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This article never really tackles the fact that p(infected|vaccinated) != p(vaccinated|infected). With high-vaccination rates in Israel, that matters a lot. I

This article never really tackles the fact that p(infected|vaccinated) != p(vaccinated|infected). With high-vaccination rates in Israel, that matters a lot. In fact, the scariest statistic it gives--that nearly 60% of serious hospitalizations are fully vaccinated) gives the p(vaccinated|infected), not p(infected|vaccinated). Trivially, and to make the point, if 100% of people are vaccinated, then 100% of hospitalizations will be among the vaccinated--which tells you almost nothing about how likely it is to be hospitalized when vaccinated (beyond that its nonzero). An embarrassing failure for science.org

Buttons840 5y ago
p(i|v) = ( p(v|i) * p(i) ) / p(v) p(v|i) = 0.6 p(v) = 0.6 p(i) = ?; but it's high (record case counts) p(i|v) = p(i); high If Israel has a 60% vaccination rate, and 60% of those in the hospital are vaccinated, then doesn't this mean the vaccine has no effect on the chances of being hospitalized?
- pgalvin 5y ago
  No, because you assume that a 10 year old has an equal probability of being hospitalised as a 90 year old (for example). Israel has a low overall vaccination rate because they have a very young population. If you restrict the sample to just >50 year olds (majority of hospitalisations), then both statistics look very different.
  - nradov 5y ago
    Based on CDC data a 90 year old has at least 30× the risk of hospitalization compared to a 10 year old. https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/burden.html https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/burd...
- mint2 5y ago
  That is why considering age is important and why interacting variables make it so easy for statistics to mislead when talking to people who are less verse or aren’t aware of the topic being studied. About 78% of those above 12 are vaccinated in Israel, and the rate is even higher for those more susceptible to the virus. Without quantifying those factors, it’s going to lead to a garbage in garbage out assessment.
- jonnycomputer 5y ago
  Well, the article says 78% of people 12 yo and older are vaccinated in Israel. Not sure what percent if you drop it to include everyone. 87% of those who were hospitalized were 60 or older (which doesn't match the general population). I imagine that vaccination rates are much much higher than 60% among those over 60. In the US its around 80%. But also, hospitalizations are much more likely the older you get. Moreover (and this was the point of the paper the article was discussing), the effectiveness of the vaccine may dwindle with time, and the 60+ crowd were among the first to get vaccinated. So, no, I don't think you can do so simple a calculation and conclude that. Instead of back of the envelope estimates, I think I'd just point to this study: https://www.nejm.org/doi/full/10.1056/NEJMoa2108891 https://www.nejm.org/doi/full/10.1056/NEJMoa2108891 Abstract: Background The B.1.617.2 (delta) variant of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes coronavirus disease 2019 (Covid-19), has contributed to a surge in cases in India and has now been detected across the globe, including a notable increase in cases in the United Kingdom. The effectiveness of the BNT162b2 and ChAdOx1 nCoV-19 vaccines against this variant has been unclear. Methods We used a test-negative case–control design to estimate the effectiveness of vaccination against symptomatic disease caused by the delta variant or the predominant strain (B.1.1.7, or alpha variant) over the period that the delta variant began circulating. Variants were identified with the use of sequencing and on the basis of the spike (S) gene status. Data on all symptomatic sequenced cases of Covid-19 in England were used to estimate the proportion of cases with either variant according to the patients’ vaccination status. Results Effectiveness after one dose of vaccine (BNT162b2 or ChAdOx1 nCoV-19) was notably lower among persons with the delta variant (30.7%; 95% confidence interval [CI], 25.2 to 35.7) than among those with the alpha variant (48.7%; 95% CI, 45.5 to 51.7); the results were similar for both vaccines. With the BNT162b2 vaccine, the effectiveness of two doses was 93.7% (95% CI, 91.6 to 95.3) among persons with the alpha variant and 88.0% (95% CI, 85.3 to 90.1) among those with the delta variant. With the ChAdOx1 nCoV-19 vaccine, the effectiveness of two doses was 74.5% (95% CI, 68.4 to 79.4) among persons with the alpha variant and 67.0% (95% CI, 61.3 to 71.8) among those with the delta variant. