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Math error in herd immunity calculation from CNN epidemiology expert

Michael Weissman and Sander Greenland write:

Sanjay Gupta and Andrea Kane just ran an extensive front-page CNN article reporting that some residual T-cell immune responses cross-react with SARS-Cov-19, perhaps enough to provide many people with some protection. The article seemed straightforward and reasonable enough until it got to this strangely erroneous statement:

For herd immunity, if indeed we have a very large proportion of the population already being immune in one way or another, through these cellular responses, they can count towards the pool that you need to establish herd immunity. If you have 50% already in a way immune, because of these existing immune responses, then you don’t need 60 to 80%, you need 10 to 30%—you have covered the 50% already.

The source was Prof. John Ioannidis of Stanford Medical School, who since at least March has been making assertions (often challenged by statisticians and epidemiologists) minimizing the dangers of Covid-19.

What’s wrong with his analysis? Let’s look at a very simple and extreme case, just to clarify the logic of the problem, ignoring for now the practical issues, such as that immunity is only partial. Suppose 50% of the population is completely protected without infection, the other 50% is completely vulnerable, the initial reproductive number R0 (the average number of persons infected by each case as the epidemic begins) in a completely vulnerable population would be 4, infection always confers immunity, and our actual population is fully mixed. Then, since 50% of the people encountered by an infectious person would be immune, the R0 in our population would be 50% of 4, i.e. 2 (which is within the range of initial R0 estimates for Covid-19 in whole populations).

From that estimated R0 of 2, the standard estimate of the herd immunity threshold would be (1-1/R0) = 50%. The Ioannidis analysis would then say that, since 50% of the population is already immune, you should correct that estimate by subtracting that 50% from the estimated 50% herd immunity threshold. So you need to achieve only 0% more population immunity to reach herd immunity, meaning you start off with herd immunity and there isn’t an epidemic. With a slightly lower R0, Ioannidis’s analysis would give a negative herd immunity threshold.

That’s mathematically wrong. We got the R0=2 from watching the initial exponential growth in a mixed population, so there is an epidemic. Furthermore, within the vulnerable fraction of the population, the herd immunity threshold will only be achieved when 50% of that subpopulation has been infected. That 50% represents an additional 25% of the whole population beyond those who were immune to start. That’s a lot better than the 50% from applying R0=2 to the whole population, but it’s not 0%. With a R0=5 in the subpopulation, we get R0=2.5 in the whole population, and herd immunity requires 60% immunity in the subpopulation, which translates to 30% additional immune in the whole population, not 10% as in Ioannidis’s analysis. And so on.

In real life, things get a lot more complicated, among other things because of partial mixing of populations with a spectrum of susceptibilities, and because the reproductive number declines as preventive actions are taken and the disease spreads. But before dealing with those complications, one needs to develop equations that give sensible answers under simple assumptions.

In the immortal words of Barbie . . . Math class is tough!

P.S. More discussion in comments. Let me explain: Math is hard for me too! I’m not saying that the CNN epidemiologist made a trivial error; I’m saying that it’s hard to hold all these numbers in your head at once. That’s why we have algebra and all those x’s and y’s. When I say, “math class is tough,” I’m not being dismissive. Math is legitimately tough.

177 Comments

  1. Keith E. says:

    I’m not sure the correction is correct.

    In a given population, what is the difference between 80% previously infected (hitting the threshold for herd immunity), and 50% having innate prior immunity plus 30% more having been previously infected? The critical parameter for herd immunity is the percentage of the population that isn’t going to catch and spread the disease. The _manner_ in which an individual acquired immunity is irrelevant, isn’t it?

    • Michael Weissman says:

      The manner is indeed irrelevant. But his calculation of the threshold is just plain wrong.

      • Eric B Rasmusen says:

        I don’t get it. Your calculations are saying that the manner matters— whether you’re in the first 50% or in the second 30% of the total of 80% who have antibodies. You must be saying something more, but please do expand on they this isn’t interchangeable.

        I wonder if there’s some implicit model where you’re assuming that 50% immunity means 100% of people on the east side of town and 0% on the left, and to stop spread we need 80% randomly distributed on both sides, or something like that.

        • Michael Weissman says:

          No, we assume the opposite simple limit, complete mixing.

          • Wayne says:

            I don’t disagree overall, but I’ve experimented a lot with compartmental models, which assume complete mixing, and that’s a BIG assumption. All models are wrong, but is complete mixing useful? It feels like we’re seeing a collision between the idea of super-spreaders and social network hubs on the one hand and old-school, simple (partial differential equations) compartmental models.

            Most useful compartmental models that I’ve seen run individual SEIRs on nodes of a network to provide some non-complete-mixing-ness to an otherwise complete-mixing modeling technique.

            If mixing is not complete, the herd immunity calculation may not be valid. Again, not the original point, but complete mixing bothers me a lot.

            • Sander Greenland says:

              Wayne: No disagreement, I’m just emphasizing that complete mixing is an assumption of convenience to illustrate what can happen if we use a formula that assumes homogeneity (which is itself an extreme and unrealistic assumption) to assess herd immunity under heterogeneity. See my first reply to Carlos Ungil above, where (by my calculation anyway) the problem looks even worse with no mixing at all.

        • Anoneuoid says:

          Yea, this correction isnt very clear. The key point is that the apparent R0 value was estimated from data on a 50% immune population that was assumed to start out 0% immune.. So then the “real R0” would be double that.

          The niave herd immunity threshold is calculated as 1 – 1/R0, so it would be 75% instead of 50% using apparent R0 of 2.

          Also, I dont remember where that 1 – 1/R0 comes from but it obviously breaks down for R0 under one so its some kind of approximation even for the simple well mixed population SIR model case.

          • Juan Vesga says:

            I think the explanation by Weissman and Greenland is clear.
            You say “The niave herd immunity threshold is calculated as 1 – 1/R0, so it would be 75% instead of 50% using apparent R0 of 2”. that is not quite correct. You cannot have a 75% HIT in a population with 50% previous immunity.

            I think the concepts of transmission are necessary here , not to play too much with maths and end up in a Ioannidis mixup. R0 is not a biological attribute of the virus, is an epidemiologcal indicator of the potentail of transmission in a population. In this case that population has 50% of immunity previous to the seeding event of the epidemic. So the “apparent” R0 is all that matters, because that is what is actually happening in terms of transmisson in our comunity. If that R0 is 2, then 50% of that population will need to get infected to bring R0 to 1 and for the epidemic to die. But 50% are already immune so that threshold is 50% of that, that is 25%, and so on. If we take R0 as inmutable, biological parameter we risk getting to the 0% HIT , which makes no sense.

            • Carlos Ungil says:

              > You cannot have a 75% HIT in a population with 50% previous immunity.

              Why not? If 75% is the share of people who should be immune for the epidemics to go from growth to decline (given its transmission dynamics) what difference does it make (assuming homogeneity) whether they had previous immunity, they got it through vaccination or they developed it on their own after being infected?

              • Juan Vesga says:

                Well, you can get to that number (75%) in paper, so perhaps not clear from. my part. But my point is that what matters for the purpose of this discussion is the fraction of the population that needs to be infected over the course of the epidemic to bring R0 to 1 when 50% of the population are known to be immune. Hence my second point that what matters is the apparent R0, as an indicator of what is happening. Anoneuoid’s calculation of 75% HIT for an R0 = 4, is correct in principle, but I say that if we have more information about immunity, that calculation is not useful anymore.

            • Anoneuoid says:

              R0 is not a biological attribute of the virus, is an epidemiologcal indicator of the potentail of transmission in a population. In this case that population has 50% of immunity previous to the seeding event of the epidemic. So the “apparent” R0 is all that matters, because that is what is actually happening in terms of transmisson in our comunity.

              This isn’t what R0 means. It is a parameter of a SIR model. Each infected person meets R0 other people during each timestep, infecting all who are susceptible. If 50% start out immune, then they still meet R0 people but will only infect half of them early on. Interestingly when I was modelling the early phase of the spread I needed to start out with 25% already recovered.

              • Juan Vesga says:

                I’m afraid R0 is not defined as a parameter of an SIR model. You can describe and solve and SIR model without R0. And it is widely accepted that R0 is the expected number of infections after introducing an infectious individual in a suscpetible population, i.e., the potentail of transmission in a population, as I said above.

      • Keith E. says:

        Ah, I get it. It’s not that the prior-immune people don’t contribute equally to the threshold, but that their presence changes what the threshold would calculate out to be. Basically, if 50% are immune, the disease must be more contagious then initially thought.

  2. Carlos Ungil says:

    I> If you have 50% already in a way immune, because of these existing immune responses, then you don’t need 60 to 80%, you need 10 to 30%

    BG> If R0=5 in a susceptible population you would need 80%, if half are already immune R0=2.5 in the whole population and you need to achieve 60% immunity in the subpopulation, i.e. an additional 30% to the 50% already immune in the whole population

    The maths do not look necessarily incompatible. Could Ioannidis’ “you don’t need 80%, you need 30%” corresponds to that example from Weissman and Greenland? (I don’t know.)

    • Michael Weissman says:

      No, the are actually different formulas expressed in terms of R0 and the initially immune fraction x. The correct formula cannot go negative, but Ioannidis’ method can.

      • Carlos Ungil says:

        What method can go negative? The CNN article says just this:

        “For herd immunity, if indeed we have a very large proportion of the population already being immune in one way or another, through these cellular responses, they can count towards the pool that you need to establish herd immunity. If you have 50% already in a way immune, because of these existing immune responses, then you don’t need 60 to 80%, you need 10 to 30% — you have covered the 50% already. The implications of having some pre-existing immunity suggests that maybe you need a small proportion of the population to be impacted before the epidemic wave dies out,” said Dr. John Ioannidis, a professor of medicine and epidemiology and population health at Stanford University.

        • Sander Greenland says:

          Carlos: In case it helps, let’s work through the case where R0 would be 8 in a pure susceptible population. Then at x=50% susceptible in a completely mixed population we observe R0=4 (which is at the high end of the whole-population Covid-19 estimates), leading to a need for 1-1/4 = 75% of the susceptibles to acquire immunity before R drops below 1 (assuming quite unrealistically that the R value doesn’t drop along the way, as it must in reality). That’s an additional 37.5% of the whole population beyond the initial 50% that must become immune.

          Contrast that to what you get if you assume everyone is susceptible at R0=4: 75% must become immune, so starting from 50% only 25% more need become immune. The key intuitive mistake is to apply this number derived under homogeneity (R0=4 for any subset) to a population that was assumed heterogeneous (with R0=0 in one group and R0=8 in the other if they were completely unmixed).

          Now suppose instead of complete mixing we have the opposite extreme of completely separate equal-sized compartments, one immune and the other susceptible with R0=8. The latter will need 1-1/8 = 87.5% to convert to get to herd immunity, which is about 44% of the total population, even further from the 25% derived under homogeneity.

          Mechanically, the problem here is that the nonidentified susceptibles are in a sense twice as vulnerable to infection as the fully mixed whole-population data make them appear, so they need a lot more immunity among themselves to get to herd immunity under our admittedly oversimplified model. Making more realistic assumptions could reduce the discrepancies between our example answers and Ioannidis’s, but under heterogeneity (some of which must be present) will not simplify the general answer to just adding up how many more immunes you would need under homogeneity.

          The broader point I think is that heterogeneity is tricky and can flummox even the best intuitions; that was noted in demography long ago for noncontagious diseases (e.g., see Vaupel & Yashin TAS 1985 for a primer); or at least, it defeats mine – I’m with Andrew on emphasizing that math is tough!

          • Carlos Ungil says:

            Thanks, I think I understand your maths which I summarized in my reply.

            It seems that according to you when he says

            a) “if you have 50% already in a way immune then you don’t need 60%, you need 10%”

            and

            b)”if you have 50% already in a way immune then you don’t need 80%, you need 30%”

            he actually means

            a’) “if we observe in the population R0=2.5 then we calculate that 60% immunity is needed for herd protection, but if 50% is already immune you need an additional 10%”

            and

            b’) “if we observe in the population R0=5 then we calculate that 80% immunity is needed for herd protection, but if 50% is already immune you need an additional 30%”

            which is wrong because

            a”’) “if we observe R0=2.5 the relevant R0 is 5 and the immunity needed for herd protection is 80%, not 60%, we need to add 30% instead of 10%”

            and

            b”’) “if we observe R0=5 the relevant R0 is 10 and the immunity needed for herd protection is 90%, not 80% we need to add 40% instead of 30%”

            But it could also be

            a0) “if 50% of the population is already immune and 60% immunity is required for herd immunity (consistent with an initially observed R0=1.25) an additional 10% is needed”

            and

            b0) “if 50% of the population is already immune and 80% immunity is required for herd immunity (consistent with an initially observed R0=2.5) an additional 30% is needed”

            In one case, the interval he considers would correspond to observed R0 in [2.5 5] in the interpretation where his maths are wrong and to observed R0 in [1.25 2.5] in the alternative interpretation where there are no math errrors. You may find that the former is more plausible than the latter but *it could be* that he prefers the other and finds observed R0 = [1.25 2.5] consistent with herd immunity requiring [60% 80%] immune in the population where 50% are already immune.

