Coronavirus thread

[Karl Henning]

Russia's Petty Race With the West Ends in Dire COVID Crisis

In Russia, however, the trends are heading in the opposite direction, based on even the most conservative official figures. On Wednesday, the country of 146 million people set all-time official records for daily cases (around 36,000) and deaths (nearly 1,100).

And it's possible the actual numbers are worse than the official ones. Critics have credibly accused Moscow of cooking the books in order to downplay the seriousness of the crisis and insulate the government from criticism.

[MusicTurner]

Unfortunately, a rather rapid decline here, with 1871 new cases today in Denmark. More testing is being done, but the average positive percentage among them has gone up to 2%. Hospitalizations have more than doubled within a couple of weeks, reaching 200.
New vaccinations are very few, there's opposition among immigrants and the youngsters in particular. Restrictions are likely to be re-introduced very soon.

   So, following a rise in the number of cases, with several days in a row exceeding 2000, and hospitalizations going from ~10 daily up to ~50-60, planned new restrictions were just announced here in Denmark ... including the re-introduction of a Corona Passport, albeit relevant for fewer activities than the previous one, and primarily targeted at night life, indoor restaurants/cafes, and large gatherings.

   On the positive side, the vaccines work: practically none of those vaccinated aged less than 50 years have been hospitalized; vaccination also hinders 95 % of hospitalizations for those younger than 65 years, and 76 % of those older than 65 years; a 3rd booster jab will make the last group reach 90 % as well; overall, the vaccination rate among those invited is now 88 %, the target still being set at 90 %. Proportionally, non-vaccinated people produce 15 times more hospitalizations, than the vaccinated, it was said. And the passport is likely to promote vaccinations - due to convenience, and because you'll need less testing then. After the announcement, 11,000 more people actually queued for vaccines.

  The scepticism towards restrictions from the political opposition hasn't hindered any of these plans so far, but there'll be further negotiations; signals from  at least some opposition members however seem to secure the measures. The government is not planning for any major, national close-down, it was said. But still, when they've been implemented, I suppose there'll be further actions, within maybe a few weeks; since these restrictions probably aren't going to lower the number of cases significantly, though they might reduce the growth.

[Mandryka]

   So, following a rise in the number of cases, with several days in a row exceeding 2000, and hospitalizations going from ~10 daily up to ~50-60, planned new restrictions were just announced here in Denmark ... including the re-introduction of a Corona Passport, albeit relevant for fewer activities than the previous one, and primarily targeted at night life, indoor restaurants/cafes, and large gatherings.

   On the positive side, the vaccines work: practically none of those vaccinated aged less than 50 years have been hospitalized; vaccination also hinders 95 % of hospitalizations for those younger than 65 years, and 76 % of those older than 65 years; a 3rd booster jab will make the last group reach 90 % as well; overall, the vaccination rate among those invited is now 88 %, the target still being set at 90 %. Proportionally, non-vaccinated people produce 15 times more hospitalizations, than the vaccinated, it was said. And the passport is likely to promote vaccinations - due to convenience, and because you'll need less testing then. After the announcement, 11,000 more people actually queued for vaccines.

  The scepticism towards restrictions from the political opposition hasn't hindered any of these plans so far, but there'll be further negotiations; signals from  at least some opposition members however seem to secure the measures. The government is not planning for any major, national close-down, it was said. But still, when they've been implemented, I suppose there'll be further actions, within maybe a few weeks; since these restrictions probably aren't going to lower the number of cases significantly, though they might reduce the growth.

We have about twice the rate of hospital admissions as you do, and there are no plans for any restrictions here. I leave it to others to draw conclusions.

DK pop 6M; 50 admissions a day -- 8/Million

UK pop 67M; 1K admissions a day  -- 15/Million

[MusicTurner]

As written above, the vaccines work well in reducing the number of hospitalizations and severe cases.

By far, it's the non-vaccinated that deliver the food chain for the virus, but vaccines can't be made obligatory, plus there are the youngest groups where there aren't any approved vaccines (yet). It's about 76% of the total population, that is vaccinated in Denmark.

