Case Rates, Death Rates, and Vaccination: A Puzzle

I have been following Covid figures for the U.S., for Israel, and for Santa Clara County, where I live.  In all three vaccination has been largely of the elderly, which one would expect to bring death rates down much faster than case rates. The only place where that seems to have happened is Israel. Even there, the effect does not seem to be as large as one would expect.

For each of the three I calculated the ratio between the most recent 7 day average of death rates that I could find and the earlier peak 7 day average, then calculated the corresponding ratio for case rates, assuming a 9 day lag between cases and deaths, and compared the two ratios. I chose a nine day lag because it let me match a death rate peak to a case rate peak. A longer lag might be more plausible, but I do not think it would change my results by much.

The U.S. and Israel give the death rate figures up to yesterday, while the county gives them only up to two and a half weeks ago on the theory that the more recent death figures are not reliable, so the interval for the county was shorter than for the countries. Since what I was comparing was not county to country but fall in death rate in the county to fall of case rate in the county and similarly for each country, that should not be a problem.

 

The results:

 

In Santa Clara County, case rates fell by a factor of 6.5 while death rates fell by a factor of 3.9.

 

For the U.S., case rates fell by a factor of 4 while death rates fell by a factor of 2.6

 

For Israel, case rates fell by a factor of 2.95 while death rates fell by a factor of 4.3

 

Only in Israel did death rates fall faster than case rates. I do not know if recent death rate figures for Israel are reliable, so redid the calculation using the same dates I used for Santa Clara County. That gave me ratios of 2.3 for cases, 2.6 for deaths. Deaths were still falling faster than cases, but not by very much.

 

Israel has had the highest vaccination rate of the three, so it makes sense that it would look better on the deaths vs cases comparison. But at this point, 11% of the U.S. population has been fully vaccinated, another 12% have received one dose. Vaccination has been largely, although not entirely, of the elderly. People 65 and over are  about 20% of the population and about 80% of all deaths from Covid, so one would expect vaccination alone to have cut deaths roughly in half. For Israel, 80% of adults over 60 have received two doses of the vaccine, which should have cut deaths relative to cases more than in half, a larger effect than my calculations show.

 

I  see two possible explanations for the pattern. One is that older people are not only much more likely to die if infected, they are also much more likely to show symptoms if infected; people who are infected but don’t show symptoms are unlikely to be tested and so don’t go into the count of cases. That would explain why deaths don’t fall faster than cases but not why, in two of my three areas, they fell substantially slower. And it requires that older people are not only more likely to show symptoms but as much more likely to show symptoms as to die. That does not seem to be the case, according to a source I found online.

 

The other possible explanation is that many of what are counted as deaths due to Covid are actually deaths while having Covid, people who die from some other cause but are tested and found to be infected. We would expect the number of those to be proportional to the number of cases.

 

If the first explanation is correct, figures on the number of cases overstate how fast it is falling, since symptomatic cases are falling faster than asymptomatic ones. Since asymptomatic cases are apparently still contagious, although less contagious than symptomatic cases, that implies that the risk of getting Covid from a random stranger has not fallen as fast as the decline in cases would imply.

 

If the second explanation is correct we have badly overestimated how deadly Covid is, hence probably over reacted to it.

P.S. (3/22): I now have a third and more plausible explanation of my puzzle. I was using a 9 day lag between case and death because that was the lag in the peaks. But even if, on average, it takes nine days from detecting a case to a death, the actual lag is a range, say sixteen days to two days (actually longer, but that will do for my example). I was starting my calculation with the date when cases were at their peak, and nine days later for deaths. That meant that I was including in deaths ones from cases well before the peak, when the case rate was lower, which pulled down the death rate, making the drop from then until now smaller.

To test this conjecture, I redid my calculation starting two weeks later. Now I got the expected result. For all three cases — Santa Clara County, the U.S., and Israel, death rates fell faster, not slower, than case rates nine days earlier.

The CDC gets life expectancy wildly wrong

According to a CDC spokesman, U.S. life expectancy has fallen by a year as a result of Covid. A little arithmetic shows that that cannot be close to correct. 

