COVID Prevalence and the Difficult Statistics of Rare Events

In a post titled Defensive Gun Use and the Difficult Statistics of Rare Events I pointed out that it’s very easy to go wrong when estimating rare events.

Since defensive gun use is relatively uncommon under any reasonable scenario there are many more opportunities to miscode in a way that inflates defensive gun use than there are ways to miscode in a way that deflates defensive gun use.

Imagine, for example, that the true rate of defensive gun use is not 1% but .1%. At the same time, imagine that 1% of all people are liars. Thus, in a survey of 10,000 people, there will be 100 liars. On average, 99.9 (~100) of the liars will say that they used a gun defensively when they did not and .1 of the liars will say that they did not use a gun defensively when they did. Of the 9900 people who report truthfully, approximately 10 will report a defensive gun use and 9890 will report no defensive gun use. Adding it up, the survey will find a defensive gun use rate of approximately (100+10)/10000=1.1%, i.e. more than ten times higher than the actual rate of .1%!

Epidemiologist Trevor Bedford points out that a similar problem applies to tests of COVID-19 when prevalence is low. The recent Santa Clara study found a 1.5% rate of antibodies to COVID-19. The authors assume a false positive rate of just .005 and a false negative rate of ~.8. Thus, if you test 1000 individuals ~5 will show up as having antibodies when they actually don’t and x*.8 will show up as having antibodies when they actually do and since (5+x*.8)/1000=.015 then x=12.5 so the true rate is 12.5/1000=1.25%, thus the reported rate is pretty close to the true rate. (The authors then inflate their numbers up for population weighting which I am ignoring). On the other hand, suppose that the false positive rate is .015 which is still very low and not implausible then we can easily have ~15/1000=1.5% showing up as having antibodies to COVID when none of them in fact do, i.e. all of the result could be due to test error.

In other words, when the event is rare the potential error in the test can easily dominate the results of the test.

Addendum: For those playing at home, Bedford uses sensitivity and specificity while I am more used to thinking about false positive and false negative rates and I simplify the numbers slightly .8 instead of his .803 and so forth but the point is the same.


Another reason to do the Hanson variolation experiment. If we took 1000 healthy young volunteers and deliberately infected them then we could have some real data about asymptotic events and not have to guess. We are steering blind at the moment.

I think that is a thought experiment that is destined to remain stylized for a long time.

And not just because of problems for the informed consent, or compensation for injury.

If it is up in the air how viral load effects onset and severity, how would anyone develop a framework for 1,000 people?

Do you really need 10 times 1000, in order to have a range of regimes?

No, just two viral loads, one fairly small, the other one somewhat larger. If the smaller one works better then you can do further experiments.

Is there any medical agreement on what those two starting levels are?

Each round seems like it would take half a month or more to complete. Ideally you want another round just to prove that developing antibodies also generates immunity to a 'larger' viral load.

How much, BTW, is a small versus large viral load?

On the other hand antibody testing could allow you to segment and isolate. For example, have antibody positive staff work on Covid patients and negative work on non-Covid patients.

Taleb suggested he start with himself. Hanson responded by offering to bet money.

hanson also said health care workers were the ideal candidates
for sars cov 2 injection

Sadly the other problem in the study is that participants were recruited with an ad that offered them a free test at a time when testing was very hard to get there (and still probably is). The ad was also easily able to be forwarded by those that saw it.

Hence those recruited were likely heavy with people who were worried they were exposed but could not get tests.

It’s interesting to see the attitude here: Must Debunk This Study. Their results are in line with testing done in Vo, Italy which found 3% of the population was infected and asymptomatic -

More testing will be done and should be done. Then we will have a firmer idea of how widespread the infections are which will lower the IFR.

Also, states will be opening up faster then you think. NJ is running out of tax dollars. In PA they have stopped paid leave for Liquor Control Board employees. Incentives matter.

It’s a beautiful day here in PA. Get out and roam!

Rich, don't forget to bring an extra "COVID is a lie" poster for your covidiot buddies. When you hold up the sign, wear a mask too for extra irony.