[MusicTurner]

Well, you could say, let the non-vaccinated go to their own hell, of course, and let's accept a bigger number, maybe even a much bigger number, of dead people among the outcast. Not the attitude here, it would be considered a failure of government. Also, a lot of virus will increase the risk for all, including the most vulnerable people in society, those forced to isolation etc. It is one of about 4 countries, where there hasn't been any total mortality above average during the pandemic. The health sector is believed to be able to deal with a maximum of about 1000 corona hospitalizations, though less will of course be much preferable, since the strain affects other sectors in it.

Goodnight.

[71 dB]

If this is so, then why the fear and the restrictions?

This is extremely simplified math to illustrate why:

If the risk of hospitalisation is X for vaccinated, it is about 10*X for unvaccinated. So, if 80 % of people are vaccinated, the effective risk is 0.8*X+0.2*10*X = 2.8*X. If the hospitals can take say 2.5*X, there are serious problems. If 90 % of people were vaccinated instead, the effective risk would be 0.9*X+0.1*10*X = 1.9*X and the burden to hospitals would be much lower.

[amw]

All good points. Thanks.

How do you feel about the Merck pill which has now been approved for use in Britain?

https://www.reuters.com/business/healthcare-pharmaceuticals/britain-approves-mercks-oral-covid-19-pill-2021-11-04/

About the same—it's very strange to approve a drug on the basis of a single clinical trial whose results haven't been made public. I certainly hope it'll work out and prove effective, but would be extremely unsurprised if it turned out to have unforeseen negative side effects severe enough that the approval had to be rescinded.

[Mandryka]

Well, you could say, let the non-vaccinated go to their own hell, of course, and let's accept a bigger number, maybe even a much bigger number, of dead people among the outcast. Not the attitude here, it would be considered a failure of government. Also, a lot of virus will increase the risk for all, including the most vulnerable people in society, those forced to isolation etc. It is one of about 4 countries, where there hasn't been any total mortality above average during the pandemic. The health sector is believed to be able to deal with a maximum of about 1000 corona hospitalizations, though less will of course be much preferable, since the strain affects other sectors in it.

Goodnight.

Are you sure that the problem isn't vaccine waning, rather than the number of unvaccinated? A friend of mine recently estimated the half life of the vaccines at one month - that's to say the antibody titre count in vaccinated people halfs every month. I'll post the argument details if you want.

[Spotted Horses]

Are you sure that the problem isn't vaccine waning, rather than the number of unvaccinated? A friend of mine recently estimated the half life of the vaccines at one month - that's to say the antibody titre count in vaccinated people halfs every month. I'll post the argument details if you want.

Who is this friend and where does he get his numbers. The number I keep seeing for the mRNA vaccines (independent scientific studies, FDA, CDC reports) is that antibodies decline by about 50% after about 6 months.

Antibody levels are reported because they are easy to measure. There is more to the immune system than antibodies. Making an antibody is a time consuming process. The immune system starts generating random sequences and when one is found to stick, the immune system starts mass producing the effective antibody. The human immune system also has 'memory' cells which allow it to produce the antibody again, without going through the search process. Immunity doesn't necessarily fade as fast an antibody studies suggest.

[Mandryka]

Who is this friend and where does he get his numbers. The number I keep seeing for the mRNA vaccines (independent scientific studies, FDA, CDC reports) is that antibodies decline by about 50% after about 6 months.

Antibody levels are reported because they are easy to measure. There is more to the immune system than antibodies. Making an antibody is a time consuming process. The immune system starts generating random sequences and when one is found to stick, the immune system starts mass producing the effective antibody. The human immune system also has 'memory' cells which allow it to produce the antibody again, without going through the search process. Immunity doesn't necessarily fade as fast an antibody studies suggest.

See what you make of this

The data is in this paper

https://jamanetwork.com/journals/jama/fullarticle/2786096

The analysis I received was as follows, I haven't enquired about the US vaccine efficiency studies he refers to. 