Total deaths so far are about 500,000 out of a population of about 330,000,000. The average death cost 12 years of life. Multiply that out and the average person lost not one year but .018 year of life.That's an error of almost two orders of magnitude. Including deaths indirectly caused and additional deaths over the next few months might increase it a little, but there is no way it can be one year or even close.

Dr. Peter Bach explains the error on his blog. What the CDC apparently did was to calculate what the effect on life expectancy would be if mortality rates stayed at their 2020 level,  how much Covid would reduce life expectancy if the pandemic was repeated every year forever.

After an error of that magnitude, it is difficult to take seriously any factual claim they make. It will be interesting to see if they admit the error.

P.S. To be fair, I have not found the claim on the CDC web site, only in media reports that attribute it to "Robert Anderson, who oversees the numbers for the CDC." 

P.P.S. I have now found it on the CDC web site in the form of an interview with Elizabeth Arias, who apparently produced the number:

https://www.cdc.gov/.../podcasts/2021/20210219/20210219.htm

 

I posted a version of this to FaceBook. Some people defended the CDC on the grounds that the usual way of calculating life expectancy is by measuring the current mortality rate as a function of age and projecting it it into the future. The problem is that, as you can see by the interview, Elizabeth Arias makes no attempt to explain that what she is describing is a measure that she knows, in this case, badly misrepresents what it is supposed to be measuring. 

Have We Reached Herd Immunity?

I have been looking at the number of new cases per day, both for Santa Clara County and for the U.S., and the pattern is striking. Over the past month, number of new cases per day in the U.S. has gone down by a factor of about 2.4, for the county by a factor of about 3.5. Death rates are also down, although by much less, but one would expect death rates to lag case rates by a few weeks. I don't think the explanation can be the weather, since it's still winter.  I don't think it can be vaccination because there has not yet been enough of it to substantially affect the case rate.

The other obvious explanation is that the previous high was created by a lower level of precaution due to XMas and New Years. But that explains only a reduction in the rate of increase, not a reduction in the level, since all those people infected during the holidays were then around to infect other people. The fact that the level is falling means that each infected person is passing the infection on to fewer than one person, which is the definition of herd immunity.

If behavior is held constant, herd immunity ought to first appear as a constant rate of infection, each person passing the disease on to one other, then gradually become a shrinking rate. It looks as though we reached herd immunity under non-holiday behavior something close to two months ago, infection rates kept going up due to the holiday bump, and by the time that ended we were far enough into herd immunity (with non-holiday behavior) so that rates were falling. 

I was still surprised that they were falling so fast until I looked at how many cases had occurred recently. I haven't made an exact calculation, but it looks as though, for both the county and the country as a whole, the surge in cases over the two months of the peak  roughly doubled the cumulative total. It wouldn't be that surprising if that had pushed us well past the start of herd immunity.

There are two qualification to be made to the optimistic conclusion that the pandemic is almost over. One is that the requirement for herd immunity depends, among other things, on how people behave. If everyone concludes the pandemic is over and drops all precautions against passing on Covid, cases might start increasing again. The other is that there are at least two new variants of Covid now spreading through the U.S., and we cannot be sure that people immune to the old variant will be equally immune to the new. If, to take the most pessimistic possibility, the protection provided by having had Covid turns out to have no effect one of the variants, we are back to ground zero and in trouble.

My guess, however, is that neither will happen, and that in another few months the case rate will be back to last spring's lows. And falling.

Why Trump Shouldn't be Impeached

As best I can tell, while Trump is morally responsible for the recent riot he is not legally responsible, since everything he did that contributed to it was something he had a legal right to do. But requirements for impeachment, other than a majority vote in the House to impeach and two-thirds in the Senate to convict, are unclear, so that is not, in my view, the fundamental issue.

Our legal system has so far been pretty stable. One reason is an implicit rule: When power shifts, the winners don't punish the losers. Impeaching Trump after he has left office, as a punishment not a way of removing him from power, violates that rule. That would be a  dangerous precedent, one step further towards making political conflict something closer to a civil war. 

People will, of course, argue that this is a special case, that Trump is uniquely guilty. But once the precedent is established other people, in a polity already sharply divided, will find other special cases.