Like the whole COVIDiot state of Oklahoma? Real hot bed there.

Nice dodge on his points, though.

Funny how science suddenly becomes right-wing propaganda when msnbc doesn't like the results 🤷‍♀️

The opportunity for smarmy self importance is infinite.

Back in the real world, lockdowns and quarantines have expiry dates. We are experiencing this in real time.

The people who have to work have come up with solutions to make it as safe as possible. Look for more, for everyone.

For example. Almost every place that collects large numbers of people have elevators. They all are stainless steel, and have buttons that get touched every time they are operated. Surfaces where the virus can maintain viability for days.

A short term solution please. A medium term, meaning retrofit. And a long term in new installation standards.

Etc. Pontificating how stupid people are may feel real good, but you sound like a blithering idiot.

We could use magic carpets to move from one floor to another.

"Almost every place that collects large numbers of people have elevators."

In theory, the easy answer in both Coase-ian terms and epidemiological terms is: wash your hands after you exit the elevator.

In the real world, yeah they are part of why there are more infections in cities than in less dense areas. However it's possible that the bigger risk comes from breathing the same air as the other people in the elevator, rather than from the buttons.

I'm not qualified to evaluate the science, but it's clear enough which information must be attacked and which mustn't be.

Howard W. Campbell, is it you?

Tabarrok is using the correct terminology: prevalence (which is a term of art) as opposed to the positivity rate. Here's an explanatory Atlantic article I found helpful: And here is another Atlantic article by economist Paul Romer and oncologist Ezekiel Emanuel on who should be tested (not those who are symptomatic):

Testing guidelines change. Back in February, with many fewer cases, testing was done to separate the small pool of those infected with coronavirus from the much larger pool of those with other respiratory conditions. Things evolve and by mid-April in many places (think Spain or Italy) , testing people with respiratory conditions is not particularly relevant to determining that they have an uncommon viral condition.

Things change as we learn about a new pandemic. Next flu season, testing the symptomatic will again make sense, if only because how each disease will be handled is different.

That may be so Tyler but the numbers in the Santa Clara study are at least somewhat supported by the serologic study in Gangelt, Germany with a much higher positivity rate of 15% and a infection fatality rate of 0.37%. You can also see the death rates in Iceland and UAE where widespread PCR testing has been done and they come out to 0.5% only. If you triangulate these data from different, unconnected parts of the world, a sub-0.4% infection fatality rate seems likely.

Or somewhat unsupported, as Gangelt was the center of the most intense German outbreak. Santa Clara by contrast does not seem to have had a light German case load, much less an average one.

Here’s a good interview with Dr. Jay Bhattacharya, one of the authors of the study, discussing the results of the study and two more studies in the works

Well worth a listen if you want to understand this critically important work.

good interview and interesting study
did you notice how easily the interviewer overtly overinterpreted the results to match his priors?

No. He offered his interpretation as a layman and Dr. Bhattacharya either agreed or corrected him.

watch the interview again
see how easily his "interpretation as a layman" was bigly synergistic with his biases.
doesn't mean hes not purty smart and a good interviewer.
the hoover institute stuff is always good stuff

Points that Bhattacharya raises:

- SARS CoV II probably cannot be eradicated if at these levels of prevalence.
- Contact tracing is impossible at these orders of prevalence (and I'd add will not do much more than slow things at low prevalence).
- Original models should be revisited taking into account that lower IFR and hospitalization ratios are likely. (I'd add seems IFRs likely 0.3-0.5%, even if not exactly at these rates). How much of original modelling informed by WHO declaring 3% IFRs? Does this weight "some social distancing + mitigation" more strongly? Can healthcare systems even realistically *get* "overwhelmed" at these hospitalization and IFRs, and so does the original argument that lockdown is the only way to keep healthcare systems from being overwhelmed even stand?

All true whether it is at those levels of prevalence, or now, or whether the under-counting of formal testing is 50x or *only* 20x.

Seem useful enough to make.