            It seems that your critique is based not just on the quote but also on its attribution.

            • Sander Greenland says:

              Carlos: Yeah, I think you are correct, our mistake is we should have said something more conditional like “if the herd immunity of 60-80% had its origin in the formula 1-1/R0, then the subtraction is wrong because that formula assumes homogeneity.” I think the reasons we pounced (like cats on a string) on Ioannidis’s statement as unconditionally wrong are that (1) the 60-80% looks like what has been bandied about from inserting Covid-19 R0 estimates in the formula, and (2) we’ve been conditioned to assume the worst case from witnessing less ambiguous missteps in his previous statements in published controversies over “coining”, “credibility ceilings”, “statistical significance”, etc. and online over “zombie statistics” (https://absolutelymaybe.plos.org/2019/11/30/the-power-of-zombie-statistics-systematic-review-edition/), and of course covid incidence and fatality (e.g., https://twitter.com/GidMK/status/1283233517225168897). Our bad – even if we weren’t generous enough to give him the benefit of the doubt, we should have been appropriately cautious in attributing error.

              Given the flaming heat of the covid topic, there is one more caution I’d add: In some of the earlier controversies it’s not clear whether the statistical missteps made much of a practical difference, e.g, as in the “coining” controversy. Our present point may not matter either given the crude state of current knowledge. On the other hand, determining covid incidence, fatality, and transmission rates involve such stakes so high as to warrant painstaking scrutiny of all details behind any estimates and their uncertainty assessments.

              • Martha (Smith) says:

                “On the other hand, determining covid incidence, fatality, and transmission rates involve such stakes so high as to warrant painstaking scrutiny of all details behind any estimates and their uncertainty assessments.”

                +1

              • Brent Hutto says:

                Yes, to mix metaphors there is a danger of getting into angels on the head of a pin type methodological arguments while the real elephant in the room is not having reliable estimates for any parameters of any model.

                Anyone who painstakingly scrutinizes the available data and applies a realistic degree of uncertainty may well conclude that we still have a pitifully meagre ability to understand the past or predict the future of this pandemic. Must less to assess the efficacy of various interventions intended to control it.

                When someone like Ioannidis starts with made-up parameter values for a methodologically incorrect formulation of a model and proceeds to make authoritative-sounding declarations, it isn’t enough to take his made-up values and propose a more correct model. Reifying made-up parameter values is just as seriously misleading as applying them to patently incorrect models.

      • Michael Weissman says:

        Whoops, shouldn’t blog and zoom simultaneously. x in the formulas below is the fraction NOT immune.

    • Michael Weissman says:

      x(1-1/R0)= x-x/R0 is correct.
      Ioannidis uses (1-1/R0)-(1-x) = x-1/R0.

      • dhogaza says:

        Hmmm at my first glance I thought 1-x/R0 … but regardless, applying 1-1/R0 is certainly wrong if the entire population is not susceptible.

      • Angelos Athanasopoulos says:

        Michael

        It seems to me that both formulas are correct, they just differ to the extend of assumed mixing between the immune and the susceptible groups ( x, 1-x, keeping your notation).

        Your x-x/RO formula implicitly assumes completely assortative matching (susceptibles only matching with other susceptibles, immunes with immunes).

        Ioannidis formula is correct if one assumes proportionate matching (i.e. the probability of a susceptible matching with an immune person is 1-x).

        Indeed Ioannidis formula can give negative values. But this means you have no epidemic to begin with. The classic 1-1/RO heard immunity threshold only makes sense if R0>1, i.e. you have an epidemic.

        Ioannidis formula implies that you cannot have an epidemic if (1-1/R0)<(fraction of immune), which is the definition of herd immunity: IF (1-fraction of immune)<(1-1/R0) then an infection introduced in such a population will not spread.

        Reference (not my work but seems correct to my basic math skills): https://www.medrxiv.org/content/10.1101/2020.07.15.20154294v1
        Look at Table 1 and formulas in the paragraph just underneath.

        Do I have this right?

        • Angelos Athanasopoulos says:

          Correction Immune=1-x, Not immune(Susceptible)=x.

        • Michael Weissman says:

          Angelos- I don’t think so. It’s true that the formula I gave works for completely isolated immune/susceptible populations. As we explained in the OP, however, we actually derived it for the opposite limit, a completely mixed population.

          A formula that can give negative HIT, i.e. show that an epidemic is impossible, using R0 derived from observing the epidemic, cannot be correct. It reminds me of an old 1940’s cartoon, Barnaby and Mr. O’Malley, in which Atlas the mental giant says he could prove that it wasn’t raining if only his slide rule weren’t getting so wet.

          • Angelos Athanasopoulos says:

            Michael

            Thank you for your reply

            For sure the Ioannidis formula ( and the Gupta paper) could not disprove that existence of an epidemic (that would be absurd as you nicely show with your anecdote). However if somehow you come to believe that there is a pre-existing immune part of the population (and given your assumptions about mixing) then your estimate of the R is bounded from below so that the formula is positively valued. In other words, if you get new information and you learn that part of the population is immune you should update upwards your estimate of R and downwards your estimate of HIT.

            From a decision making point of view you should use both pieces of information together: The disease is more transmissible that you thought, but it will burn out sooner ( with lower loss of life?).

            But I believe that you can say that you learned that the disease is more transmissible and then go out and act upon this new insight because this new knowledge is conditional on you believing that there is pre-existing immunity ( which would possibly imply the opposite course of action).

  3. Steve Sailer says:

    How many cities have had two major spikes?

    • Divalent says:

      A number of cities in Iran are in bad 2nd waves.

    • Phil says:

      I think Madrid is having a second spike now.

      • David J. Littleboy says:

        Tokyo is having a second spike now.

        (One could argue that these spikes are tiny compared to almost anywhere else, which would be true, but Japan has a very small number of ICU beds, and these spikes are fully adequate to cause major disasters. All-cause death (in April and May, I think) exceeded all-cause deaths for the averages of those months over the previous 5 years by twice the COVID-19 deaths, and suicides (a major problem in Japan, despite the lack of guns) were down during that period.)

        • confused says:

          I think places hit lightly can definitely have a second wave. The question is whether places already hit hard still can.

          Japan has 1,023 reported COVID deaths according to Johns Hopkins tracker. That’s less than 10 per million people. Even if it’s way under-reported… that’s still very low compared to Europe or the Americas.

          >>Japan has a very small number of ICU beds,

          Do you know why that is?

          I was surprised back in March to find how low ICU capacity in places like Italy was relative to the US, given that their health systems seem to be generally considered “better” than US, and their population skews older. (And Japan is even older than Italy.)

  4. Uh oh. Ioannidis alert! Ioannidis alert! Runnnnnnnnnnnn! lol

  5. I have tears in my eyes b/c I’m laughing so hard. I’m gonna email John to get his 1 + 2 = 4 badass over here.

  6. Joshua says:

    I’ve been watching (from a non-statically literate distance ) some of the debate about the math related to the impact of heterogeneity on teaching a herd immunity threshold. – in particular some responses to this modeling which shows the HIT to be between 10%-20%.

    https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v3

    I posted a link a few months ago to an earlier paper by that same group hoping to get feedback but didn’t get many nibbles. I’d still love to see what y’all smart folks here think.

      • Michael Weissman says:

        Yes, looks like a very nice response.

      • confused says:

        Yeah, that seems fairly reasonable (I’m not an expert).

        I’m not sure really high seroprevalence in Iquitos is incompatible with a low herd immunity threshold in most of the US, though. Latin American cities are a *lot* denser and have *very* different contact patterns (way more multigenerational households, less car-dependence, etc.) than most US ones.

        I’m not sure that everyone talking about this is really talking about the same thing, though. Sweden seems to be burning out well below 40%; I’d be surprised if even 20% of the Swedish population has had it (if the real IFR is 0.5%, 20% of the population infected would imply 0.1% of the population dying or a bit over 10,000 deaths, and the death rate over the last several weeks doesn’t look high enough to get there any time soon).

        But if the rate of infections drops low enough that it’s no longer acting like a pandemic — just part of the background of disease — is that really “herd immunity”? I guess not really, because infections are still happening. But it’s not really pandemic/epidemic either, in that situation…

        • Joshua says:

          Infections just don’t stop at the HIT, in the least because of “overshoot.”

          https://www.nytimes.com/2020/05/01/opinion/sunday/coronavirus-herd-immunity.html

          • confused says:

            Right.

            So the problem I’m seeing is… if the HIT is probably much higher than 20%, and infections keep going well past that, why is Sweden’s rate of new deaths so low when they can’t be even at 20% unless their IFR is really anomalously low?

            I mean, maybe they’re not technically at herd immunity. But I’m not sure the rate of COVID deaths seen over the last month in Sweden qualifies as a crisis any more.

            Now maybe when people go totally back to normal the infection rate will increase.

            But it’s still *really* hard for me to believe herd immunity at 60%-70% + overshoot beyond that -> 70%-90% of the US might get infected in 12-18 months as being at all compatible with what’s happening in Sweden.

            To me it seems like those early models assumed Lombardy/Wuhan like R0 would apply everywhere, when in the US that was pretty much just NYC/NJ area. Houston looks to have peaked, and Phoenix has clearly peaked, and neither is on track to a NYC-like death rate. (Maricopa County is about 4.5 million and Harris County is about 5 million, so the same death rate would suggest >10,000 deaths.)

            • Joshua says:

              I think we’ve been through this before?

              Even if you go with the Gomes et al. estimate of 10%-20%, the HIT depends on heterogeneity and heterogeneity depends on behavior.

              Seems to me that behaviors in Sweden are not all that different than in other the other countries that are the most similar (Norway, Finland, Denmark). Similar amounts of social distance despite different government mandates. And Sweden has many structural advantages regarding covid outcomes (baseline health status, health care access, ability to work from home, % who live in single-person households, low % of grandparent primary-caregivers, distance from Lombardy, population density, amount of travel to/from China, etc.). There may be some structural disadvantages as well (amount of international travel early on, limited medical intervention with older people who are positive)…

              Yet seen has far worse results with respect to infections, and thus serious illness and deaths, and perhaps serious long-term sequallae resulting from less serious illness. Different people attach different values to those differences in outcomes, but thus far there seems little benefit to Sweden’s approach from an economic standpoint.

              That may change over time, but if a vaccine is developed and made widely available, Sweden traded-off deaths and illnesses for little benefit except perhaps the ability to say that they didn’t mandate certain behaviors.

              As it stands now, if today all deaths and infections stop in Sweden at current rates in the other Nordic counties it would take them years or decades to each Sweden’s per capita deaths and illnesses from covid.

              I think you’re maybe over-fitting with Houston and Phoenix as well. You have. I idea whether results are a functiom of behavioral changes rather than a result of reaching a HIT, and even if they’re approaching a HIT whether it could be because people have isolated themselves – which is a HIT that is tenuous at best and may not extend very far if behaviors change once again.

              At any rate, I think once again you may be “over-fitting.”

  7. Michael Weissman says:

    Aha- Maybe I’ve figured out how people can be missing this very simple math problem. Within a purely susceptible population, R0 is NOT equal to the R0 that you’d infer from the initial exponential growth. It’s bigger, R0/x. Does that help clear up some of the questions above?

    • Bob76 says:

      Hmm. I thought I understood things. But perhaps I am confused. Should the statement be “within a purely susceptible SUBPOPULATION . . ” It’s R0/(%in subpopulation)?

      Bob76

    • confused says:

      Yeah, I think that makes the difference.

      Though I have to wonder how well bounded the R0 in the initial phase actually is, due to testing limitations. IE, if there was a lot more COVID around in February than we knew about, then wouldn’t the R0 in March when we started testing non-travel-related people look artificially high?

      The whole thing seems to be a complicated mess, as some places seem to be “burning out” at a comparatively low infection rate without increasing measures (I think the decline in deaths in Sweden is now pretty clearly real) while others see a high infection rate (Bergamo, Italy; now apparently Iquitos, Peru). And South Dakota seems to have a weirdly flat rate of cases without doing all that much.

      Maybe the R0 differs more due to pre-existing contact patterns between different societies than we think?

      • Sander Greenland says:

        Definitely varies a lot although I think professional ID modelers know that well.
        E.g., compared to the Dakotas, Italy has a way higher population density, with much closer personal contact habits at the start of their curve.

        • confused says:

          I agree… but didn’t e.g. the Imperial College model use an R0 from Wuhan and Lombardy for the US population as a whole?

          It must be notably lower in the US as a whole, since basically every place in the US except the Greater New York area (which is only ~6% of the population) is really low-density compared to Wuhan and Lombardy.

          The Houston outbreak seems to have peaked (and Houston has a mask order, but nothing like NYC’s lockdown) and while deaths are high, it doesn’t look to be on track to anything like NYC’s deaths per capita*. Houston is a big city by total population, but fairly low-density and very car-dependent (basically no mass transit and not very walkable).

          *Harris County has over half NYC’s population (~5 million vs. ~8.4 million) so the same deaths per capita would be over 10,000 total.

    • Michael, thank you and Sander for weighing in.