From the paper there were 97 boosters given an average of 221 days after last vaccination to an elderly population (median age was 70 years).

Titer before booster 440 AU/mL
Titer after booster 25,468 AU/mL

Let's assume that the after titer looks a bit like the titer at the end of their second dose, then that is a fall of 25468/440 = 58x in 221 days, or a half-life for antibody titer of 221(days) x log(2)/log(58) = 38 days. Amount of protection from infection, symptoms, hospitalisation and death will depend on absolute antibody titer, but protection is halving about every month and a bit.

That rate was noted previously by Vaccine Efficacy studies in the US.

[Spotted Horses]

See what you make of this

The data is in this paper

https://jamanetwork.com/journals/jama/fullarticle/2786096

The analysis I received was as follows, I haven't enquired about the US vaccine efficiency studies he refers to. 

From the paper there were 97 boosters given an average of 221 days after last vaccination to an elderly population (median age was 70 years).

Titer before booster 440 AU/mL
Titer after booster 25,468 AU/mL

Let's assume that the after titer looks a bit like the titer at the end of their second dose, then that is a fall of 25468/440 = 58x in 221 days, or a half-life for antibody titer of 221(days) x log(2)/log(58) = 38 days. Amount of protection from infection, symptoms, hospitalisation and death will depend on absolute antibody titer, but protection is halving about every month and a bit.

That rate was noted previously by Vaccine Efficacy studies in the US.

The half-life calculation is correct, but there are some assumptions. This assumes the level after the initial shot is the same as the level after the booster. At the time of the booster the levels might have been higher than after the initial vaccination, since the immune system has had prior exposure to the antigen. It might be decaying from a lower level.

Any my previous comment applies, there is more to the immune system than antibodies. There are memory cells that retain the ability to make the antibody again. That is not as quick a response than having a high antibody level, but it is a stronger response than making antibodies after initial exposure. And, these are 70 year olds, not a representative sample.

Again, what I seem to hear from U.S. public health agencies is in the neighborhood of 50% loss of efficiency after 6 months.

[MusicTurner]

Are you sure that the problem isn't vaccine waning, rather than the number of unvaccinated? A friend of mine recently estimated the half life of the vaccines at one month - that's to say the antibody titre count in vaccinated people halfs every month. I'll post the argument details if you want.

You may have point there, and it might be a problem in the longer run, but it's not being focused on right now. It will require a good deal of math, predictions and knowledge to calculate. The 3rd, improving booster jab is planned for, almost 10% of the vaccinated having got it, and mine for example likely in January; details will be presented soon. They say that all unvaccinated are very likely to get the virus, within half a year to one year.

Hospitalizations and health cost are of course a dimension of all this; individual sickness, long-term effects and the amount of fatalities are also aspects of it. But add to this the gradual improvements in new vaccines, treatment options, and new medicine ... it's been called a 'race', or even a (morbid) 'dance'.


BTW, a survey of political voting and vaccine refusal was presented here. As you could expect, the vaccine refusers are mainly from the right-wing side of the political specter, who are also sceptics towards regulations and the welfare state. Or they are non-voters:

- Party D ('Surely, scr*w the immigrants. Scr*w the poor, so they can learn. Help The Rich, via diminishing the tax and state burden')(21% of voters refusing);
- Party I ('But some immigrants, including Non-Western, can be good for profits and non-state dynamics. Help The Rich, diminish the state')(15% refusing);
- Party O ('Well, keep parts of the welfare state for us real Danes, but sc*ew the immigrants. And let's remember, the old days were just better.')(9% refusing)
- Didn't vote at all: 12% refusing
- Various very small parties, fringe parties, esoteric parties, vegans, spiritualism, etc.: 16% refusing

Traditional, central parties with government experience have about 3% - 7% refusers (Parties A, B, V, K)

Established leftist parties have about 7% - 8% refusers (Parties F, Ø)

( Source: https://nyheder.tv2.dk/politik/2021-11-09-saerligt-to-partier-har-hoej-andel-vaccineskeptikere-blandt-deres-vaelgere )

[Karl Henning]

Coronavirus infections rise in northern states, Mountain West, as holidays near

[MusicTurner]

Your still very infectious after you've been vaccinated

https://www.bbc.co.uk/news/health-59077036

Now there are, on the contrary, surveys here saying that non-vaccinated will be 6-9 times more infectuous for others, than the vaccinated. Somewhat disputed terrain, it seems.