Dr. Bhattacharyas/os study is a bigly flag advancer
that's why in the grand tradition of the scientific method/m&m we get to throw rocks at it
-all the points you/he made are based on bigly extrapolating his study
onto the rest of the population. not a good idea until it is replicated
-" SARS CoV II probably cannot be eradicated if at these levels of prevalence." not true with a effective vaccine
-"Contact tracing is impossible at these orders of prevalence"
not true for many areas that currently have low incidence of disease
slowing spread of the disease is still efficacious"
-"original models should be revisited …."
a true statement whether or not his study replicates
-"Can healthcare systems even realistically *get* "overwhelmed"
Italy, detroit, neworleans and newyork would probly say yes

In the context, he is fairly clearly tackling about eradication through NPI, but it's probably still fairly likely to be true with an effective vaccine. After all, flu is still with us.

If his comment is effectively "Contact tracing is impossible at (even 1-2%) orders of prevalence", and your rebuttal is "not true for many areas that currently have low incidence of disease (that is lower than this)", that's.... not actually a rebuttal or even a disagreement!

Of course, replicate.

New York's healthcare system is "overwhelmed"? I thought they still had excess quite a bit of capacity / beds? North Italy's a somewhat unique case still, with no really ramp up at all before they got hit. Right now, we'd be talking about most countries that have seriously ramped up capacity about 3x (or at least those with their shit together have)...

-all depends on whether 50-80 times previously reported prevalanece is
an accurate number and how much immunity one gets with a positive antibody test
-- any hospital without enough masks/ppe is somewhat overwhelmed
if health care workers are getting sick
-been reported that some are also also running out of common meds
-there is supposed to be 2 additional similar studies out soon from the same investigators one in el lay and one with baseball teams

If you test people who are not at the hospital due to illness but are there to deliver a baby, you get prevalence of 15% (in Germany and in NYC). That's a big change in the denominator when calculating fatality.

Wasn't another thought that in hot zones too many exposures happen in hospitals?

In other words, how fast do you swab that incoming mother? And of course if it's in the hospital you need super good procedures for clean sampling.

Someone delivering a baby today, though, has probably had multiple contacts with waiting rooms and health care professionals in the last month or two. If they were positive 15% of the time does it follow society in general is already 15% positive?

That plus the disease hits men harder as well as those over 40. Sampling just pregnant women will likely give you a lower Infection Fatality Rate unless you are calculating it only for that subgroup of the population.

This is all anecdotal, but there are plenty of reasons to believe that pregnant women would be less likely to be infected than the general population.

They're not regularly spending time in 'hospital' settings, they're going to a doctor's office sure, but not one who generally has a lot of patients with infectious diseases.

On the other hand, they're hyper-aware of the coronavirus and probably being far more careful than the average person is. I know a few currently pregnant women and they've been avoiding all kinds of public interactions since well before the official shutdown was imposed. Their risk seems to me lower than others' is.

Also, regarding men vs. women, from what I've seen the infection rate is about equal, it's the rate of severe illness that differs between the two sexes.

No-one has calculated IFR or hospitalization rates from the pregnant females for this very reason.

There is a calculation of asyptomatic rates from them (85%), but this clearly has to be understood within their demography. In general asyptomatic and mild rates would probably work better computed for demographic controls, and is seems a little suspicious to me when we get studies returning the same 50% rate in contexts without regard to demography.

There are not very strong reasons to believe they are more likely to be infected than others were in NYC at the end of March - early April, roughly 22 days ago now.

OK so shifting gears assume 15% is correct not just for pregnant women in a city but all of society at the time the study was done (beginning of March?)

What do I have to believe to make that consistent with everything else? For example, the virus only appeared in November in China. The bulk of deaths in the US didn't really pick up until the end of March, start of April. Does this mean the virus spreads super fast? If it does then it means we'll see a surge of death but then it will vanish amazingly fast as herd immunity has already that consistent with any data from Italy, China, NY, anywhere?