      The question I have is; wouldn’t it have been useful for the US to have tested at least 60,000 to 160 million in January or February? In other words, it might have been easier to calculate ‘herd immunity’? At least approach a more accurate denominator. I could be wrongly characterizing the question. Just struggling to understand. Thanks.

      • Kyle C says:

        U.S. commercial labs didn’t have testing capability ready until March, so it’s a moot point.

        • Kyle,

          Yes, in hindsight US labs didn’t have the testing capacity. But that doesn’t invalidate the question I raised. Nearly every expert has conceded that we had tested symptomatics almost exclusively. So what makes current calculations yield an accurate denominator.

          Bob Redfield {CDC] hypothesized in late June or early July that there may be upwards of 20 million infected. Not the 2,7 million CDC figure given at the time. That’s no trivial number toward estimating herd immunity as well.

          Besides that CNN article, in my non-expert opinion, is covering a lot of issues. I have to think about it some more.

    • Anoneuoid says:

      It isn’t really a math problem/error. That is why people are not seeing it. It isn’t framed right and should really only take a few sentences.

  8. Weston says:

    Wait…

    Using the initial R_0:

    Herd Immunity % = 1 – 1/R_0
    % immune = y

    “Revised” Herd Immunity % = (1 – 1/(R_0 * (1 – y))

    Then to get the percent of the vulnerable population for herd immunity:
    (1 – 1/(R_0 * (1 – y)) * (1 – y)
    = (1 – y – 1/R_0)
    = (1 – 1/R_0) – y

    Does that not mean we can just subtract the initial immune percent from the herd immunity threshold to get the “revised” herd immunity threshold? Maybe im making a mistake

    • confused says:

      I think the problem is this part: “We got the R0=2 from watching the initial exponential growth in a mixed population,”

      IE – the R0 was calculated from the observed rate of spread assuming an immunologically-naive population. If a significant proportion of people were already immune, then that’s not an R0 (R0 assumes no one is immune). So the “real” R0 for the equation would be higher than the calculated one.

  9. Joshua says:

    David Young, on another blog, has been kind enough to explain how you’re all wrong. I’m sure he’d want to explain it to you himself, but his shyness and humidity prevents him from doing so – so I thought I’d post his correction for your edification.

    –snip–
    dpy6629 | August 3, 2020 at 9:48 pm | Reply

    This looks to be another invalid criticism. The original statement says nothing about calculating R0 and thus they appear to have assumed that R0 is known before the herd immunity threshold is calculated. The criticism is that pre-existing immunity will affect the calculation of the HIT, but its not a criticism of what they said. It’s about how to calculate R0. At best its an additional point which Ioannidis knows perfectly well as its obvious.
    –snip–

    Lest anyone forget – David has before explained how Andrew doesn’t know what he’s talking about:

    –snip–
    dpy6629 | April 19, 2020 at 11:29 pm |

    Josh, This Gelman is a nothingburger. He admits he’s not an expert on serological testing and that he doesn’t know if the Ioannidis paper is right or not. I think I’m done with your low value references

    • Joshua says:

      His humidity AND his humility.

    • Sander Greenland says:

      Not sure if that’s a serious comment, but indeed, Ioannidis said nothing about R0 in the quote. In fact he didn’t say where his herd immunity figures came from at all. But still his quote and your “David Young” (at a humid blog address?) are at best careless and misleading: If you assume extensive heterogeneity (as in the quote) you shouldn’t base your estimate of how much more immunity is needed by subtracting the initial immunity prevalence from some single herd-immunity threshold as in the quote. Yes that would work if you built the HI threshold from a model that included that initial immunity prevalence; but in that case it’s a circular result (much like Ioannidis’s 2005 claim that “most published research findings are false”, derived using assumptions that made it so). I don’t think Ioannidis was being circular here though. Looks more like he just pulled the numbers out of the air and then did the subtraction, which can land you very far from the correct answer, *even* if you get the initial immunity prevalence and “population average R0” right (as our examples show).
      [BTW when I see descriptors like “obvious” or “clearly” my BS detector goes off loudly, as they herald a lack of proper explanation – often because there isn’t one.]

  10. RE: In other words, if there is a level of herd immunity, that changes how fast the virus ripples through different communities and populations.’
    —-

    This hypothesis sounds plausible. I would speculate that there are several models that can depict this more or less accurately.

    Moreover, I don’t want to lose sight of the question; Why do some experience hardly any viral symptoms, which has not been explored quite so assiduously.

  11. Radford Neal says:

    Ioannidis’ calculation is correct if the R0 value being used is that for a completely-susceptible population (with neither immunity from covid-19 infection nor cross-immunity from some other virus, as it’s speculated might actually be the case for 50% of the population). It’s wrong if the R0 value is for a population that has the speculated 50% immunity already.

    In practice, the R0 value would have to be estimated, presumably from the spread in the initial outbreaks of covid-19. It is not clear what this R0 value means. If there is no heterogeneity in pre-existing immunity to covid-19 (eg, 50% everywhere), the estimated R0 will be for such a population, and Ioannidis’ calculation would be wrong. But it seems entirely possible that there is heterogeneity in pre-existent immunity, since there will be regional variation in previous viral infections. In that case, it also seems quite possible that the locations of the initial outbreaks of covid-19 were preferentially in the places where there is less pre-existent immunity to covid-19, in which case the R0 estimated from these initial outbreaks might be close to that for a completely-susceptible population, and Ioannidis’ calculation could be close to correct.

    • Michael Weissman says:

      Obviously, clearly (just kidding here, but I do often commit those sins)….

      No algorithm can be right if it can easily take real data from a real epidemic that initially grows exponentially and gives a result that HIT < 0 for it.

      Say there were the sort of dichotomous 50/50 susceptibility assumed in Ioannidis' toy calculation. Fine, I like starting with toy models too. Then say that the initial data happened to look like R0=1.25 rather than say 2.5. Ioannidis' method gives HIT= 20%-50%= -30%. So it's nonsense. A simple correct toy model (dichotomous susceptibility, full mixing) gives HIT = 10%, which is a reasonable starting point.

      So he's got a result that comes from some entirely unspecified method and that gives complete nonsense when applied to numbers just a bit different from the Covid numbers. It also happens to support the same position- nothing to worry about, just get back to work- that his other erroneous confidence intervals, made-up numbers, etc. happen to support.

      • Andrew says:

        Michael:

        Yes, this is related to our discussion the other day of negativity and positivity. The critical argument that you and Sander offered is based on assumptions, and we should be aware of that, but that’s also the case for the original statement in the CNN article, where the statement was presented with no justification at all. We should not hold be required to hold the criticism to a higher standard than we held the original statement

      • Radford Neal says:

        Well, I wouldn’t want to assert that Ioannidis really understood what what was going on, and would come to the right conclusions in particular cases, since I don’t know what he actually thinks. But I think your example doesn’t really show that the calculation has to be wrong.

        If some regions have 50% prior immunity, and other regions have 0% prior immunity, and the epidemic starts in one of the 0% prior immunity regions, and grows exponentially with R0=1.25, then the epidemic would not take hold at all in one of the 50% prior immunity regions (assuming such regions don’t differ in other respects). The mathematical expression of this is that the herd immunity threshold is negative. You might think that’s nonsense, and that it should instead be zero, but it actually makes sense in that the prior immunity isn’t just barely reducing the herd immunity threshold to zero, it’s more than sufficient.

        • Michael Weissman says:

          In your model (fully unmixed) the R0 of 1.25 in the susceptible subpopulation would give an HIT of 20%. If one didn’t realize that the population was inhomogeneous, that would lead to the incorrect conclusion that HIT =20% in the whole population. That HIT applies only to the subpopulation, so only 10% need be of the whole need be infected to reach the HIT. That’s just the same as for the opposite, fully mixed model.

          I don’t understand how you can claim that an epidemic that initially grows exponentially starts off with negative herd immunity. The logic seems to be (correct me if this is wrong) “We know we’re in the 50% that’s immune. Those other guys getting sick don’t count.”

          • Radford Neal says:

            I think we’re thinking of different contexts.

            I’m thinking of where somebody estimated R0 from Wuhan (say), where suppose there is no prior immunity, and then wonders what the herd immunity threshold is in (say) Afganistan, where suppose 50% of the people are already immune. I think it would make sense to say that the herd immunity threshold in Afganistan is negative, if you could make some people be un-immune who currently are immune and still have enough immunity to stop the virus from spreading.

            If I’ve understood correctly, you’re thinking of what the overall herd immunity threshold is for Wuhan+Afganistan. Given that a bunch of people (in Wuhan) did get sick, it’s obvious that in that sense the herd immunity threshold is positive – although the whole question doesn’t really make sense if Wuhan and Afganistan aren’t well mixed.

      • Carlos Ungil says:

        > he’s got a result that comes from some entirely unspecified method and that gives complete nonsense when applied to numbers just a bit different

        If the method is entirely unspecified how do you know what does it give when you apply it to different numbers?

        (I agree with the first part: the only calculations I see in their quote are 60%-50%=10% and 80%-50%=30%.)

        • Michael Weissman says:

          Sorry, as usual I sacrificed clarity for brevity. The algorithm “subtract the pre-immune fraction from what HIT would have been in a homogeneous model” is completely explicit in his remarks. What is entirely unspecified is the method by which he came up with that algorithm.

    • Mikhail Shubin says:

      By definition, R0 is a growth rate in the totally susceptible population, this is where 0 comes from, it assumes t=0

  12. BTW, I asked John Ioannidis to convey his response to Sander Greenland and Michael Weissman’s commentary. He agreed to my posting his response to Andrew Gelman’s blog.

    John Ioannidis: ‘I had a very long, 1-hour discussion with Andrea Kane about this topic and Andrea condensed this complicated discussion in a single paragraph. I think she is an amazing journalist and if there is an error in the simplification (necessary when you try to convey a message to a large audience), the blame is all mine. However, I believe that the message eventually is correct as phrased, even if some math genius like Sander gets into deeper water trying to see complex formulas behind my phrasing. My discussion with Andrea covered many aspects of why the HIT is not necessarily 60-80%, but probably much smaller. The paper by Gomes’ team is very relevant in this regard: https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v3. When you take into account both pre-existing immunity and population heterogeneity, in many places HIT may be in the 10-30% range. But maybe not in every place. We are still learning. The formulas that Sander uses are pretty standard, but they are also rather naive compared to reality, which typically has a more complex stochastic structure – this may also explain why some places are hit particularly hard, while in others no epidemic wave is ever established and spread is aborted very early. With many thanks to Sander, Andrew, and all other friends in the blog.”

    • Michael Weissman says:

      Yeah, no. The method he gave, which was reported not as a paraphrase but in quotation marks, was extremely simple and just plain wrong. It would always underestimate HIT. It doesn’t take a “math genius” to multiply by 0.5 rather than subtract 0.5. Yes, we explicitly said that’s a major simplification, but unlike Ioannidis’ subtraction, which he did not identify as a simplification, multiplication is not a nonsense simplification.

      How hard would it be to say “whoops, my bad, I gave a wrong calculation but heterogeneity does still reduce HIT from the initial estimates”? We all make mistakes and some of us have to say things like that pretty often. Why not just say it?

      • Sander Greenland says:

        Michael: Look above at my exchange with Carlos Ungil and see what you think. As far as I can see, Carlos proposed a way in which Ioannidis’s example numbers could have been derived correctly (by assuming a low R0 and then proceeding as we outlined), and if that were the case then we were mistaken ones in attributing an error to him.

        Ioannidis’s conveyed reply didn’t clarify how he got his numbers. Fortunately it doesn’t matter for the point that one ought to use consistent assumptions when doing a derivation, and in particular that an HI threshold derived under homogeneity will be misleading about the HI threshold under (the far more likely case) of heterogeneity. That’s the point I’d like to see emphasized, because homogeneity assumptions are ubiquitous and yet rarely plausible in social or biomedical systems. Their ubiquity is still understandable since they drastically simplify models and calculations (often down to additive relations), and sometimes even reduce total prediction error (despite being false) due to shrinkage effects. But as with null hypotheses in general (which they exemplify) they are also often harmful, and yet creep in everywhere precisely because they are part of standard defaults and initial calculations (to the point it seems that some think nature prefers nulls when she could not care less).

        • Michael Weissman says:

          Sander: You’re being extraordinarily generous. In context, it’s hard to see where numbers like 60%-80% could possibly come from other than a homogeneous model using initial apparent R0. That’s exactly the range usually given by that method for Covid-19. Perhaps more importantly, nobody has been using any other way, except again more sophisticated heterogeneous models, of estimating HIT. And no realistic heterogeneity estimates of HIT that I’ve been in the 60%-80% range. But if the model already has realistic heterogeneity in it, doing another subtraction is double-counting.
          So yeah, if there were some entirely different way of getting HIT that we haven’t heard of, didn’t use initial apparent R0, and it somehow ignored the heterogeneity, and it happened to give the same numbers that the crude homogeneous model gives then subtracting the prior immune fraction wold be right. None of that sounds remotely plausible.

          You may have noticed that Bergstrom read this exactly as I did, and had the same response.