Also, the youngest children, obviously unvaccinated, are pointed to as very important carriers of the virus, besides the unvaccinated - and new possible vaccines for them have probably been developed too late to avoid that in the oncoming winter months.

[Mandryka]

Nice explanation of how vaccines work here

https://twitter.com/drneilstone/status/1459267407550332930?s=21

[T. D.]

(IMO) the US "vaccine mandate" is going to get struck down in court:

https://www.cnbc.com/2021/11/13/federal-appeals-court-calls-biden-vaccine-mandate-fatally-flawed-and-staggeringly-overbroad-.html

Story concludes with
...David Vladeck, a professor of law at Georgetown University, told CNBC that there's a "high probability" the case will ultimately end up in the Supreme Court, where there's a conservative majority.

"There are justices on the court who want to rein in the administrative state and this is a case in which those concerns are likely to come to the fore," Vladeck told CNBC on Monday.

[Que]

Your still very infectious after you've been vaccinated

https://www.bbc.co.uk/news/health-59077036

Very is a very relative term...

Less likely to become infectious, and if so, for a (much) shorter period of time.

The BBC article focuses on people living together, which is a very specific situation in which the risk of cross infection is the highest.

[Holden]

Interesting article on modeling Covid outcomes. I've done a copy and paste as it's behind a paywall

Lies, damn lies and modelling? Why COVID forecasts haven't all come to pass


   
Lies, damn lies and modelling? Why COVID forecasts haven't all come to pass

Rachel Clun

Hundreds of thousands of deaths. ICUs in overwhelmed hospitals struggling to cope under extreme pressure on beds and ventilators. The numbers were splashed in headlines across Australia.

In March last year, federal government modelling said that in a worst-case scenario up to 150,000 Australians could die from COVID-19. Modelling also forecast nearly 3000 cases a day in Victoria during an October peak of the latest outbreak and hundreds of cases in ICU and hospital.

Victoria could be recording thousands of COVID-19 cases a day by late October, modelling has shown.

But thankfully neither of these scenarios – nor other grim, headline-grabbing forecasts – have come to pass.

Critics have said this is proof that the scientists and public health experts behind the modelling are wrong and just want to see the country locked down for good.

But modelling is not a crystal ball prediction of the future. The experts behind some of the country's best-known modelling, from the Doherty Institute and Burnet Institute, have been saying that for anyone who cares to listen.

It's a tough science communication gig, according to Dr Nick Scott, head of modelling and biostatistics at the Burnet.

"You can't expect them to be correct for more than a week or even two weeks at most, in the same way that you could never expect a weather forecast to be accurate that far out," he says.

Why does it change? Why does some modelling paint a disastrous picture? And why do different experts or institutions end up with wildly different results?

Firstly, modelling is based on data. And at the beginning of the pandemic, there wasn't much of it.

"Your model will only be as good as the information you have," says Professor Jodie McVernon, director of Doherty Epidemiology at the Doherty Institute.

New variants. Different public health measures. More information about how effective vaccines are. As all this changes, so too does the modelling. "The model projections are basically the best we can do with the available evidence at the time," Scott says. "Over time, our picture of that data gets clearer and clearer."

Even in the months since completing the major modelling used to underpin the country's reopening plan, the data has vastly improved, McVernon says.

"At that point, Delta was a brand new thing, we didn't know as much about it, we hadn't had as much opportunity to see how well the vaccines worked. And so we made a whole set of assumptions based on what we knew back in July," she says.

But after going back and adjusting some of their parameters for the latest November modelling, McVernon says when they were put in the model, they got essentially the same results as July.