For the same reason I am bothered by people who gloat over the prospect that Trump, once out of office, will be prosecuted for things he did in business before he was president. Obviously having been president doesn't give legal immunity — anyone who wants to sue him will be, and should be, free to do so. But criminal prosecution is at the discretion of the prosecutor; Obama protected illegal immigrants who he didn't want arrested by instructing law enforcement not to arrest them. If Trump gets prosecuted by officials who are his political enemies for business dealings he did not get prosecuted for when they happened, it will be pretty clear that it isn't the dealings he is being prosecuted for. 

That again would be an unfortunate precedent.

Fauci, Lying, Greyhound Racing, and Trump

“When polls said only about half of all Americans would take a vaccine, I was saying herd immunity would take 70 to 75 percent,” Dr. Fauci said. “Then, when newer surveys said 60 percent or more would take it, I thought, ‘I can nudge this up a bit,’ so I went to 80, 85.”

“We need to have some humility here,” he added. “We really don’t know what the real number is. I think the real range is somewhere between 70 to 90 percent. But, I’m not going to say 90 percent.”

Doing so might be discouraging to Americans, he said, because he is not sure there will be enough voluntary acceptance of vaccines to reach that goal.

(NY Times, Dec. 24, 2020, “How Much Herd Immunity is Enough.”)

Poll information about how many Americans would take a vaccine is not evidence about how many people must be immune to achieve herd immunity. By Fauci’s own account, his changed statement reflected not what the scientific evidence showed but what he thought it prudent to tell people it did. He had just publicly admitted, in the New York Times, that he was a liar.

If he is not telling the truth, what is he doing?

Greyhound racing uses a mechanical rabbit, kept moving ahead of the dogs to give them something to chase. Too close and they might catch it, too far ahead and they might lose interest. The most plausible conjecture I can come up with to explain Fauci’s account of what he is doing is that he is following the same approach. In order to get people to do what he wants, whether that is getting vaccinated or wearing masks, he has to persuade them that it will do some good. If they believe the problem is almost solved, each individual may figure that others will solve it and he can slack off, or may decide to maintain precautions for a little while longer, at which point the pandemic will disappear and he can stop. If, on the other hand, people believe the solution is very far away, it is tempting to give up on it.

The solution, as for the greyhound race, is to keep adjusting the estimate, subject to what you can get people to believe and how close the rabbit has to be to motivate the dog to run.

In the short run this approach, like other versions of lying to people for their own good — telling them, early in the pandemic, that masks were useless to them, in order to save masks for medical personnel, or that a lockdown would be only for a few weeks, in order to get people to go along with it — looks attractive, a way of saving lives. In the longer run, it risks persuading an increasing number of people that they should not believe what authority figures tell them.

That is not a wholly bad thing, given that elite opinion, as filtered through the media, is frequently unreliable, sometimes, as in this case, deliberately dishonest. But there is a problem, currently illustrated by the number of Americans who believe Trump’s claim that he really won the election. The more people who distrust elite sources of opinion, the harder it is to get people to coordinate on a common view of reality. If you cannot trust the President’s advisor on the epidemic or, in other contexts, the New York Times, to tell you the truth, why should you trust the people who tell you that the election was, on the whole, honest, that although there were probably, as in most elections, a few glitches here and there, there was nothing nearly large enough to reverse the result?

If there are no elite information sources that you trust, you might as well believe what you want to believe, as people are very much inclined to do.

Postscripts on the Pandemic:

Fauci's quoted statements provide further evidence that what he says reflects what he wants to tell people, not his scientific opinion.

“If you really want true herd immunity, where you get a blanket of protection over the country ... you want about 75 to 85 percent of the country to get vaccinated,” Fauci, the longtime head of the National Institute for Allergy and Infectious Diseases, said in a live-recorded interview with Rameswaram, the host of Today, Explained. “I would say even closer to 85 percent.” (Vox, 12/15/20)

Current estimates imply that more than 100 million Americans have had the disease already (91 million as of September, according to the CDC). The same mechanisms that make vaccines work also imply that those people are immune to the disease, at least for a while. If those people are put at the back of the queue for vaccines, vaccinating 70% of the population will make 100% immune, at least if immunity does not turn out to expire in less than a year. If we make no attempt to avoid vaccinating those who have had the disease, 70% vaccinated should mean about 80% immune. Fauci is  ignoring that, presumably because taking account of it reduces the percent vaccinated that he can claim we need.