          • So the article that John Ioannidis cites in his response has no relevance or validity?

            https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v3

            • Michael Weissman says:

              Sure it’s relevant. It’s a calculation of how extreme heterogeneity effects on HIT might be. People in the know (that would not include me) say that their extreme cases are somewhat unrealistic, e.g. giving HIT well under the infected rate in NYC. But they don’t do something really dumb like taking the HIT estimate from the homogeneous model and then simply subtracting the percentage of the population who may have some immunity. As I noted, that algorithm can easily give negative HIT, which cannot be a correct description of an observed epidemic.
              What the new T-cell results may indicate is a specific mechanism that may account for some of the heterogeneity that people were already trying to estimate, as in that paper.

            • Michael Weissman says:

              Sameera- Interestingly, if you take the coefficient of variation from the 50/50 all-or-nothing immunity model, CV= 1.0, and check what it would do to HIT in the Gomes calculation, it would only be ~30% reduction, i.e. from ~67% down to ~45%. Their calculation is for a gamma distribution rather than the double delta function, but it’s a reminder that this particular finding sheds very little new light on the heterogeneity corrections. When you further take into account that nobody really thinks that detection of some T-cell response means anything like complete sterilizing immunity, the CV shrinks dramatically, so these findings are almost irrelevant to the basic heterogeneity modeling. It could be very interesting, however, to see if differences in the prior partial immunity have something to do with broad patterns, such as low rates in SE Asia.

          • Carlos Ungil says:

            > In context, it’s hard to see where numbers like 60%-80% could possibly come from other than a homogeneous model using initial apparent R0. That’s exactly the range usually given by that method for Covid-19.

            Ioannidis has presented in the past results quite different from the usual ones, based on his unusual assumptions. If the range he gives in this example is the standard one it could be because he uses the usual assumptions and the usual method (which would be wrong for this problem) or his unusual assumptions and a different method (which could be right). I just don’t know, probably you’re right. But I wouldn’t say you’re obviously and clearly right. This is not an 8th grade algebra problem.

    • Michael Weissman says:

      A fable:
      Say that you’re teaching 8th grade algebra. You give a problem 4x=8, solve for x.
      One kid says “Easy x=8-4=4.”
      You say ” No, it’s x= 8/4=2.”
      The kid says ” I believe my answer eventually is correct as phrased.”
      Why?
      “The answer isn’t 8 but probably much smaller. Besides, on many of your problems the answer is 4, although not on every problem. And you know there’s all sort of fancy math where who knows what goes on. We can’t all be math geniuses ….”

    • Andrew Davis says:

      “Our inferences result in herd immunity thresholds around 10-20%, considerably lower than the minimum coverage needed to interrupt transmission by random vaccination, which for R_0 higher than 2.5 is estimated above 60%. We emphasize that the classical formula, 1-1⁄R_0, remains applicable to describe herd immunity thresholds for random vaccination, but not for immunity induced by infection which is naturally selective.”

      https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v1

  13. Anonymous says:

    ” I believe that the message eventually is correct as phrased,….”

    As the King said in Huck Finn:
    “I say orgies, not because it’s the common term, because it ain’t — obsequies bein’ the common term — but because orgies is the right term. Obsequies ain’t used in England no more now — it’s gone out. We say orgies now in England. Orgies is better, because it means the thing you’re after more exact. It’s a word that’s made up out’n the Greek ORGO, outside, open, abroad; and the Hebrew JEESUM, to plant, cover up; hence inTER. So, you see, funeral orgies is an open er public funeral.”

  14. Navigator says:

    Greetings,

    Is it possible that population heterogeneity (I assume it is understood as individual differences among people in susceptibility to getting infected in the first place) is only a function of viral load they happen to be exposed to.

    I don’t think it can be studied or modeled, but what if there is no real heterogeneity (everybody gets infected given enough viral load)?

    Also, medical personnel have learned to deal with COVID better (fewer put on ventilators, etc.), and along with some medications they effectively decrease IFR, without the real infection rate going down.

    Is anyone adjusting for that when reporting deaths/hospitalizations and such?

    Thanks

    • Michael Weissman says:

      The story that prompted this particular discussion of heterogeneity was based on the finding that roughly half of some samples taken from before SARS-Cov-19 existed in people still showed some T-cell reaction to it. So that’s a different sort of heterogeneity than what you’re describing. I don’t think that the sort of individual transmission randomness that you discuss requires any heterogeneity correction to the simple models. If, however, there are whole subpopulations, not fully mixed, that tend to get different exposures, then heterogeneity corrections are needed.

      At least one prominent prognosticator, Yougang Gu, is including a tendency for IFR to drop, partly for the reasons you give, in his predictions.

      • Navigator says:

        >The story that prompted this particular discussion of heterogeneity was based on the finding that roughly half of some samples taken from before SARS-Cov-19 existed in people still showed some T-cell reaction to it.<

        Thank you for the response Michael. I'll assume it would be due to previous exposure to viruses from corona family.

  15. Michael Weissman says:

    Just a note on semantics, not directly about Ioannidis. Many people are saying (sorry for that phrase!) that if half the population is previously immune, then we should say that R0 is twice the apparent R0 inferred from the initial growth under the homogeneity assumption. That’s ok but I don’t think it’s optimal notation. I’d prefer to say that R0 in this population is what it seems to be. The reason is that actual prior immunity is not all-or-nothing. I don’t see how the “R0 is what it would be in a completely non-immune population” generalizes to a useful definition that applies to a real population with a continuous spectrum of partial immunity. So I’d prefer to use the “R0 is what it seems to be in the population” definition, which is immediately usable. Then the heterogeneity effects can all go into actual models, not into redefining terms.

    • Andrew Davis says:

      Epidemiology is not my field, so perhaps I’m missing something, but isn’t this what the “effective” reproduction number, Re, is about?

      “In reality, varying proportions of the population are immune to any given disease at any given time. To account for this, the effective reproduction number Re is used… or the average number of new infections caused by a single infected individual at time t in the partially susceptible population. It can be found by multiplying R0 by the fraction S of the population that is susceptible. When the fraction of the population that is immune increases (i. e. the susceptible population S decreases) so much that Re drops below 1, “herd immunity” has been achieved and the number of cases occurring in the population will gradually decrease to zero.”

      ^^

      https://en.wikipedia.org/wiki/Basic_reproduction_number#Effective_reproduction_number

  16. David J. Littleboy says:

    Isn’t there a seriously basic math error going on here?

    If there’s 50% a priori immunity (this is seriously problematic idea itself (see: Sweden), but…),
    And you need 80% (which is way too low for a disease this nasty, but…)

    Then you need to immunize not 30%, but 60% of the population. Since you don’t know a priori who is a priori immune*.

    And, another problem is that the concept of an HIT itself is problematic: my understanding is that there isn’t a threshold in the sense of number of cases falling precipitously, but that rather there’s a continuous decrease in the number of cases as immunity increases. The threshold is thus a _political_ decision: how many cases are acceptable.

    *: I suppose you could argue that you can test people, but that still means you have to test enough people to find the 30% to immunize, and thus that means testing 60% and immunizing half of those. Assuming the vaccine is 100% effective, which it isn’t going to be. And how good is “a priori immunity” actually? 50% of people test positive for antibodies/T-cells/whatever and you send them home. Some are going to get sick anyway.

    • Carlos Ungil says:

      > Then you need to immunize not 30%, but 60% of the population. Since you don’t know a priori who is a priori immune*.

      It seems that the discussion is not about how many need to be immunized by vaccination (you’re right, you don’t know who should get it) but how many need to be immunized by going through the infection (the virus knows!).

      • David J. Littleboy says:

        ” how many need to be immunized by going through the infection”

        Shouldn’t that cause the discussion to be stopped immediately (as criminally stupid or unbelievably immoral)???

        Besides, we’ve already tried this (Sweden) and we know it doesn’t work.

        It looks to me that the bottom line here is that Ioannidis messed up from the start and now is hell-bent on digging a deeper hole for himself.

        • Carlos Ungil says:

          I don’t think this kind of calculations are stupid or immoral. They are needed to evaluate the best way to proceed in an smart and moral way!

        • confused says:

          >>Besides, we’ve already tried this (Sweden) and we know it doesn’t work.

          I don’t know. Sweden’s death rate in the past 3-4 weeks has been quite low.

          One might say the *cost* is unacceptable, but that’s quite different from saying it *doesn’t work* – in the sense that infections don’t drop dramatically, to the point that the disease is no longer really a crisis.

          Now, Sweden could still have a fall second wave or something. But saying that “we know” it doesn’t work seems much more certain than the data supports.

          Ioannidis was certainly wrong when he was talking about ~10,000 deaths / 1% infection rate for the whole US. But then there were a lot of predictions that were wrong in the other direction.

          (And total deaths in Sweden don’t look *that* high to me. They are at about 0.05-0.06% of the population; the 1957-8 pandemic was 0.06% of the US population and until COVID it was basically forgotten, leaving essentially no mark on history; my family members who are old enough to remember it, don’t remember it, though they remember polio.)

          • David J. Littleboy says:

            “And total deaths in Sweden don’t look *that* high to me.”

            “However, the Scandinavian nation ranks eighth among countries with the highest number of COVID-19 deaths per 100,000 people. It outranks the U.S. and Brazil, which are the world’s first and second…”

            Of course, that was as of July 30, and the US is working hard at catching up.

            I suspect that when we’ve killed off the elderly, the overweight, the smokers, and the minorities, we’ll see fatalities fall, too. Seriously, though, the question then arises, how nasty a disease is COVID-19 for survivors? Hearing loss, mental illness, heart disease (among dozens of others) are all reported as long-term aftereffects. So the idea that the disease “is no longer a crisis” just because deaths are going down is problematical.

            I submit that talking about heard immunity without a vaccine is really seriously obnoxious, if not unbelievably amoral. Really. It’s not a bug you want to catch. And if you don’t want to catch it, planning on having 30%, or even 10%, of the population catch it, is, again seriously obnoxious.

            • Anoneuoid says:

              Covid isn’t killing off the smokers. Smokers are being selected for survival by covid.

              • David J. Littleboy says:

                It ain’t that simple: current smoking is slightly protective, but previous smoking is aggravatative. (Is that a word? If not, it should be.)

                “What the researchers discovered about risk of death from COVID-19 among smokers is that in the minimally adjusted model, which only accounted for age and sex, smokers and former smokers were at 25 percent and 80 percent, respectively, higher risk of dying from COVID-19 compared to nonsmokers. However, when the researchers adjusted their model for all potentially confounding covariates, they found that former smokers were only at 25 percent higher risk of dying from COVID-19 than nonsmokers, and current smokers had a slightly lower risk of dying from COVID-19 than nonsmokers.”

                That’s a big adjustment! (And the article didn’t quantify “slightly”.) But since the article was based on a really large study and there’s almost no such thing as a “former smoker” (quitting is really hard), you’re right to call me on this.

                I’m probably being too in-your-face here. Sorry. I really get irritated by the idea of HI without vaccine: I really do think it’s beyond the pale.

              • Sander Greenland says:

                That’s a speculation based on some observed inverse associations, which some have argued are artefacts of subject-selection bias and covariate overadjustment (the “Table 2 Fallacy”), e.g., see https://zenodo.org/record/3968834#.XyrPSShKiqN

              • Anoneuoid says:

                That’s a speculation based on some observed inverse associations, which some have argued are artefacts of subject-selection bias and covariate overadjustment (the “Table 2 Fallacy”), e.g., see https://zenodo.org/record/3968834#.XyrPSShKiqN

                I couldnt get the link to work.

                But you don’t get such a large proportion of “missing smokers” in dozens (maybe hundreds by now) of studies of SARS and SARS2 spanning 17 years (but not for MERS, influenza, or other illnesses), in every country checked, according to both clinical/pcr diagnosis and antibody studies in an environment very biased against smoking, due to a statistical artifact. Then add in that covid mimics high altitude sickness, which is also helped/prevented by smoking.

                It is a real, very large, protective effect. This should have been accepted back in mid April. Actually it should have been studied back in 2003.

              • Sander Greenland says:

                I don’t think any level of certainty about protection by smoking is at all warranted.
                The link works for me, but here’s a tweet discussing the “Table 2” (misadjustment) fallacy which may explain the covid results – it is different from subject-selection bias:
                https://twitter.com/TaylorMcLinden/status/1290721462978924544
                Also, people self-select for smoking in myriad ways (one is just the opposite of what Fisher speculated to defend his habit 60 years ago: smokers have lungs that can tolerate the irritation from tobacco tars for years on end). There is no adjustment for the resultant downward confounding in the sources you cite.
                For these reasons the only item I’d be certain about is that any credible uncertainty analysis would not claim smoking is protective for severe covid-19. I’d be especially cautious because of reports of prolonged adverse vascular effects from covid-19 including thrombosis, and we already know smoking has prolonged adverse vascular effects including thrombosis.

              • Anoneuoid says:

                I’d be especially cautious because of reports of prolonged adverse vascular effects from covid-19 including thrombosis, and we already know smoking has prolonged adverse vascular effects including thrombosis.

                Seems to be partly because the smoker’s body is already adapted in multiple ways to thrombosis, hypoxia, etc. Same for allergic asthma. Probably also the same thing will be found in people who periodically travel to high altitudes and experience the same intermittent hypoxia, etc.