So why didn't Sydney, for instance, end up with thousands of hospitalisations and ICU admissions, and a peak of 2000 cases a day?
Jodie McVernon, Director of epidemiology at the Doherty Institute in Melbourne.

Jodie McVernon, Director of epidemiology at the Doherty Institute in Melbourne.Credit:Simon Schluter

McVernon says it's important to note that if the modelling said there was going to be hundreds of new cases a day, that's a scenario, not a prediction. "That was allowing you to compare one strategy with another strategy; a different coverage level, a different set of measures, to see whether you would expect one [strategy] to be better or worse," she adds.

New data has also played a role, specifically around the effectiveness of vaccines. In a huge positive, they have been far more effective at preventing hospitalisation and severe illness than originally thought, with all three vaccines currently being used in Australia performing better in real-world settings than they did in the original trials.

"It's actually quite a clear example of why projections will change over time when new data becomes available," Scott says. "In updated models, we have the benefit of more data on vaccines. So that all goes in and it helps to inform the next set of decisions that need to be made."

As the data changes, so too do the questions that governments want answered.


"In very early scenarios, the biggest question we had was 'how severe was this disease going to be?'," she said. "And we had vast ranges of possibilities right back at the beginning."

Models themselves can also vary – from back-of-the-envelope calculations to detailed and complex mathematical equations. Assumptions about things including how effective the vaccine will be can have a huge impact on the results.

"While most modellers will try to use the best available evidence, the way they incorporate that into the model might be slightly different," McVernon says. "So we have seen some models that have had more pessimistic predictions about clinical cases and others that have been less so."

Projected case numbers and hospitalisations are one thing. But what governments and policymakers really want to know from the modelling is what is the best decision they can make.

The original modelling looked at scenarios around how bad the pandemic could be for the country. The latest tranche was much more detailed. Rather than looking at a national scenario, there are granular investigations of outbreaks in school settings, Aboriginal and Torres Strait Islander communities, local government area-specific modelling and a look at the risk of COVID-19 from international arrivals.

"The more information we have, the more we can bring that into the model. And that will actually make it more likely to produce meaningful outcomes," McVernon says.

Modelling is also not in itself a solution. It's up to governments to decide what actions they should take and what risks they're willing to bear.

"The reason that the actual model is useful is that a lot of these things are not linear," McVernon says.

This has become increasingly obvious as states and territories reveal opening plans: NSW and Victoria are more willing to continue living with levels of COVID-19 in the community, while Western Australia wants at least 90 per cent of its population vaccinated before it considers fully reopening.

The strength of modelling is it pulls together all the pieces of information at hand – the effectiveness of vaccines, the effect of social distancing and working-from-home measures – puts them in one spot and shows what happens when governments do or don't combine them.

"They just need continual updating. But they are helpful when you need to make a decision about what you're going to do tomorrow or next week," Scott concludes.

Rachel Clun is a federal political reporter at The Sydney Morning Herald and The Age, covering health.

[prémont]

Now there are, on the contrary, surveys here saying that non-vaccinated will be 6-9 times more infectuous for others, than the vaccinated. Somewhat disputed terrain, it seems.

At our PM's latest press conference, Brostrøm or Ullum said something like this, referring to an article from England without elaborating it further. i have not seen any facts about this, which must be categorized as very good news.

[Karl Henning]

Innumeracy plus bad-faith actors plus internet rapidity

Covid misinformation spreads because so many Americans are awful at math

Two-step calculations are hard enough for some, but assessing vaccine effectiveness requires multiple steps.

By James Surowiecki

James Surowiecki is a journalist and the author of "The Wisdom of Crowds."

On July 25, Jeremy McAnulty, the director of health protection for the Australian state of New South Wales, turned himself into a meme. While presenting the state's daily covid-19 hospitalization numbers, McAnulty said 141 people were in the hospital with covid, 43 of those in intensive care. He provided an age breakdown of the hospitalized and of those in the ICU. And then he said something utterly unexpected: "All but one are vaccinated."