I'm not sure we can say anything about pregnant women in the sample. Two weeks before they might have been attending baby showers or working because they want their family leave to kick in with baby as much as possible. They probably didn't go to the hospital, but then the hospitals at that point weren't that bad, but they did go to doctors' offices with crowded waiting rooms filled with people

Pregnant women sampled March 22-April 04 as I remember. Average over the time so probably lower at beginning than end. Deaths lag about 3 weeks and hospitalizations lag a week.

Probably not the case that "Well, this can't be true because where are all the people dying in early-mid March, even at low IFRs".

Look at how hospitalizations and deaths have increased and the predicted increase, and think about why those tailed off far faster than predicted by IMHE.

For exhaustive modelling read - . I do not endorse the IFR figure they give exactly (it seems relatively low, and NYC appears to be running slightly hotter on deaths than their model), but it seems that there is broadly nothing that is hugely inconsistent with the study of pregnant and modeled deaths and hospitalization.

Sign by the time I'm done with this I'll want to enroll in a graduate program for epidemiology. Unfortunately there'll probably be 100,000 other people.

Shocking that Alex would choose a lefty talking point for his “rare event” example.

I guess “babies who survive their abortions” wouldn’t get him as many party invites.

At the heart of every right-wing crank is somebody who doesn't get invited to parties.

That's another thing I never stoop to. I never make unsubstantiated personal attacks to "win" some unrelated argument.

just to be clear, I'm saying I never do these drive-by insults, and the only reason I can *imagine* for anyone else doing them is butthurt about some past discussion.

I'll stand by my analysis. Anyone who enters a thread, and their first comment is an ad hominem attack, is a butthurt loser.

I don't do that. But I do defend myself against the butthurt losers who make it their life.

Top kek. The lack of self awareness

Sorry, that was a swing and a miss. And a telling one.

I didn't make a random ad hominem.

Read it again. Randy made fun of Alex. I made fun of that very message, and not Randy, in any aspects other than that.

Now, are you Team Randy on this?

Do you also believe that Alex only holds pinons so that he can go to parties?

If not, WTF are you even complaining about?

That that this also satisfied the tit-for-tat condition:

Randy was certainly not minding his own business!

For a long read and a more serious answer here is Ryan Avent:

And the other six serology studies we have at this point? The research is all pointing in one direction.

Additionally, Abbott now boasts a nearly perfect blood test:

“It showed a sensitivity of 100% and a specificity of 99.6%,” said Alex Greniger, assistant director of the UW Virology Lab. “Diagnostically, this is one of the best tests we can offer,” he said.

The problem with taking a meta-analysis of very low prevalence serology is that they may all have the same systematic issue (at low bounds, all massive serology will have the "Is this really sample error or real?" questions, that depend on comparing an expected false positive to real result, which depends on the false positive rate being very precisely specified.)

Hence the high prevalence serology and high prevalence PCR carried out in hotspots probably tells us more, more clearly. (And there's plenty of that already, and will be more, soon, most likely that go in exactly the same direction).

An unknown infection rate of 50-80 times higher than confirmed cases seems an outlier. The Gangelt numbers, at 50 times, would result in an infected rate of 30%, twice as high as the (extrapolated) tested/unknown ratio. But then, the Santa Clara numbers are also extrapolated, resting on a considerably more tenuous foundation.

Gangelt Infected:Tested ratios almost certainly aren't generalisable outside Germany (if this is what your post is aimed at doing, prior).

It's quite laughably ridiculous to suggest that's the case, since Germany is by common acknowledgement likely on the very, very high end of tested:real cases.

What is generalizable is probably the local IFR (adjusted for demography), and somewhat less the total infected prevalence relative to the first case...

Both Santa Clara and Gangelt are looking at antibodies, and both are fairly pioneering studies in this regard. Most global testing is PCR.

JWatts - April 17, 2020 at 2:10 pm: "This must be a prior post. Obviously passive aggressive, but obscure enough to be nearly indecipherable."

On the other hand, maybe the U.S. is different - at least between states. 'Nearly one third of 200 Massachusetts residents were infected with antibodies linked to the novel coronavirus, according to a pilot study.