              • Anoneuoid says:

                Now the paper loaded. I see it is about some multiple adjusted hazard ratios. I don’t care about any of these arbitrary statistical models that adjust for this and that because for all practical purposes there are infinitely many different specifications you can choose from to get you any result you want. This is the “forking paths” or “multiverse”, that Andrew mentions.

                Looking at the raw data I see that 0.02% of smokers died, 0.11% of former smokers died, and 0.05% of nonsmokers died. I also see that 6.5% of the deaths were current smokers when they made up 17% of the population.
                https://www.nature.com/articles/s41586-020-2521-4

                This is consistent with ~60% reduction in risk of being diagnosed with covid as seen in the other studies.

                Anyway, point is you aren’t going to see this consistent effect across decades, continents, and cultures, for only SARS and SARS2 but not other stuff in between due to a statistical artifact.

              • Sander Greenland says:

                Anoneuoid, you are going ever further into speculative mechanisms to defend an initial questionable claim. That’s not a problem if you recognize and admit that’s what they are, speculative mechanisms which might turn out to be operating – or not. But such speculation becomes a health hazard when presented as if there are data that locks together tightly to exclude all alternative possibilities (such as smoking is in fact harmful and the reported inverse associations are instead artefacts), and there isn’t anything near such data.

                Now, if you have done or know of a thorough literature review and analysis which proves smoking is protective, please post it for critical review and (if your product) please submit it for publication. Otherwise, I’ll note that this kind of excessive certainty seems to be inversely related to the actual amount of data information, and has been the endless bane of “soft” sciences like health and medical science. As the HCQ mess has illustrated, the current pandemic has only amplified the problem as people have panicked in seeking ways to reduce their risk, and some health professionals and researchers (as well as media figures) have offered them certainty, e.g.,
                https://www.newsweek.com/key-defeating-covid-19-already-exists-we-need-start-using-it-opinion-1519535?amp=1&__twitter_impression=true
                https://medium.com/@gregggonsalves/statement-from-yale-faculty-on-hydroxychloroquine-and-its-use-in-covid-19-47d0dee7b2b0
                https://www.dailykos.com/stories/2020/8/3/1966092/-Vaccines-Hydroxychloroquine-What-to-say

              • Michael Weissman says:

                Re your “forking paths” comment below, you seem to disagree with Yogi Berra, who advised “when you come to a fork in the path, take it.”
                But seriously, what you’ve done is to take a particular fork, one that is neither optimal for simple prediction nor for causal prediction. The multivariate models are, pretty much by definition, best for simple prediction given a set of predictive variables, even though the coefficients change if you add new variables. (Only “pretty much” because they assume particular functional forms, e.g. linear logit and because “best” doesn’t have a unique definition.) If you’re considering smoking and trying to predict what effects it would have, then everything that Sander mentioned comes into play.

              • Anoneuoid says:

                If you’re considering smoking and trying to predict what effects it would have, then everything that Sander mentioned comes into play.

                It really does not. I’ve explained my reasoning twice now and it is going unaddressed. What artifact is going to lead to “this consistent effect across decades, continents, and cultures, for only SARS and SARS2 but not other stuff in between”?

                Then it just happens to make sense that SARS and SARS2 mimic high altitude sickness, which is also the rare thing helped by smoking. And other situations that lead to intermittent hypoxia (similar to smoking) such as asthma and high altitude also appear to confer protection against covid.

                Please explain what statistical artifact explains all this?

                On the other hand, it makes perfect sense that smokers bodies adapt to low oxygen levels which leaves them less likely to become seriously ill with covid (an illness characterized by low oxygen levels).

                But the smoking effect is so huge and consistent I bet there is more going on too. Eg, remodeling of the respiratory tract (perhaps ACE2 expression is increased higher up so immunity is raised there before the lungs get involved), nicotine binding to SARS2, SARS2 interacting with the same receptors as nicotine, etc.

              • Sander Greenland says:

                Anoneuoid: I listed several artefacts (alternative explanations) including the simple confounding explanation that those who choose to smoke tobacco, a potent lung irritant to many, and especially those who choose to keep up the habit have very resistant lung tissue and/or better initial lung capacity. There are also subject-selection biases which may operate as well. Having more belief instead in the preventive power of tobacco is not evidence against such alternatives. Evidence for your claim would require multiple knock-out studies demonstrating that these alternatives cannot explain all the observations (not just that your claim can explain them all). Absent RCTs of habitual tobacco smoking (which do not exist), it takes multiple lines of refutation of alternatives to establish an effect like the one you are advocate, not just hypothetical mechanisms. That is why it took decades to establish that smoking was a major cause of lung cancer (the first studies noting the association date from before WWII, not 1950 as some writings say) in the face of fierce denial by Fisher and tobacco companies.

            • Radford Neal says:

              It may turn out that none of the vaccines work. It may turn out that none of the treatments are very good. That could just be the reality. Reality is not moral or immoral. It just is.

              Discussing the implications of such a situation is not immoral. Indeed, it would be immoral for responsible health authorities to not consider what to do if that turns out to be the reality.

              • David J. Littleboy says:

                Tokyo had their new confirmed cases per day numbers down to 10 per 14 million for a week. But it shot back up and is now at all time high levels, thanks to the idiot central government. The prefectural governments are starting to realize that the central government is incompetent. But it’s a mess. But it did work for a while.

                If there’s no vaccine, you do what Tokyo did: close the bars/restaurants/theaters, cancel all even slightly large events, test everyone you think needs testing, and trace contacts as best you can. It actually works pretty well. Opening up without a willingness to close down again is a bad idea, though.

                So given the worst case reality you hypothesize, we can certainly keep the disease at low levels, by using aggressive, but perfectly ordinary, means. Several countries have already done this. Korea, New Zealand, come to mind.

                So, even if there’s no vaccine and only palliative treatments, we can live with the bug with only a very few people getting sick. Talking about HI for a disease that can be controlled is friggin’ nuts.

              • Radford Neal says:

                Really? Have you thought this through? You’re actually willing to keep such measures going FOREVER?

                Has it occurred to you that the economic and psychological impact of such measures could kill more people than are saved from covid?

                Has it occurred to you that even if you would favour such a policy, the general population would not, as demonstrated by the many other risk trade-offs that people make all the time (like driving faster than 20 miles per hour)?

                Maybe none of these things have occurred to you, if you think that even discussing such a scenario is “seriously obnoxious”.

              • Radford, in reality there’s no such thing as FOREVER. So the question is how long do we extend those measures? I think David’s point is that extending them to 12 or 16 months is probably a good idea and by then we will have a LOT more information about vaccines. before that point we discover that giving people vaccines makes everything worse or hardly works or whatever, then we need to switch strategies, but switching strategies before we have any information about how effective vaccination will be is defeatist in an “obnoxious” way in my opinion.

                Much of the economic consequences are really manufactured, that is, they occur because of our terrible policy not because they’re inevitable. Still, changing policy may feel like “inevitably impossible” in our current political climate.

              • I am hopeful that rapid COVID-19 saliva test strips to be utilized in homes, schools, workplaces, nursing homes, assisted care facilities may be a game-changer.

            • ” Hearing loss, … are all reported as long-term aftereffects.”

              Is there a good reference for how prevalent these are? There’s a big difference between major aftereffects occurring in one-in-a-million cases and one-in-ten, and I haven’t seen actual rates discussed. (I haven’t actually searched.)

              • David J. Littleboy says:

                I doubt that there’s a good reference yet: it’s still anecdote city.

                But there are aftereffects of any illness that depend on severity. Two weeks of bed rest (full immobility), even without disease, leaves most with aftereffects they never fully recover from. Things like post-covid hair loss and increased levels of mental illness after ICU care are (thought to be) par for the course of just being sick.

            • confused says:

              >>However, the Scandinavian nation ranks eighth among countries

              I meant the death rate is not that high compared to past really bad pandemics, not compared to other countries’ experience with COVID.

              A population death rate comparable to 1957 flu (which is practically *forgotten* except by public health types) doesn’t – IMO – obviously justify vast disruptions to society.

              >>I suspect that when we’ve killed off the elderly, the overweight,

              Those groups have a higher death rate, but it’s not like COVID is a death sentence even for higher-risk groups.

              >>Seriously, though, the question then arises, how nasty a disease is COVID-19 for survivors?

              That is an important question.

              >> So the idea that the disease “is no longer a crisis” just because deaths are going down is problematical.

              Infections are going down too in Sweden though.

              >>I submit that talking about heard immunity without a vaccine is really seriously obnoxious, if not unbelievably amoral.

              I disagree.

              >>It’s not a bug you want to catch. And if you don’t want to catch it, planning on having 30%, or even 10%, of the population catch it, is, again seriously obnoxious.

              Nobody *wants* to catch it. But there’s a limit to the amount of effort/disruption that is “worth it” to reduce your risk of catching it.

              Think of it as expected value.

              Given my age, health, and being male I probably have something like a 0.1% chance of death if infected (that’s probably high comparing to e.g. the US Theodore Roosevelt, but let’s be conservative). So the “expected loss of value” of my life if infected is 0.1% of the total – let’s double that for less-than-fatal long term effects, 0.2% of my total value.

              Given my age, health, and sex I probably have a remaining life expectancy of ~50 years.

              Therefore, if I lose more than 10% of my quality of life for this year (2% of my remaining life expectancy) to avoid catching COVID, that’s not rational in terms of expected value.

              (And actually, much less, since my chance of catching it wouldn’t be 100% if I took no measures.)

              • Michael Weissman says:

                You’ve omitted externalities from your calculation. For an infectious disease, they are not a trivial contribution!

              • confused says:

                If you mean the risk of infecting other people… sure, except the same calculation applies to other people.

                The older you are, the greater your risk of dying of COVID if you are infected … but also, the shorter your remaining life expectancy, so “this year” is a greater proportion of your total expected life.

                I think this would only show a gain for a relatively small proportion of the population… those old enough to have a significant risk, but *not* old enough to have say <10 years remaining.

                You can do the same "expected value" idea for all of, say, the US.

                Say… (Number of COVID deaths) x (average remaining life expectancy of people who die of COVID) vs (Population taking measures to avoid COVID) x (Average % of quality of life lost by taking measures) x (Time over which measures are taken).

              • Joshua says:

                confused –

                > A population death rate comparable to 1957 flu (which is practically *forgotten* except by public health types) doesn’t – IMO – obviously justify vast disruptions to society.

                We go through this once again. You don’t have control over “disruption to society.” If you have a raging pandemic, you will have “disruption to society” whether you like it or not.

                We are not Sweden. We do not have many of the structural advantages they have for dealing with covid with no shelter in place orders (very high % of single-person households, low rate of comorbidities associated with poor outcomes from covid infections, good access to healthcare, structural support for working at home, low % of grandparent primary caregivers, low % of multi-generational households, less travel to/from hotspot, etc.)

                Take the proportionately more deaths from covid in Sweden versus other Nordic countries, higher rate of serous illnesses, higher potential for long-term problems with harmful covid sequallae, and import that to the US, which does not have all those structural advantages.

                Think of the implications here. Think of the faster rate of illnesses and deaths here on a scale some 33 x Sweden and make it much, proportionally much worse here because we don’t have those structural advantages.

                You have no idea what the disruption to society from that would have been. And we don’t see, at least as of yet, significant economic advantages for Sweden from their policies. They seem to have had more or less the same social disruption as their Nordic neighbors.

                All the additional deaths in Sweden, and what we would likely have experienced had we followed a similar course, may be seen very differently if a vaccine is developed.

                At their current rates it may take the other Nordic countries years, perhaps decades, to reach Sweden’s per capita deaths and illness from covid even if all death and illness from covid ends tomorrow in Sweden . Their rates could increase and it could happen sooner. Or it could never happen.

                At any rate, I just request when you talk of things like “disruptions to society” you acknowledge that you don’t actually know whether the disruptions were more or less impactful from shelter in place orders than they would have been otherwise.

                Counterfactuals are hard.

              • confused says:

                Sure, the US has structural disadvantages vs. Sweden, but we have advantages too (lots of ICU capacity per-capita, a slightly younger population, a large dispersed country so resources can be moved from lightly-hit places to hard-hit places). I can see the US doing slightly worse “on balance” but not several times worse.

                And yeah, I can acknowledge that I don’t *know* there wouldn’t be equally-bad or worse social disruptions if we’d approached it very differently.

                But – while possible – that seems very implausible given what happened with the past four pandemics in US history.

                >>If you have a raging pandemic, you will have “disruption to society” whether you like it or not.

                I think this is actually really dependent on government/business/media/etc response. Sure, 2009 was very mild, but why was there so little social disruption in 1957 and 1968?

                The assumption that large-scale social disruption is an *inevitable* consequence of a pandemic with a relatively low death rate (say less than 1918-19 flu) seems not well supported by history.

              • Joshua says:

                confused –

                > (lots of ICU capacity per-capita,

                Did you factor in the occupancy rate and surge capacity?

                > a slightly younger population,…

                A sightly younger population because of more minorities who have higher rates of infection and mortality, poorer access to healthcare, more cormorbidities, less ability to work from home, higher rates of multi-generational households, more grandparent primary caregivers, more preople per household…

                Do you really think that the advantages vs. disadvantages come anywhere close to balancing out relative to Sweden? Really?