There is, however, a reason to raise our estimate of the requirement for herd immunity, having nothing to do with changes in what people will believe. There are now two new and more contagious variants of the disease, one first detected in the UK, one in South Africa. The more contagious the disease, the larger the number of people who must be immune for herd immunity.

 

P.S. Someone pointed me at a recent piece by Bill Maher criticizing the media and the medical establishment for their failure to trust their audience with the truth about Covid.

Defamation Law vs Censorship

Mac Isaac, the laptop repairman with whom Hunter Biden apparently left a laptop, has sued Twitter. His complaint is not that Twitter locked the New York Post account of the contents of the laptop's hard drive. It is that their explanation for locking it was the claim that the account was in violation of Twitter's hacked material rules, and that Twitter, in explaining that policy, defines a hack as

an intrusion or access of a computer, network, or electronic device that was unauthorized or exceeded authorized access.

By Isaac's account of what happened, his access to a laptop that had been dropped off at his shop for repair and then abandoned was authorized, hence not a hack. It followed that Twitter was making false statements which, according to Isaac, have had large negative effects on him. On the face of it, it looks like a legitimate case.

What made the story of particular interest to me was that Isaac is doing something I had thought about doing, decided not to do, and suggested to a law firm that they might do in similar cases — with regard to Facebook, not Twitter. 

About a year ago, I discovered that Facebook was blocking all links to my web page. Anyone who attempted to put up such a link got a message saying that the page violated Facebook's community standards. I went through the procedures on Facebook to object, never got any response. Eventually they stopped blocking it, still with no explanation.

Facebook is a private firm, and as such has a legal right to decide what messages they will or will not publish. They do not have a legal right to defame me, which, assuming that nothing on my page actually violated their community standards, they were doing. The problem had been solved when they stopped blocking the page, and in any case was never a large enough problem to justify the trouble of a court case. But it occurred to me that it might justify a class action by someone else, so I emailed a law firm that seemed appropriate with the suggestion.

Mac Isaac, or his attorney, apparently had the same idea in a much larger case, and has now acted on it. I wish him well.

How to Waste Vaccine

The CDC estimates that, as of the end of September, there had been 53 million Covid infections in the U.S., 7.7 times the number of reported cases. The current figure is 16.2 million cases, so if the ratio holds, total number of infections is about 125 million. That is probably too high, since the ratio of infections to cases goes down as the amount of testing goes up, so I will guess a current figure of 100 million.

The U.S. has contracted for enough vaccine from the two sources that have been or almost certainly will be approved to vaccinate another 100 million over the next few months. Combine those numbers and we should have 200 million people who either have had the disease and so are very nearly immune or have been vaccinated and so are very nearly immune, getting us at least close to the level required for herd immunity. Add in the number who will have gotten the infection by then and we should probably be over that level, which means the number of infections should start falling.

There is one problem with this optimistic story. As best I can tell from online discussions, the current plan for allocating the vaccine does not include any attempt to avoid giving it to people who have already had the disease, not even to those who have been diagnosed with it. If so, about a third of the first hundred million doses will be wasted on people who don't need them.

One possible argument for doing it that way is that having Covid does not create perfect immunity, there having been a few cases reported of someone who got the disease, recovered, and was later reinfected. But the vaccine does not create perfect immunity either — reported effectiveness for the first two is about 95%. If as many as five percent of those who had had the disease and recovered were still vulnerable to it, we should have had a lot more than a few cases of reinfections.

To make that argument more precise, consider that, as of the end of September, there had been about seven million reported cases. If infection gave only 95% immunity, about 350,000 of them should have still been vulnerable, a little more than one thousandth of the population. Since the end of September there have been another nine million cases, so more than nine thousand of them should have been known reinfections, individuals who were diagnosed with the disease, recovered, and were then diagnosed again. That did not happen. It follows that, while infection may not give complete immunity, it gives considerably better immunity than the vaccines.