This was, to anyone who knew anything about the coronavirus and the vaccines, not just improbable but effectively impossible. The simplest, most obvious explanation was that McAnulty had misspoken, saying "vaccinated" when he meant "unvaccinated." And this was exactly what had happened. When he took questions a short while later, a reporter asked about his statement, and he said: "I think I misspoke before. Of the 43 people in intensive care units, 42 have not been vaccinated."

But it was too late. Anti-vaxxers around the world flooded Facebook and Twitter with clips of McAnulty's misstatement. The right-wing "news" site Gateway Pundit picked up and amplified the false information. These posts and tweets of course omitted the fact that McAnulty had quickly corrected himself, with some adding a lie by claiming that McAnulty had been speaking not just of ICU patients in New South Wales but of all the covid hospitalizations there. They trumpeted what he had said as evidence that the vaccines were "literally useless" at best and downright harmful at worst.

The speed and efficiency with which McAnulty's misstatement traveled testify to the way anti-vaxxers and vaccine skeptics use social media to disseminate the message that the vaccines are unnecessary, ineffective and dangerous. But they also demonstrate how the successful spread of that message depends on an unfortunate fact: An awful lot of people just don't do math. The message lands easily because of the general innumeracy — and specifically the ignorance of statistics — of the people consuming it. It takes only an elementary grasp of math to see that McAnulty's initial statement was self-evidently unbelievable. At the time, most of New South Wales's population was unvaccinated. So even if the vaccines were totally ineffective, meaning vaccinated and unvaccinated people were equally likely to be hospitalized, some unvaccinated people would have ended up in the hospital with covid. But tens of thousands of people happily believed otherwise without a second thought.

What's often called motivated reasoning is at least partly to blame — people believed something that was mathematically nonsensical because they wanted to believe it. But too many people couldn't recognize it as mathematically nonsensical. Americans are generally bad at math. A 2012 global study of the math skills of 16-to-65-year-olds found that American adults were less numerate than adults in most other developed countries. On a scale ranking skills from Level 1 to Level 5, with Level 5 the highest, 60 percent of Americans were at Level 2 or below, and almost 30 percent were at Level 1, which meant they struggled with even two-step calculations. That's a serious problem when it comes to evaluating vaccine effectiveness, since doing so requires multiple steps: looking at what percentage of total covid hospitalizations or deaths are among the vaccinated, looking at what percentage of the population is vaccinated, and then adjusting for that and for age to calculate how much more likely an unvaccinated person is to be hospitalized or die.

Lots of people, of course, never get that far. They make simpler mistakes: thinking that if 30 percent of people testing positive are vaccinated, that means 30 percent of vaccinated people tested positive, or believing that if a vaccine is 95 percent effective against hospitalization, that means 5 percent of vaccinated people will end up in the hospital. And it isn't just random people on Twitter who make these errors. CNN, in an article on how to fly safely, infamously suggested that a 90 percent effective vaccine would still mean that 10 percent of vaccinated fliers might catch the coronavirus. (What it really means is that a vaccinated person's risk of being infected on the plane would be 90 percent lower than an unvaccinated person's risk.)

Innumeracy, as the CNN example suggests, is not the province of any one group. And both sides in the information war over vaccines have used dubious statistics. But since the numbers show that vaccination offers excellent protection against hospitalization and death, covid skeptics and anti-vaxxers have become adept at exploiting people's innumeracy to instill doubts.

Some of these tricks are straightforward. When Vermont, which has the highest vaccination rate of any state, saw coronavirus cases rise from a very low base in late summer to a few hundred a day, and saw hospitalizations climb into the double digits, vaccine skeptics didn't say that Vermont still had some of the nation's lowest case and hospitalization rates, or that its absolute numbers were still very small. Instead, they said Vermont's cases were up "10,000%." Saying "Vermont has 300 cases a day" wouldn't have had quite the same effect, especially given that states like Florida were recording five times as many cases at the time. They also failed to mention that unvaccinated people in Vermont were far more likely to test positive for the coronavirus and to be hospitalized for it. The mere fact that Vermont's cases were up was taken as evidence that the vaccines don't work.

