it. The CDC link implies that a typical flu season sees ~30 million symptomatic cases. (Or ~45 million in 2017-2018; only ~9 million in the relatively mild 2011-2012 season.) Let's call it about 10% of the population. Maybe Covid-19 is so good at spreading that it infects 50% of the population in a single season. Is that "five times as bad?" I'm not sure what the right way to think about that is, but I don't recall anyone warning us all to be concerned about the 2017-2018 flu season because it was five times worse than the 2011-2012 season. A simple utilitarian response is, "Yes, it's five times as bad because there is five times as much illness." But a response that applies the existing default rule is something like, "No, this is a risk that we're all inured to and that we all find acceptable. It's like bemoaning that traffic fatalities increased because we're driving more."

I don't know how individuals should feel about this. "I'm five times as likely to get fatally ill this year, so I should worry five times as much" or "This hazard is below the threshold for risks that typically concern me, so I shouldn't worry too much." The knock-on effects of everyone getting sick at once is certainly worth our concern. But I'd like to see more flesh on this argument. How much can they really do for you if you get a really bad case? How much does medicine (in the broad sense of the word) actually help? How costly is it to "flatten the curve" compared to the cost of letting the virus rip through? It was darkly amusing to watch a Twitter thread in which Robin Hanson pointed out the very high mortality rate of people placed on ventilators, implying that they didn't help many people survive. He had claimed that something like 90% of people put on ventilators didn't recover (this was from a particular sample from a particular study). Some chimed in to correct him, "No, no, no, it's more like 60% who die on ventilators." And I've seen lower figures for this claim, too, but by all accounts a large percentage of patients on ventilators never recover. It's worth considering what kinds of medical attention actually help, and to what extent will people miss out on actual life-saving healthcare if the system is over-crowded.

What Are Public Officials Trying to Accomplish?

This has been my greatest point of frustration regarding the policy response to Covid-19: What end-game do you have in mind? Are you trying to "flatten the curve" in the sense of slowing the rate of growth? Or do you think you can completely halt the spread of the virus? I think state epidemiologists need to communicate much more clearly what their goals are and how those goals are achieved by any particular policy response. (Like school closures or shuttering businesses.) They should be explicitly tying these decisions to the output of an epidemiology model. I could cut them a little slack if they shuttered schools and businesses for a couple of weeks to buy some time. If they just needed a little time to get enough test kits or masks or gloves, a blunt approach might make sense without any kind of formal modeling. But beyond a short shut-down, we should all be demanding explicit justification for such measures. We should be demanding that epidemiologists share their models and various modeling assumptions so that informed members of the public can comment on and critique them. "Flatten the curve" is just rhetoric unless some epidemiological model shows that our efforts are actually flattening (and achieving that flattening at an acceptable cost).

Robin Hanson puts it quite well in this post. Many policy responses look as though they are intended to completely halt the spread, and that's probably the wrong approach. We are taking a giant risk here. Suppose we shut down parts of the economy for two months, but find out that the virus comes roaring back as soon as we open up again for business. If the spread of the virus is inevitable, if, say, 50-80% of the population is eventually going to get it anyway, then we shouldn't be in lock-down mode. We should take a more realistic approach that slows the spread but allows the spreading to happen. I just wish our governors and mayors would be straight with us. "Yes, we're trying to squash. If the virus comes back after we re-open the economy, we're going to go through this all again." Or "We ran a sophisticated epidemiology model, and it said this was the optimal time to close schools. It also tells us when to reopen them, which will be..." They need to be telling us clearly their basis for making these decisions, because they might be wrong in many dimensions. Their epidemiology model might be using the wrong assumptions, or perhaps we're being mislead by something as banal as a coding error. There needs to be more public scrutiny of how these decisions are made.

Another serious problem that I haven't seen anyone else point out: their epidemiology models might be solid, but their values and goals could be misaligned with ours. Public health officials tend to take a puritanical "avoid deaths at all costs" approach to policy, which  is grotesquely misaligned with what the public actually values. A young person might be willing to take a small risk of getting very sick to keep earning his income, and older people might be willing to risk getting sick to see their grandchildren. Public health officials who are merely counting bodies and trying to minimize deaths are not taking our values and preferences seriously. We need to remind the public health bureaucracy that it's isn't their job to tell us what they think we should want. They shouldn't be picking policy goals and back-fitting the modeling and the messaging to it. They should be acting more like engineers, telling us what will happen under various scenarios and policies. A government epidemiologist who is trying to decide policy, rather than merely inform it, is going beyond her mandate. Note that the FDA has been puritanical about e-cigarettes; they insist on decreasing the amount of vaping at all costs, even though this almost certainly leads to more smoking and more total deaths. The CDC has been puritanical about the use of opioids. The fact that some (very small) fraction of patients end up abusing their pain medication is seen as completely unacceptable. In both cases, our public health institutions are over-ruling the actual preferences of individuals. They are actively advocating and crafting policies to compel us to make the choices they think we should make. They are obsessed with the tableau that population-level statistics presents to the world. (Thus and increasing trend of teen vaping or opioid-related deaths "looks bad," and that is seen as a justification to overrule people's private decisions.) I don't think they're likely to represent our values or make the right trade-offs during a pandemic.

So let's be clear about what we're trying to do. Are we moving from the red curve to the blue curve? Or are we just postponing the red curve, which will rip through the population once the edicts have been lifted? Politicians really need to keep their powder dry. There is a limited budget for pulling the "shutter society" lever. If we've closed schools and shuttered businesses without a substantial fraction of the population getting sick (and thus acquiring immunity), what have we accomplished? And where do we go from there? People will eventually tire of stay-at-home orders and begin to flout them. And working parents who can't work from home will not tolerate indefinite school closures. We risk the possibility that the public becomes exhausted with social distancing protocols and start ignoring them, perhaps at exactly the wrong moment.

Maybe people's private efforts are adequate to slow the rate of spreading. We have a lot of tools at our disposal as individuals, like voluntary distancing, sanitation, masks, gloves, and less frequent ventures outdoors. Businesses can voluntarily implement protocols that slow the spread of the virus, like cleaning surfaces, cancelling large gatherings, allowing telecommuting for people who can work from home, and keeping different shifts from overlapping with each other. Obviously, businesses are already doing all of these things. Individuals and businesses have many different kinds of arrows in their quiver. If the virus gets worse, there are levers of control that they can pull harder. If it starts to recede, they can afford to relax and be less cautious. Government actions should be justified based on some kind of "value added" calculation that accounts for this private action. Maybe private efforts get us 90% of the way to optimum curve-flattening. Or maybe those efforts are totally inadequate to get population-level flattening. I don't know, because they're really not telling us.