Another possible argument is that tests for whether someone has already had the disease have a significant false positive rate. Checking online, it looks as though the false positive rate for most such tests is below ten percent (specificity>.9). At ten percent, that means that if you skip the people who test positive you are vaccinating an additional ten people for every false positive you are not vaccinating, which sounds like a substantial positive. If we had enough vaccine for everybody it might be better for everyone to get vaccinated, but we don't.

If my analysis is correct, current policy is lethally stupid. 

People who know more about this than I do are invited to correct either my interpretation of what is currently being done or my argument for what ought to be.

Why Not Add Gluten?

I'm currently on a low glycemic index diet, following advice from Bredesen's book The End of Alzheimer's. So far as I know I don't have Alzheimer's, but I do have one copy of the genetic variant that makes it more likely and I have observed what I think is age-related cognitive decline, most notably the fact that I can no longer easily memorize poems. Given the theory behind Bredesen's book, I think his approach has a reasonable chance of helping even if the cause is normal aging rather than Alzheimer's.

Being on such a diet raises an interesting set of problems — how to replace high glycemic foods I like, which include wheat, rice, potatoes, and things made from them such as bread and pasta, with low glycemic substitutes. I have found some solutions to that, including a southern Indian pancake made from mung bean flour, which we happened to have some of, that works for enchilada-like dishes, crepe wrapped around a filling. Also barley as a substitute for rice, barley being apparently the one grain with a really low glycemic index.

The challenge is bread. Looking around the web, I find multiple recipes using almond flour or coconut flour. But, as some of the recipes concede and my limited experience confirms, the result is not very much like a wheat bread. To quote one such recipe: 

When making this paleo and keto almond flour bread, it is important to adjust our expectations. The yeasty aroma and gluten-induced fluffiness that we love about traditional bread cannot be achieved without yeast and gluten.

So this is more of a quick bread that fills the need (if you still have it) to make a sandwich or to have a slice of bread for breakfast.

This raises an obvious question. Almond flour or coconut flour or mung bean flour doesn't have gluten. Wheat flour does. Why not add some of the gluten from wheat flour to one of the other flours and then make an ordinary raised bread, using yeast or sourdough?

One reason is that some people are, or at least believe they are, allergic to gluten — the webbed recipes routinely describe the bread as low-carb and gluten-free, and obviously regard the latter as a plus. I am not, to the best of my knowledge, allergic to gluten. Gluten has some carbohydrate as well as a good deal of protein, so adding it probably raises the glycemic index of bread, but as best I can tell it should only take about ten percent of the flour being straight gluten to produce something that will rise like wheat flour, which shouldn't raise it by much. 

My one experiment along these lines so far, an attempt at a sourdough bread made mostly from mung bean flour, was a flop, with an off taste that neither I nor other members of my family were willing to eat, but it doesn't follow that there is no way of doing it. Almond flour seems to be the preferred ingredient for the quick breads that I have found recipes for, so I may get some of that and continue my experiments, probably using yeast instead of sourdough.

The question is, why isn't this already being done — or is it? There are a lot of people out there who are diabetic or near-diabetic and are looking for low carb/low glycemic index foods. There are a lot of foods out there advertised as fitting that requirement. Are there raised yeast breads made from one of the nut or bean based flours with added gluten? If not, is the reason that it isn't doable, in which case I am wasting my time trying to make one?

Anyone know?

The Audiobook of my novel Salamander is Out

I have a bunch of promo codes, which can be used to get a free copy in exchange for agreeing that, if you like it, you will post a favorable review somewhere, most likely although not necessarily on Amazon. If you want one, email me for it. 

So far as I can tell, Audible is providing me promo codes for the U.S. but not for the U.K., which may mean that the ones for the U.K. went to Robert Power, who narrated the book. If you are in the U.K. and want one I can forward your request to him.

My email is ddfr@daviddfriedman.com.

I also have promo codes, U.S. and U.K., for the audio versions of The Machinery of Freedom and Future Imperfect, both narrated by me.

The Real Scandal Behind Qualified Immunity

Police officers attack someone, beat him up, arrest him with a false claim that he assaulted them or resisted arrest. Unfortunately for them, someone recorded the action on his cell phone. Eventually charges are dropped and the victim sues. The police officers defend themselves under the doctrine of qualified immunity, the legal rule that holds that they are not civilly liable unless their act was not only illegal but obviously illegal, sometimes interpreted as requiring a past case where the same act was found illegal by a court. 