Similarly, when vaccine skeptics focus on countries that have had (or have) high case rates despite also having high vaccination rates, like Israel and Britain, and compare them unfavorably with the United States, they never mention that these other countries test far more than the United States does. That means that those countries identify many more infections than the United States does, and that their larger per capita caseloads are largely an artifact of testing. This summer, for instance, Southern states with low rates of vaccination had much higher positive test rates than Israel did, suggesting that their coronavirus infection rate was much higher as well. But because they were testing so much less, the states' case counts looked better. And so the most common social media refrain from vaccine skeptics in July and August was "What about Israel?," not "What about Tennessee and Mississippi?"

The most important place where innumeracy has helped foster vaccine skepticism is in the debate over vaccine effectiveness against severe illness and death. Vaccinated people can, and do, get severely ill and die of covid. So skeptics regularly point to the absolute number of deaths from breakthrough cases, or the share of total covid deaths accounted for by vaccinated people, as proof that the vaccines are failing.

The problems with this "analysis" are straightforward. First, if you're trying to determine the effectiveness of vaccines, you need to know more than the percentage of hospitalizations and deaths that vaccinated people account for. You also need to factor in the percentage of people who have been vaccinated, and adjust accordingly to determine the mortality and hospitalization rates for vaccinated and unvaccinated people.

Second, to get a true picture of vaccine effectiveness, you also have to adjust for age. There are two basic facts about covid and vaccines: Since the pandemic began, seniors have accounted for most covid deaths and severe illness; and seniors are the most vaccinated group, while most unvaccinated people are young. As a result, naive comparisons of the covid mortality and hospitalization rates for vaccinated and unvaccinated people understate vaccine effectiveness, since so many unvaccinated people are young and therefore less likely to be hospitalized with covid or to die of it.

To correctly measure vaccine effectiveness, then, you need to compare the mortality and hospitalization rates for vaccinated and unvaccinated people of the same age. And when you do this, it becomes clear how risky being unvaccinated is. In Oklahoma, for instance, the state says around 17 percent of seniors are not fully vaccinated. But those 17 percent account for 70 percent of all senior hospitalizations in the state over the past month. That means unvaccinated seniors in Oklahoma are 11 times more likely to be hospitalized for covid than vaccinated seniors are.

The math behind that "11 times" number isn't complicated. But it isn't obvious, either, and it does take a willingness to do it yourself, which lots of people understandably can't or don't want to do. As a result, simply presenting big numbers without context — a 10,000 percent increase; 3o percent of hospitalizations — ends up being an effective technique for making vaccines look bad. And while there are lots of people on social media debunking fake stats and providing more rigorous statistical analysis, if you don't trust them, there's no reason you'll trust their math.

Public health authorities have often made this situation worse by the way they collect (or don't collect) data and present it. The Centers for Disease Control and Prevention's state vaccination numbers, for instance, sometimes conflict with the numbers provided by state departments of health, and it's not clear why. While some states — among them Oklahoma and Connecticut — do a good job of presenting data on cases, severe illness and death among the vaccinated and unvaccinated, plenty of other states do much less. Go to Florida's covid-19 website, and you will search in vain for the daily numbers of reported cases and tests. And the state offers no data at all on hospitalizations and deaths by vaccination status.

Public health officials have also hurt their credibility by oscillating between making statistically dubious claims about vaccine effectiveness — Anthony Fauci's saying that coronavirus surges like the ones we saw last year were unlikely once the vaccination rate reached 50 percent in a community, for example — and making scary, dubious claims about the risks of the delta variant to the vaccinated. There is no quick fix for innumeracy. But public health officials can help mitigate the problem by being rigorous in their messaging and careful to present data in a clear, comparative way. (Connecticut's weekly covid reports, for instance, show not just the absolute numbers but also the relative risk of infection and hospitalization for unvaccinated people in an easy-to-understand format.) If they don't, their mistakes will be weaponized by anti-vaxxers to spread fear, uncertainty and doubt.