Physicians at the Massachusetts General Hospital said they found evidence of widespread COVID-19 exposure in the city of Chelsea.

Chelsea, located just north of Boston, had the state's rate of coronavirus infections at 1,900 cases per 100,000 residents.

Researchers collected drops of blood from residents in Bellingham Square on Tuesday and Wednesday after advertising the study.

Of the 200 voluntary participants, 64 had antibodies created by their immune systems to fight the coronavirus. ''

The math would seem to suggest a much smaller undercount factor of around 15, which is much more in line with Italy than Santa Clara. Of course, American testing needs to be looked at per state - Mass is at 22,958 (about 10% higher than Germany according to Worldometer), while Caifornia is at 6,294 (even less than the UK rate).

Just to make it more difficult, the virus is mutating possibly resulting in a less deadly strain in some locations.

The virus doesn't seem to mutate much. There's even a mechanism to correct mis-copying (see protein NSP14 here):

This is a key concept in diagnostic testing and screening, called "positive predictive value" (and it's partner, negative predictive value). All testing providers and consumers are taught about this, but it's knowledge that does not persist for many people. But it's important here - a useful diagnostic test is very frequently not a useful screening test

+1 we gotta lotta screening tests that are over-rated
a lotta screening tests are not excellent screening tests

Does this mean we can get on the NBA playoffs now?

I know this website is against state licenses but is medicine the final frontier? Nurse practitioner lobbies are trying to get full practice authority but states like California are saying not yet. Any takes on this? Will this bring health care costs down?

I can answer your last question.

No, it will not.

"Since defensive gun use is relatively uncommon under any reasonable scenario there are many more opportunities ..."

That needs punctuation, Mr T.

So in other words, bone up on Bayes' Theorem.

Hi, are you an epidemiologist? Great. This is the global mainstream media and political system calling. Where did we find your number? Yeah, don't ask.

So, look, there's a brand new disease going around, since, lemme see, yeah, last month. There's no data on it. Yeah, none. Well, there's some data, coming from, um, China. Yeah, I know. China. Right?

Anyway, there's no data to speak of. But what we are seeing is bad. What we are getting from social media is the thing is more contagious than John Travolta with herpes and a bag of cocaine. Yeah, and deadly too. Looks like maybe as much as 15% are drowning in a sea of their own blood. Yeah, China is adding morgues on former soccer fields, I hear you can see them from space.

Yeah, fugly. Okay, so here's a weird story, like the first doc to go public with this, this Chinese dude, yeah, he got it. and so he died, after kicking around for a damn month. Yeah, exactly, friggin' shoot me already.

So, yeah, there's no cases in the US yet. I mean, we don't think so. You see, well, here the thing. We can't test for it. I know, it sucks right? Pretty sure it is only transmitted by direct droplets and face contact. What do we mean by 'pretty sure?' Okay you got us. We have no freaking clue how it is spread. What's that? No. We have no idea about acquired immunity either.

Okay, so here's the problem. I've got all these annoying eggheads breathing down my neck. Yeah , the public health nerds. They're all freaked out. So far the President is holding firm that this is a partisan seasonal flu hoax. But the public health guys aren't buying it. And they say we need more ventilators. Like a LOT more. wtf man. You think those grow on trees? Those a-holes are always happy to spend other peoples' money.

Yeah, so these jerk-offs are whining about PPE. I mean, go down to Costco and buy some masks if you're worried ffs. Anyway, they say a sudden influx of people with severe respiratory distress would overwhelm our ICUs and have people dying in the hallways on gurneys. I'm like, get real. We have the finest medical system in the world, we spend like multiples more per capita than anyone else. Our hospitals are ginormous. Beautiful. We got this. I have one word for these guys: cowards. chicken. freaking. little. if you ask me. No, ignore Italy man. I mean, c'mon, it's Italy amiright?