                > I can see the US doing slightly worse “on balance” but not several times worse.

                My guess is that it’s nowhere close. Simple life expectancy favors Sweden. Factors specific to covid, seems to me, certainly multiply that advantage.

                > But – while possible – that seems very implausible given what happened with the past four pandemics in US history.

                These comparisons, imo, are not very instructive. It’s pure guesswork, not close pstalleks.

                We have an entirely different media environment. People were staying home prior to the SIP orders. Life was already greatly disrupted in the places where community spread was happening. Add in people getting fired if they didn’t show up for work, with no ability to collect unemployment insurance. No stimulus checks or loans.

                > I think this is actually really dependent on government/business/media/etc response.

                Of course it depends on the response. That’s my point!

                > Sure, 2009 was very mild, but why was there so little social disruption in 1957 and 1968?

                Because the circumstances and environment were so different. Again, that’s my point. The pandemics were different different. Things were shutting sheen prior to the SIP orders. Unlike those other years. Again, that’s my point. The SIPs came about, in part, BECAUSE the conditions were different!

                > The assumption that large-scale social disruption is an *inevitable* consequence of a pandemic with a relatively low death rate (say less than 1918-19 flu) seems not well supported by history.

                I don’t know about inevitable (in all circumstances), but that’s basically an irrelevant point.

                You are ignoring a basic logic: reactions are different because conditions are different – whether you’re competing US to Sweden, or NY to Montana, or 2020 to 1987. You’re reasoning as if these are all independent variables, and they aren’t. There is an interaction.

              • Joshua says:

                confused –

                Still the start of the first quarter. Lots o’ stuff out there like this. It isn’t just deaths. Lot’s o’ non-fatal infections may be a very big deal. You are advocating a huge gamble.

                Even if you believe the same number will get infected either way (just getting to the HIT sooner or later), with a faster rate of infection you stress the healthcare system more and lose out on the potential of time to improve0 treatments. With the potential of a vaccine the gamble gets even bigger.

                And what is the payoff? Less economic damage? Less disruption? Maybe. In reality you just don’t know. A big gamble for a dubious payoff.

                The bigger problem, imo, is that you’re effectively gambling with the lives of healthcare workers and minorities (along with elderly people and people with comorbidities) as your poker chips.

              • confused says:

                >>Do you really think that the advantages vs. disadvantages come anywhere close to balancing out relative to Sweden? Really?

                Close to? Yes. I said I would expect Sweden likely to have a slight advantage… but quite marginal at best.
                >>Of course it depends on the response. That’s my point!

                OK then I don’t know what we are actually arguing about.

                I think it’s more likely that if the public messaging had been consistently “this is like the 1957/1968 flu pandemics, wash your hands and stuff and cancel big sporting events/concerts but otherwise go on with life as normal” society would not have been drastically disrupted at anything like the levels that actually did happen.

                I thought you were saying that vast social disruptions were inevitable regardless of the response.

                So do we actually disagree here?

                >>You are advocating a huge gamble.

                Sure. But IMO what we’ve done is *also* a huge gamble. Modern society/economy/infrastructure is a really complex network. There are lots of second-order effects that weren’t considered sufficiently, IMO, when decisions were made in March/April.

                >>And what is the payoff? Less economic damage? Less disruption? Maybe. In reality you just don’t know. A big gamble for a dubious payoff.

                It’s what I said elsewhere about expected value. It’s not actually worth it for most of the population to lose say 1/3 of their quality of life for 1/30 of their remaining life expectancy, vs. a 0.1% – or even 0.35% – population death rate. The “expected amount of quality of life lost” for the interventions is actually greater than that of the disease.

                IE – raw number of deaths isn’t the measure that really matters IMO; it’s total “life” (not just “lives”) lost.

              • confused says:

                Whenever I comment on this stuff, I always feel like I come across as minimizing COVID more than I really intend to.

                I don’t at all doubt that it’s a real crisis.

                It’s more that I think the “second-order” costs (social disruption of various sorts, mental health effects, loss of education, etc) were insufficiently considered when decisions were made (and still are insufficiently considered, to some degree).

                IE – not that COVID is less bad than generally thought but that the “second-order” issues are worse than generally thought.

              • Anoneuoid says:

                IE – not that COVID is less bad than generally thought but that the “second-order” issues are worse than generally thought.

                Don’t forget that smoking cigarettes is worse than covid. Even if it would reduce infection rates by 60% it is not worth it.

                Yet during the 20th century no one shut down the economy over smoking and in fact it seems to be the most productive and progressive century in written history.

              • confused says:

                >>Don’t forget that smoking cigarettes is worse than covid. Even if it would reduce infection rates by 60% it is not worth it

                Even if you were *certain* that smoking would reduce your risk of catching COVID, it still probably wouldn’t be worth it if you compared years of life lost to smoking vs. expected years of life lost from COVID.

                If I started smoking today I’d probably lose at least several years of life expectancy.

                Whereas a 1/1000 chance of death from COVID (which is probably too high as I am 30 with no comorbidities… but being male raises the risk somewhat) probably corresponds to something like 1/20 of a year.

              • confused says:

                Actually, 1/20 of a year is way too high as I wouldn’t be *guaranteed* to catch COVID.

                Probably more like 10-20% of that. (If 20% of Texas gets COVID… and I don’t do a lot of bars and big parties in a normal year, and live by myself, so my risk would likely be less than average even with zero precautions.)

                So… 20% of 1/1000 of maybe 50 years of remaining life expectancy = 1/5000 of 50 years = 1/100 year or about 3.65 days of expected loss of life expectancy.

                Yeah there’s no way starting smoking would be worth it.

              • Joshua says:

                confused –

                > Close to? Yes. I said I would expect Sweden likely to have a slight advantage… but quite marginal at best.
                >>Of course it depends on the response. That’s my point!

                So we’re just going to disagree on this. Better baseline health. Related, lower comorbidities. Much higher % of people who live alone. Much lower number of grandparents caregiving for their grandchildren. Much lower rate of multi-generational households. Much higher ability to work from home. Much better systems for taking paid leave from work. Less travel to/from China and other hotspots. Only one, large and dense urban center. Smaller %’s of poor and minorities who are at particularly high risk. Better access to healthcare.
                Extrapolating from one country to another is obviously complicated and I generally think doing so is more a reflection of bias than anything else – but to the extent that it can be done I think that Sweden has major structural advantages in terms of likely outcomes if you’re going to follow a “let it spread” policy. No way that I know of for quantifying the differences, but I”m actually kind of surprised that you’re arguing this point. It really seems that obvious to me. On virtually any metric that we can logically assume contributes to higher spread and higher mortality – Sweden has advantages. But I guess you look at it similarly as to how I do, in the sense that you think it’s obvious that there’s no significant difference.

                > OK then I don’t know what we are actually arguing about.’

                I’m saying that anything is theoretically possible. Sure, it’s theoretically possible that we could create a universe where the media didn’t respond to a pandemic by highlighting the threat. Similarly, we could live in a universe where the media doesn’t focus on crime as a threat or terrorism as a threat. But we are stuck in the universe in which we live. And as such, I don’t think it’s likely that absent SIPs, there would have been less economic damage. If you want to use Sweden as an example, it doesn’t support your contention that SIPs have a dramatic effect, differentially. And I would argue that without the social supports such as availability of unemployment and stimulus loans, the outcomes here would tip further in the direction of worse outcomes from no SIPs.

                So if you want to say it could theoretically be different, then we are in agreement. If you want to say, as you confidently repeatedly, that the SIPs have “caused” the economic harm, differentially (paraphrasing), then I disagree – as my view is that we truly don’t know what the economic effects would have been absent the SIPs, but there’s good reason to think they could have been as bad or even worse.

                > I think it’s more likely that if the public messaging had been consistently “this is like the 1957/1968 flu pandemics, wash your hands and stuff and cancel big sporting events/concerts but otherwise go on with life as normal” society would not have been drastically disrupted at anything like the levels that actually did happen.

                Perhaps. But the Trump and Fox News essentially tried that and it didn’t work out very well. But even if the Demz and other media outlets had promoted a similar message – unless they prevented reporting of deaths and illness, we may have seen an even stronger reaction. With no SIPs it is quite likely that hospitals in NY and other places hit early would have been over-run – similar to Lombardy or even worse. It would be pretty hard for the media to portray that as “just a bad flu” with any credibility. I just don’t think that your counterfactual matches the real world very well.

                > I thought you were saying that vast social disruptions were inevitable regardless of the response.

                Inevitable? I don’t know. I think it’s likely. But more to the point, I am rejecting your argument where you consistently frame it as if you know, with a high degree of certainty, that it is the SIPs which has caused the economic damage.

                > Sure. But IMO what we’ve done is *also* a huge gamble.

                Yes. I agree. That’s what decision- and policy-making in the face of uncertainty entails. At some level, you have to gamble. For me, the key is to hedge against the high damage function outcomes even if they are relatively low probability. And it’s also key to consider the impact on people who are more at risk, and even more importantly the fate of those who are sacrificing for the sake of others – front line healthcare workers and essential workers who make it possible for people like me and you to stay relatively safe.

                > Modern society/economy/infrastructure is a really complex network. There are lots of second-order effects that weren’t considered sufficiently, IMO, when decisions were made in March/April.

                No doubt. That is inevitable. There are ALWAYS unintended consequences from actions. There certainly would have been had we gone the “let it spread” pathway. Unfortunately, it looks to some extent like we’re managing to combine the worst of both worlds.

                > IE – raw number of deaths isn’t the measure that really matters IMO; it’s total “life” (not just “lives”) lost.

                That is a value judgement – not a mathematical fact. You treat it as if it’s a mathematical fact.

              • Joshua says:

                confused –

                I will note, to my surprise, the Sweden has a higher % of urban population (not by a huge marging:

                https://en.wikipedia.org/wiki/Urbanization_by_country

              • Anoneuoid says:

                Even if you were *certain* that smoking would reduce your risk of catching COVID, it still probably wouldn’t be worth it if you compared years of life lost to smoking vs. expected years of life lost from COVID.

                I think you missed my point. Reread the second paragraph.

              • confused says:

                >>So we’re just going to disagree on this.

                Looks like it, but…

                >> But I guess you look at it similarly as to how I do, in the sense that you think it’s obvious that there’s no significant difference.

                No, I don’t think it’s obvious either way, at this point.

                >> And as such, I don’t think it’s likely that absent SIPs, there would have been less economic damage.

                Ah, I think here’s where we’re talking past each other.

                I am not just talking about SIP orders but a much broader response.

                Yes, given the situation in late March where a lot of businesses and local governments had already taken dramatic actions — by the time the actual SIP orders came into effect — I will agree with you there.

                I was talking more about a bit earlier stage in the process, and media, business, and local government response as well as state/federal government.

                If we had had the same media/public/business/local government response and no SIPs… yeah you are likely right, no clear advantage and maybe some disadvantage.

                (Although I’m not just talking about economic damage but broader social effects too…)

                >>With no SIPs it is quite likely that hospitals in NY and other places hit early would have been over-run – similar to Lombardy or even worse.

                Ah well here we genuinely disagree. NYC maybe. But I don’t think “other places” – ie pretty much anywhere in the US except greater New York City – was ever going to see hospitals overwhelmed to the point of triaging/turning people away.

                People were predicting that in Phoenix and Houston and month and a half ago, and it didn’t happen (without SIP orders). While Houston hit 100% normal capacity, surge capacity was never even close to being reached.

                >>For me, the key is to hedge against the high damage function outcomes even if they are relatively low probability.

                Eh, see, I think the low-probability / tail-risk outcomes of social disruption are potentially worse (though less likely) than an unrestrained COVID pandemic.

                >> and even more importantly the fate of those who are sacrificing for the sake of others – front line healthcare workers and essential workers who make it possible for people like me and you to stay relatively safe.

                True to a degree, but I’m really not comfortable with valuing this over “lowest overall harm”.

                And anyway, if we’d gone about normal life, “essential workers” wouldn’t have been more at risk than anybody else, because the rest of us would still have been going to work.

                >>That is a value judgement – not a mathematical fact. You treat it as if it’s a mathematical fact.

                Sorry, I didn’t really mean to. I agree it’s a value judgment.

              • Joshua says:

                confused –

                The horse is on life support – doctors are recommending putting down the club.

                > I am not just talking about SIP orders but a much broader response.

                That helps to clarify – but still, I think that you’re advocating for something that could never have realistically existed in this universe.

                > Ah well here we genuinely disagree. NYC maybe. But I don’t think “other places” – ie pretty much anywhere in the US except greater New York City – was ever going to see hospitals overwhelmed to the point of triaging/turning people away.

                You’re portraying an environment where everyone just looked at this casually, as if it were “just a bad flu.” The ramifications of such an approach would have been very far-reaching. No ramp up in PPE, no ramp up in testing, no adoption of mask-wearing, no closing down of movie theaters, ongoing sporting events, mass political rallies. I have no idea how you’d project the effects of such a different course of events. Some hospitals were near overwhelmed to overwhelmed in other places as it is! And we’re not done yet. We don’t know what’s going to happen going forward, in the fall, when a flu hits, perhaps a flu that actually matches the descriptor of a bad flu.