The defense sometimes fails, often succeeds, a result that has gotten quite a lot of criticism, much of it probably deserved. What mostly doesn't get criticized is the fact that actions which are, on their face, obviously criminal — beating someone up is assault and battery, whether or not the perpetrator is a police officer — are being punished, if at all, only by a civil suit. 

The reason is quite simple. Legally speaking, the victim of the crime is not the person who was beaten up, it is the state he lives in. If Mr. Smith assaults me and the case comes to trial, it will be not Friedman vs Smith but State of California vs Smith. Criminal prosecution is controlled by the state, so crimes the state does not want to prosecute don't get prosecuted. If Mr. Smith happens to be a police officer, the state knows that prosecuting him, convicting him, and locking him up for a year will make it harder to hire police officers, as well as provoking conflict with the police union. So, most of the time, it doesn't. A civil case is created and controlled by the actual victim, so in practice civil cases are usually the only way of punishing criminal acts by people the state approves of, such as its employees.

This issue was first brought to my attention in a case where the crime in question was not assault and battery but first degree murder, the killing of two Black Panthers by Chicago police back when I was a graduate student in Chicago. None of the killers were tried, but the city, state, and county ended up settling civil claims for well over a million dollars. 

There is a possible solution, one that actually existed in a legal system ancestral to ours. In England in the 18th century, any Englishman could prosecute any crime. In one famous case, a magistrate instructed troops to open fire on a crowd of demonstrators, several people were killed, and the magistrate ended up tried for murder. 

If he had been convicted the King could have pardoned him, but pardoning an official, or a policeman, who has been convicted of murder is a much more visible act than never charging him. And England in the 18th century still had in law, although not in practice, a legal action, the Appeal of Felony, which was an entirely private suit for a criminal penalty. The King was not a party to the suit and so, according to Blackstone, could not pardon a convicted defendant.

For more on the subject, see the chapter on 18th Century England in my Legal Systems Very Different from Ours. A late draft is webbed.

Covid: Cases vs Deaths

News stories keep reporting record numbers of cases but not record numbers of deaths. Santa Clara County, where I live, shows detailed information on both, and the divergence is striking: Looking at the graphs, the case rate began to climb rapidly about a month ago, the death rate appears to be holding roughly steady. We would expect deaths to lag cases, but not by a month.

The divergence is less striking in the U.S. figures, but it's still there. Roughly speaking, over a period when case rates are more than tripling, death rates are doubling. I don't have the data in a form that would let me do a more precise comparison, but that seems to be the pattern so far.

Three possible explanations occur to me. One is that we have more testing, with the result that more of the milder cases are being spotted. If so, the reported increase in cases exaggerates the real change. A second is that we have gotten better at treating Covid, which would be good news but consistent with the increase in cases being real. A third is that fewer of the patients are old. Has anyone here spotted an analysis of the data that can distinguish among those alternatives? 

Two Sections of my Next Book Up For Comments

As I have mentioned here before, I am currently mining fifteen years of blog posts for one or more books. I now have drafts  of the first two sections of one book webbed for comments, a section on libertarianism and a much shorter section on religion. Feel free to comment here or by email to ddfr@daviddfriedman.com.

Evidence that Aging Can Be Reversed

There is a recent report out on an Israeli experiment which seems to have reversed two of the cellular processes associated with aging — shortening of telomeres and cellular senescence. It used hyperbaric oxygen, given daily over a period of months, and the effects appear to be large.

It's possible that the result will turn out to be mistaken — the confidence intervals for the various effects include zero, although most of them are significantly positive. It is also possible that the experiment is changing the cellular markers and not whatever underlying biology they are associated with.

The obvious next things to do are to repeat the experiment, ideally with more subjects and varying the procedure, and to observe the subjects of the first experiment to see whether physical effects of aging are being reduced.

But if it's real, it's huge, since the experimental results are for humans, not mice, the procedure should be easy to duplicate at relatively low cost, and we ought to have much clearer results in only a few more years. I've been saying for a long time that the cure for aging will probably come in time for my children but not for me, but perhaps I was wrong.

I would be interested in comments from anyone here with relevant expertise.