Look at the UK. Now there's a country with some stones brother. Their fogeys faced down the Nazis, and they are ready to take one for the team this time too. Winston goddamned Churchill. Sure, they'll gladly die for the good of the Russian bankers if necessary, I mean, for the economy.

Next, there's some of the Governors. The partisan ones. They want use this as an excuse to flex their socialist muscles and shut their economies down. What's socialist about that? I dunno. But it sounds good on Fox.

Ok, so here's the thing. We have no numbers. And we need numbers. My God we need numbers. Like yesterday. Have you ever seen a political news story, I mean health story without numbers? Right. It's glaring. So if you don't mind, would you scratch something out this weekend and get it to us Monday morning? That's be great. No, no, don't worry. We understand it's a rush job. We won't hold you to it. Yes, we will print the footnotes and disclaimers too of course. Look, it would just be nice to have something to work with. Whadayacallit? A strawman, to get the conversation rolling in some sort of direction rather than all over the damn place.

Ok, right. Yeah, you can pick a number for infection rate between 2% and 70%. And mortality, I dunno, 0.5% to 12%. Yeah, it's a real dart board job alright. But I'm sure you guys can slap some lipstick on this pig. No, everyone will forget it five minutes after it's done. That's how it works these days. Shelter-in-place? C'mon get real guy. No one is going anywhere. This is America.

Who's paying for this? Beats me, go ask the states.

3/4 too long Hemingway

everybody’s a critic

With all the debate on this study, I don't understand why we don't conduct 100 similar studies with different ways of selection. Like, why not set up testing at Ralph's grocery store line and just ask everyone who comes in if they'll allow themselves to be tested. Do variations of finding random selections of the population -- like test an entire small company. Or test a school. Compile all this data. I'm not an economist or epidemiologist, but so maybe these methods don't hold up as precise, but I imagine they would be useful.

Testing... there's not enough tests.

The problem was, is, and will remains for a while still: the lack of reliable, available, uniform testing.

"With all the debate on this study, I don't understand why we don't conduct 100 similar studies with different ways of selection."

Who is we? It's not just a glib answer. It strikes at the problem of a national health "system" without any kind of "last mile" guarantee or delivery.

"We" might like to choose 100,000(*) Americans at random and test them. But we don't have the national system or funding to do that. Those 100,000 Americans may have a GP, and be insured, or not. And even if they have their doctor and their insurance, he's not tied into a national health database.

George's long story is harsh, but ..

* - or could we wish for a million?

The head of the federal public health system - the guy who hires the leaders, sets the budgets, oversees like a $100 billion per year in funding, and establishes the priorities - has already announced that they are not in charge of testing.

I think that's not surprising under our system. He has no "presence" in all 50 states. At least not "presence" in the sense of nurses who know how to do nose swabs, labs to send them to, a database to collect the results. (AFAIK!)

He *could* try to find county level health department assistance, but that's pretty hard on the fly. Assuming your random sample of Americans map to adequately prepared county health departments.

If there were a universal testing plan that would satisfy what I call "the last mile."

oh sure the last mile is local.
and the last two miles is state.

but the other 98 miles are, or should have been, federal

Here's the message from the prez, "I am right on testing. Governors must be able to step up and get the job done. We will be with you ALL THE WAY!"

So all testing is state, but we are "with them all the way."

I've been looking my area's, southeast Florida fatality lists and here is what I found.

There are 6.1M people living in the Tri County area of southeast Florida. About 20% of the population in southeast Florida is over age 65.
As of April 17th 2020, southeast Florida recorded 427 deaths from COVID-19. Only 79 people or 19% of the total fatalities were under 65 years old (78% male and 22% female). Women age 30-65 have very little risk of dying from the virus. No one under the age of 30 has died in southeast Florida from COVID-19.
To date, for men under 65 there are about 2.4 deaths for every 100,000 men and for women under 65 there is only 0.6 deaths for every 100,000 women. Since most models show that southeast Florida is half way through the first wave of COVID-19 deaths these rates will probably double in the next month, but they are still very low in terms of the overall fatality rates for most historical pandemics.
We encounter many things in life that follow an 80/20 rule. In this case, we have 20% of the population incurring 80% of the deaths. Clearly, we need a strategy the focuses on this Pareto reality and not some one-size fits all approach.