                > People were predicting that in Phoenix and Houston and month and a half ago, and it didn’t happen (without SIP orders). While Houston hit 100% normal capacity, surge capacity was never even close to being reached.

                And that happened with the existing forces in play that focused people on mitigation. A lack of that focus could well have resulted in significantly worse outcomes.

                > Eh, see, I think the low-probability / tail-risk outcomes of social disruption are potentially worse (though less likely) than an unrestrained COVID pandemic.

                I”m not sure how you get to a disaggregated outcome. A much faster spread with more death would have likely, IMO, produced similar disruption, or perhaps worse social disruption. Again, you go back to these being some kind of distinct phenomena. That’s what I don’t get. I don’t get how you can do that. IMO, it can’t be done.

                > True to a degree, but I’m really not comfortable with valuing this over “lowest overall harm”.

                Sure, it’s a tough evaluation. We might be trading off mitigating a high cost for certain individuals against a lower overall cost. But we don’t know that there would have been a trade off. You’re betting the lives of the people who are putting their lives on the line to enable us to be protected, based on an (IMO dubious) ASSUMPTION about what have been less overall harm. Maybe it would have been, but on the one hand we have a virtually certain cost (more harm for healthcare workers, for example) and on the other we have a differential cost built on a pure assumption for which you have very little actual evidence.

                > And anyway, if we’d gone about normal life, “essential workers” wouldn’t have been more at risk than anybody else, because the rest of us would still have been going to work.

                Sorry, but I think that’s just totally unrealistic, unless you have some measure of controlling the media such that people wouldn’t even hear about a high rate of illness and death. And if you’re talking about controlling information to that extent, you’ve go other problems on your hands.

                > Sorry, I didn’t really mean to. I agree it’s a value judgment.

                Acknowledged.

              • confused says:

                Yeah, we might be beating a dead horse here. So I’ll make this short.

                No, I’m not talking about controlling the media so people don’t hear about a high rate of illness and death. But the thing is, “high rate” is relative. COVID is much more dangerous than ordinary respiratory illnesses, but we’re not talking 1918 flu level or anything.

                You might very well be right that the current social climate made avoiding major social disruption very likely/near-impossible. But I still think that’s ultimately the sum of people’s choices, not an inevitable feature of the disease.

          • Joe says:

            I think we went through this before, but without seeing mobility data, I’d be really uncertain about what drove the decrease. If Sweden is like Norway or Finland, a large part of society closes down for the summer. If many businesses are closed, and many people are basically self-isolating in their summer cottages, is it really surprising that the rates decreased?

            I agree that we should wait until it’s over before we judge their policy, but I think Sweden can only be compared with the other Nordic countries. I really doubt the others will ever have comparable fatality rates (treatments have improved, and hopefully lessons were learned about what not to do in care homes), and I think the economic impact will be comparable. There’s still other issues, including philosophical (when should a government restrict the movement of its people?) and maybe even aesthetic (how do people want to live their lives?), so I doubt we’ll ever resolve the issue.

            • David J. Littleboy says:

              Ah, I forgot. I read an article somewhere that claimed that despite all the deaths, Sweden had very low numbers/rates of positive antibody tests; that they were not getting anywhere near HI despite the deaths. They just weren’t succeeding at getting the immunity ratio anywhere near where it needed to be.

              • confused says:

                >>They just weren’t succeeding at getting the immunity ratio anywhere near where it needed to be.

                Except we don’t know what the herd immunity threshold for Sweden is. The social contact patterns and thus R0 are going to be radically different from Iquitos, Peru or Bergamo, Italy – so a high % infected in those places doesn’t rule out a low herd immunity threshold for Sweden.

                And I’m not sure herd immunity has been reached. Infections and deaths are still happening — just much slower, to the point that it may not be a crisis now.

              • Joshua says:

                confused –

                > And I’m not sure herd immunity has been reached. Infections and deaths are still happening — just much slower, to the point that it may not be a crisis now.

                Assuming that heterogeneity can lower the HIT as far as 10%-20% (I’m not convinced but I guess it’s possible), behavioral changes will affect the HIT because behavioral changes affect heterogeneity. There are many, many moving parts, and you can’t just assume that lower rates of deaths and infections means reaching HIT. Sweden still has higher rates of infection and deaths than its Nordic neighbors. Sweden seems to have a similar level of social distancing as its Nordic neighbors. It seems to have a similar level of economic disruption.

                This is the beginning of the first quarter. Too early to judge much of anything. Don’t forget that you were pointing to Texas as a successful example of the benefits of a lighter touch from government – before the spike in infections and deaths that is still ongoing. Surely then you were judging outcomes in texas too early to make a comprehensive assessment. I’d say it’s still too early.

              • confused says:

                Yeah. I definitely didn’t expect the rise in deaths to only really start 2+ months after reopening.

                But I don’t think we’re quite *that* early in the game. COVID was already in the US and much of Europe by February, maybe even January. This is early August. So 6 months at least. Deaths have been high in the US since March, so almost 5 months.

                And I’m not saying Sweden is at herd immunity. I don’t think it can be, unless either the herd immunity threshold or the IFR is implausibly low.

                A 0.5% IFR would suggest something like 1.1-1.2 million infections to get the current ~5780 deaths; even accounting for those infections not yet resolved, I can’t see even 15%, much less 20%, unless Sweden’s IFR is really low.

                I mean, their medical care is good, but *that* much better? Especially back in April when they had a lot of their deaths?

                But COVID doesn’t seem to be spreading at crisis levels there, though herd immunity may be the wrong explanation for why not.

                Could COVID have become “endemic” rather than “epidemic” in Sweden? (IE – persisting at a roughly consistent level, not exponentially growing or declining?)

              • Joshua says:

                confused –

                > A 0.5% IFR would suggest something like 1.1-1.2 million infections to get the current ~5780 deaths; even accounting for those infections not yet resolved, I can’t see even 15%, much less 20%, unless Sweden’s IFR is really low.

                So you’re not with the “Sweden has hit the HIT” crowd? That one modeling group has said you could reach the HIT at 10%-20%. So @1 million Swedes or a little more than 12 x the number of identified infections. That seems possible. And 5,766 dead would be @ a 0.6% IFR. Which seems plausible.

                Of course. At 20% that would mean 2 million infected or 24 x the number of identified infections. OK, that doesn’t seem totally impossible. And an 0.03 seems too low to me, especially since many of their deaths came before treatments were improved…but I wouldn’t completely rule it out. If course that would have to mean that the seroprevalence surveys are way off, or there’s a whole lot of immunity from T cells.

                So then, to the States…10% or 33 million to be infected…only @ 7 x the number identified. Plausible. A 0.6% IFR and…. Uh oh. That’s 165, 000 dead and we’re already there. That doesn’t seem possible that no more deaths after basically tomorrow. If we jump up to 20%, 66 million at an 0.6%.IFR, we hit the HIT at 400,000 dead. That’s a lot of dead people. Not good. We’d better hope that the IFR is more like 0.3%. But that’s a very concerning number there, IMO, because the 66 million infected, given what they’re finding with the potential long-term sequallae…that’s a lot of illness for a long time going forward..

                I hope I made some math errors.

              • confused says:

                >>So you’re not with the “Sweden has hit the HIT” crowd?

                I’m at least not convinced of that.

                I mean *something* has happened. Deaths are down a lot. And AFAIK Sweden hasn’t taken any more government measures, and one wouldn’t generally expect the population to take more measures on their own since things aren’t getting worse.

                So “Sweden has hit herd immunity” is a plausible hypothesis, and I’m not saying it’s wrong.

                But I see another possibility, where the distancing measures that *were* taken dropped the Rt to a bit over 1, and then say 10%-15% infected dropped it the rest of the way to below 1.

                In that case if everyone went *totally* back to normal you might have some degree of second spike, until the immunity level rose a bit more.

                >>That one modeling group has said you could reach the HIT at 10%-20%. So @1 million Swedes or a little more than 12 x the number of identified infections. That seems possible. And 5,766 dead would be @ a 0.6% IFR. Which seems plausible.

                Yeah. I’m definitely not ruling it out. With how good their medical system is … Iceland has a CFR a bit over 0.5%, though very small sample size (10 deaths total).

                TL;DR – I wouldn’t confidently say Sweden *has* hit herd immunity. But they could have.

                >>So then, to the States…10% or 33 million to be infected…only @ 7 x the number identified. Plausible. A 0.6% IFR and…. Uh oh. That’s 165, 000 dead and we’re already there. That doesn’t seem possible that no more deaths after basically tomorrow.

                Well, I think the US is a couple of different outbreaks. The early Northeast outbreak probably had a higher IFR. (NYC seems to have had an IFR of maybe ~1.1%, at least if you believe their seroprevalence surveys.)

                But IFR for infections happening now might be lower than 0.6%, especially in places where it’s largely a younger demographic getting infected.

                And there are probably different herd immunity thresholds for different parts of the US, it’s nowhere near a homogeneously mixing population.

                >>given what they’re finding with the potential long-term sequallae…

                I really don’t know what to think about that yet. Would really like to see good data on incidence of these things. There are so many recovered patients in e.g. the Northeast not sure why this isn’t being done (or is it?)

            • confused says:

              >>I agree that we should wait until it’s over before we judge their policy,

              True.

              >>There’s still other issues, including philosophical (when should a government restrict the movement of its people?) and maybe even aesthetic (how do people want to live their lives?), so I doubt we’ll ever resolve the issue.

              It’s the loss of quality of life that I’m really talking about, more than the economic costs.

            • Joshua says:

              Joe –

              Nice comment.

            • Joshua says:

              SWEDEN, should be 0.3% IFR at a 20% HIT.

          • Michael Weissman says:

            confused: Yes, the Swedish fatality percent is comparable to some previous flu pandemics, although it would have been much higher if no protective measures were taken. In other words, the limited damage doesn’t imply that the measures taken to limit it were worthless, especially since we can see that comparable countries that took stronger measures did much better.
            Here’s the tragic side. Treatments have already improved somewhat since a few months ago. There’s every reason to hope that with increased remdesivir supplies, the finding that cheap steroids help in severe cases, with several promising new treatments under test (nebulized interferon, EIDD-2801…), and multiple vaccines entering phase 3 trials after good initial results, it looks like many of the people who have died and will die in the next couple months would have lived if we could have just held out a little longer.

            I think most of the “predictions that were wrong in the other direction” were explicitly based on business-as-usual models. They prompted major deviations from business-as-usual, as they were meant to do, so naturally things didn’t go all that badly. So that does not, in itself, show anything wrong with the models. It’s true, however, that the most pessimistic predictions used homogeneous models, which probably were very roughly 2x worse than the real situation.

            Ioannidis’ initial 10k US fatality estimate is already low ~x15, or about ~x20 if you count all excess deaths. The discrepancy continues to grow. Since that estimate was also for pretty much business-as-usual, it’s even more unrealistic than indicated by this comparison. It was obtained by inconsistently combining a low IFR estimate from assuming that there were lots of undetected infections with an extremely lowball estimate of the total expected infections, essentially the opposite limit.

            • Sander Greenland says:

              1) In all fairness to Ioannidis, that 10K estimate being raised here was his lower bound for the U.S. He did not give an upper U.S. bound, but based on his worldwide guess of 40M I think it would have been about a million or so.

              2) Regarding Sweden, Ioannidis gave a talk using Switzerland as its comparator, which is absurd given over half the Swiss border is with hard-hit Lombardy and France, with enormous cross-border traffic (eg people can and do commute to work in Geneva from the French side). But Norway isn’t a good comparator either, as its long border with Sweden is very far from urban areas; plus nearly half the Swedish deaths were in nursing homes, which are larger facilities than those used in Norway (which from North-Sea oil is considerably more wealthy and supports more home care). Swedish deaths were also concentrated around Stockholm; Norway has no urbanization comparable to the Stockholm region.

              Denmark is the best socioeconomic match in terms such as wealth and risk from urban density (Copenhagen), and has had a fifth the reported covid death rate of Sweden’s – or about triple if we choose to factor out the Swedish nursing home outbreaks (which even the Swedish government concedes was an avoidable tragedy). I think that’s about the best estimate of the effect of mandated lockdown (of the sort Denmark used) compared to the “soft” advisory approach (of the sort Sweden used) with special isolation for nursing homes, in a country where social cooperation is the norm. Of course that’s all very crude, and whether that extends to a country like the U.S. is another matter.

              • Michael Weissman says:

                I approximately agree on the Swedish comparisons. Denmark is more densely populated. As for the nursing homes, it’s not as if the Swedish government didn’t know of their existence or that the failure to protect them was not part of the “soft” approach.
                On Ioannidis, IIRC 10k was the only prediction he chose to present. It was not his minimal estimate, since it used his midrange IFR estimate, and he played up the possibility that IFR was much lower than that. (0.3% vs. 0.05%, IIRC)
                Turns out my memory ws ok in his instance. here’s the relevant passage in full:

                “If we assume that case fatality rate among individuals infected by SARS-CoV-2 is 0.3% in the general population — a mid-range guess from my Diamond Princess analysis — and that 1% of the U.S. population gets infected (about 3.3 million people), this would translate to about 10,000 deaths. This sounds like a huge number, but it is buried within the noise of the estimate of deaths from “influenza-like illness.” If we had not known about a new virus out there, and had not checked individuals with PCR tests, the number of total deaths due to “influenza-like illness” would not seem unusual this year. At most, we might have casually noted that flu this season seems to be a bit worse than average. The media coverage would have been less than for an NBA game between the two most indifferent teams.”

              • Sander Greenland says:

                1) Denmark vs. Sweden density is nitpicking, but if you want to go there I’ll note that the difference is slight if (as arguably we should) we ignore the vast sparsely populated sub-Arctic and Arctic regions that comprise most of Sweden, which were barely touched by the pandemic, and that Stockholm (the Swedish covid epicenter) has a higher metro population than Copenhagen (and traffic jams to rival those of my native Los Angeles).
                Which reminds me: U.S. comparisons to other countries suffer spectacular problems given the vast U.S. range of density, external connectivity, culture, weather, local policies etc. So how meaningful are U.S.-wide figures given they include everything from Alaska to New York City? There’s no country I’d take as a valid comparator.

                2) As for Ioannidis’s 10K-death U.S. estimate, I hardly want to defend it but he has stated he meant it “in the most optimistic range”. So let’s look further below in his mid-March Stat essay which you quoted: He said “In the most pessimistic scenario, which I do not espouse, if the new coronavirus infects 60% of the global population and 1% of the infected people die, that will translate into more than 40 million deaths globally”.
                Now let’s compare his March statements to his defense in this interview published July 9:
                https://thehealthcareblog.com/blog/2020/07/09/a-conversation-with-john-ioannidis/
                “The 10,000 deaths in the US projection was meant to be in the most optimistic range of the spectrum and in the same piece I also described the most pessimistic end of the spectrum, 40 million deaths. The point I wanted
                to emphasize was the huge uncertainty.”
                We can see that he quotes his March 40M-death world estimate as if it were his pessimistic estimate for the U.S. Let’s chalk that up to careless wording or memory failure; allowing that the U.S. is only about 4.3% of the world population, it translates to about 0.043*40M = 1.7M U.S. deaths. Of course in March he did not espouse or even state that as a pessimistic estimate for the U.S.
                Having given these direct quotes for comparison, I must leave it to you and our readers to judge the accuracy of his July reporting of his March statements (as well as the accuracy of his March statements relative to how the pandemic has unfolded since).

            • confused says:

              >>confused: Yes, the Swedish fatality percent is comparable to some previous flu pandemics, although it would have been much higher if no protective measures were taken. In other words, the limited damage doesn’t imply that the measures taken to limit it were worthless,

              Higher? Quite probably, somewhat, as some infections were delayed until treatment was better understood.

              Much higher? This I really doubt.

              >>I think most of the “predictions that were wrong in the other direction” were explicitly based on business-as-usual models.

              The Imperial College model said 1.1 million deaths for the US in 12-18 months with “limited mitigation” much like what Sweden has done. That’s 0.35% of the US population.

              Yeah the 2.2 million deaths under total business-as-usual was not actually expected to happen, so I’m not comparing to that.

              Places like AZ and TX have taken only “limited mitigation” in this surge/wave, and are clearly past their peak infections and hospitalizations now, and are not headed for even 0.1% population fatality rate, much less 0.35%.

              There has been some marginal benefit in delaying the surge, because we know about dexamethasone and remdesivir now, convalescent plasma maybe helps, etc.

              But the mortality effects of those are not so dramatic as to allow for the possibility of anything like a 0.35% population fatality rate if everywhere had been hit before we knew about them.

              >>Ioannidis’ initial 10k US fatality estimate is already low ~x15, or about ~x20 if you count all excess deaths. The discrepancy continues to grow.

              Sure, that was obviously wrong, as I said.

              • Michael Weissman says:

                Yes, let’s say that the “limited mitigation” estimate of 0.35% was about a factor of 2 high due to insufficient allowance for heterogeneity, as I acknowledged. The US has had a mix of limited mitigation and fairly intense mitigation. So you’d expect a bit under 0.35%/2. Say roughy 0.1 to 0.15%

                NYC, which mitigated too late, seems to be already at ~0.3% total excess mortality. The US excess deaths are now about 190k, although ~30k of those were not officially reported as Covid but just miscellaneous pneumonia etc.Just about every prognosticator (US Army, MIT,…) expects roughly 1k/day for the next 6 weeks or so, with no sharp time-dependence expected after that. So long before that 12-18 month time frame, despite improved treatments, we’ll be at ~0.08%.
                It looks like the Imperial College prediction was off by about a factor of 2 for the US as a whole, although it’s hard to be precise because our measures don’t exactly match their model and we’re only ~5 months in. That’s better than a factor of ~30. I’m hoping that improved therapies come in fast enough so we’ll never have to see what the 12-18 month result would have been without them.

              • Michael Weissman says:

                On the higher vs much higher question, here’s some relevant data from Toronto. Look at the 4th graphic in the sidebar.
                https://www.cambridgetimes.ca/news-story/10129678-lockdown-worked-for-the-rich-but-not-for-the-poor-the-untold-story-of-how-covid-19-spread-across-toronto-in-7-graphics/

                Initially the case rates vs time in the rich and poor neighborhoods were very nearly the same. When the lockdown was announced the case rate almost instantly took a sharp dive down in the rich neighborhoods, but barely responded in the poor neighborhoods. Lockdowns matter a lot when people can follow them, but not when they can’t.
                In Sweden, Norway, Denmark and Finland, most people can. At this point the difference between Sweden and Norway, Denmark, and Finland is far more dramatic than any effects seen so far from treatments. But Sweden still did much better than say Lombardy, presumably because Lombards didn’t know to take measures until it was too late.
                So I think “much higher” captures it better, although admittedly the stereotype is that even in ordinary life Swedes are already much more socially distant than Lombards.

              • confused says:

                >>NYC, which mitigated too late, seems to be already at ~0.3% total excess mortality.

                Sounds plausible. But NYC is utterly unlike any other part of the US.

                >>The US excess deaths are now about 190k

                I wouldn’t assume all excess deaths are actually COVID, given that even CDC reports significant decreases in emergency room visits for heart attacks etc., but 190k sounds reasonable, given we’re over 155k reported.

                >>Just about every prognosticator (US Army, MIT,…) expects roughly 1k/day for the next 6 weeks or so

                Also seems reasonable, though I think a bit high (I think we’ll be back under 1,000 7-day-average by the end of August).

                >> with no sharp time-dependence expected after that.

                Now, this *doesn’t*. After deaths decline from the current peak in CA/AZ/FL/TX etc., what other states are going to “replace” them? The states with currently rising hospitalizations mostly have comparatively small populations.

                Maybe if NY/NJ/MA/CT etc. have a major fall second wave, but otherwise, I’m not seeing it.

                >>It looks like the Imperial College prediction was off by about a factor of 2 for the US as a whole

                Half of 1.1 million deaths is 550,000 deaths. If you’re saying 190k real excess deaths vs 156k reported, the same factor would imply about 450,000 reported deaths.

                This seems extremely pessimistic to me.

                >>I’m hoping that improved therapies come in fast enough so we’ll never have to see what the 12-18 month result would have been without them.

                One of my complaints about the Imperial College model is precisely that they projected a fixed IFR over 12-18 months. *Of course* treatments were going to improve; this isn’t 1918-19 when we had no clue what the causative agent of the disease was.

              • confused says:

                Toronto… maybe.

                I still think it’s implausible to assume every country on Earth will have good mitigation. So if the 0.35% for limited mitigation, 0.7% absolute worst case no mitigation, was accurate, then why does no country on Earth look to be trending toward anything like that high?

              • Anoneuoid says:

                All cause mortality looks like this: https://www.docdroid.net/K1SUnKO/20200805mort-pdf

              • Joshua says:

                Michael –

                > So I think “much higher” captures it better, although admittedly the stereotype is that even in ordinary life Swedes are already much more socially distant than Lombards.

                The joke is that when Swedes are told they have to stay six feet apart, they respond, “That close?”

  17. Michael Weissman says:

    Yes, on Denmark vs. Sweden, we don’t really disagree, I was just making a minor note in passing. For a comparison to the US, the issues you raise are important. A better comparison group would be the whole EU, which like the US is large, diverse, exposed, permeable, lacks a functioning central government, etc. On fatalities/pop to this point we’re only up ~50% over them, but we are currently running about 20x their current rate.(http://91-divoc.com/pages/covid-visualization/?fbclid=IwAR2rMA7bWzyU6hEsBnb_HHVJLU8O_VCnL6qdXo2V95LAHwTr8LQ_IR0gfFc)

    On Ioannidis, I agree that readers should simply check that Stat piece to see what they think. With the proviso, of course, that if they disagree with me they’re “obviously, clearly” nuts.

    I think there’s probably a direct causal path from ” If we had not known about a new virus out there, and had not checked individuals with PCR tests, the number of total deaths due to “influenza-like illness” would not seem unusual this year. At most, we might have casually noted that flu this season seems to be a bit worse than average. The media coverage would have been less than for an NBA game between the two most indifferent teams.” to “slow the testing down, please”.

    • joe says:

      I think one crucial difference between the EU and the US is that it is much easier to cut off movement between EU countries than it is between US states. The EU really reverted to pre-EU days from March to early July. The situation in the US might be much different if individual states really could prevent arrivals from other states. But I haven’t seen mobility data about whether interstate travel is a major source of infections in the US.

      • confused says:

        Also, culture. Especially in the central / south-central / interior-west US, the places that are seeing most of the deaths now (excluding CA which is a bit odd as it’s very different culturally), the culture is vastly more individualist, more skeptical of government having people’s best interests in mind, and (at least outside major cities) more risk-tolerant.

        • Joshua says:

          confused –

          > the culture is vastly more individualist, more skeptical of government having people’s best interests in mind, and (at least outside major cities) more risk-tolerant.

          Those are largely issue dependent, not universal.

          More risk-tolerant with Muslims? More skeptical about government when it comes to police or abortion? More individualist when it cubes to school prayer?

          You can’t divorce the identity/trubal politics from the values – they interact.

          • confused says:

            You are partly right… There’s an identity aspect of course, yes.

            But I think part of it is that my phrasing is wrong.

            It’s more individual/local community vs. large “faceless” bureaucratic centralized government.

            Things like school prayer* and strong support for police are not seen as “government” in this sense because e.g. police and school districts are local.

            So I should have said “skeptical of government bureaucracy” or “of centralized government” might actually be more accurate.

            *I live in a pretty red state (TX) and I’ve never heard of anyone talk about school prayer as a current issue, but maybe it is some places.

          • confused says:

            Also… another thing I didn’t mention that plays into some of the contradictions you mention is the tension between “individualist/libertarian” and “puritan” sides of American culture.

            I’d argue this tension goes back to the 17th century New England colonies and is historically fairly fundamental aspect of the US national identity, but the seeming contradiction is most visible in rural/conservative communities.

            • Joshua says:

              confused –

              “Keep your government hands off my Medicare.”

              They’re tons o’ examples.

              Read what Haidt has to say about Trump supporters and authoritarianism.

              Remember when an individual mandate was an example of personal responsibility for Republicans (when Romney was promoting it) before it became the poster boy for government tyranny and infringement on individual freedom?

              It’s like the objection to “identity politics” as a “value.” It depends on whose “identity” is being gored.

              > Things like school prayer* and strong support for police are not seen as “government”

              Of course they aren’t. That’s my point.

              • confused says:

                >>Remember when an individual mandate was an example of personal responsibility for Republicans (when Romney was promoting it) before it became the poster boy for government tyranny and infringement on individual freedom?

                Eh, I heard a lot of people saying Romney wasn’t “really a Republican” because of the healthcare stuff he’d done in Massachusetts.

                But I live in a much redder state.

                >>Of course they aren’t. That’s my point.

                OK, then I’m not sure I really disagree.

                Yeah there are internal contradictions within the culture (though I think they make somewhat more sense when you look at how it developed). But even if it’s contradictory and doesn’t make sense to you or me, the culture *does* have these

                So I think if we disagree on this it’s only about how much the *current* political situation shapes the behavior, vs how much is pre-existing cultural traits.

  18. Andrew Davis says:

    Tried to post this earlier but my comment doesn’t seem to have made it through. Perhaps bad characters in one of the quotes I pasted. Another paper by Gomes et al. that directly addresses what is being discussed here.

    “Here we fit epidemiological models with inbuilt distributions of susceptibility or exposure to SARS-CoV-2 outbreaks to estimate basic reproduction numbers (R0) alongside coefficients of individual variation (CV) and the effects of containment strategies. Herd immunity thresholds are then calculated as [SNIP], depending on whether variation is on susceptibility or exposure.

    “Our inferences result in herd immunity thresholds around 10-20%, considerably lower than the minimum coverage needed to interrupt transmission by random vaccination, which for R_0 higher than 2.5 is estimated above 60%.

    “We emphasize that the classical formula, 1-1/R0, remains applicable to describe herd immunity thresholds for random vaccination, but not for immunity induced by infection which is naturally selective. These findings have profound consequences for the governance of the current pandemic given that some populations may be close to achieving herd immunity despite being under more or less strict social distancing measures.”

    https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v1

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