We are focused on the 20%. Due to the realities of infectious disease and nature of our economy and living arrangements, this requires the participation of the other 80.

There is no reason to think that this is remotely true, but it is *easier* to blanket burden everyone then protecting the 20% without undue burden on the 80%.

Case in point: cancelling school sent millions of potentially asymptomatic child carriers to spend weeks in close proximity to their most vulnerable grandparents. A very bad strategy if you're actually concerned about the 20%, but a great one if you just want an easy way to show you're 'doing something.

Either those grandparents were already in 'close proximity' or they weren't. Those that weren't already in close proximity are unlikely to now be in close proximity because schools are closed, and those that were in such proximity are not being exposed to an increasing chance of infection as children continued to mix at school.

highly flawed premise.
i know of no one who used this opportunity to spend more time with the grandparents

I can largely agree with that for K-12, though perhaps not wholly. Parents needed someone to watch their kids during the day because the kids are no longer at school. A lot of people are working from home or not working, but some people are obviously still working: healthcare, grocery stores, some types of warehouses, etc.

Where I think that North49's criticism better holds up is higher education, at least schools with a largely residential population (so not commuter schools, not community colleges).

They had really good places - college dorms - for a sort of loose quarantine of a largely low-risk population amongst themselves, and instead they sent most of them home.

That is an interesting conclusion by an epidemiologist but I'm concerned about a few things.

* What were his GRE scores?
* How much money does he make?
* What are his political leanings? Is he a socialist?

Anonymous sources with answers OK.

The obvious solution is to the take the Stanford test to New York city, New Orleans, Chicago, and Boston.

Yes, there are problems with the Santa Clara study, but they aren't insurmountable. However, the results do align with every other serological study done to date- at some point the nit-picking reveals itself for what it always was- an attempt to preserve that high fatality rate- the amount of political capital invested in the shutdowns is at risk if the fatality rate is shown to be under 0.5%.

Well if testing is limited one solution would be combined sampling tests. You take groups of, say, 10 people and mix their samples all together and test. Imagine doing that for hundreds of such pools. A positive result would mean one or more in the pool have the virus but looking a negative result means all 10 are negative. Toss some high level math at the results and you can generate some good estimates of what the overall prevalence is in the population.

This could also work as a back to work function. Company with 100 people tests them in groups of 10. The negatives are cleared and the positives are retested in pools of 5 until the positives are narrowed. You can leverage a limited number of tests by a factor of ten or less.

+1 to Yancey.

Seems like almost every time we have testing of a wide population including people who don't have symptoms - whether serological or PCR - we find this disease is far more prevalent than suggested by case numbers. Not just more prevalent, but at least an order of magnitude and possibly quite a lot more than 10x.

The OP was about defensive gun use. I was interested until it went nowhere, because I just gave my deer rifle to the neighbor, because I mountain lion came up on his deck and ate one of his pet cats right in front of his eyes, and I thought a new gun might make him feel better. I'm over 70 years old and shooting even a 7mm-08 is like getting body-blocked by somebody from Marvel Comics or a Republican state rep from the red states, it is no fun.

The neighbor kid claims to have been a sniper in Iraq, subsequently under-gunned, but whatever he used to do back in the day he now grows dope and maybe he will give me some leaf now that I have reached out to him. Maybe it will soothe my shoulder and other bruised parts.

Then I saw the picture of the Michigan Zombies behind the glass door, and I thought, whoa! What if this percent or that percent of gun-battle participants under-report? This could get serious and maybe affect how I should deal with the zombies.

Fortunately I still have a couple of shotguns and the pistol, so all this statistical noodling is of no import.

So Alex means true positive rate of 0.8 (the sensitivity), not a false negative rate of 0.8. His math and everything else is right. Just pointing that out in case anyone else puzzles over it and potentially wastes time parsing the terms.

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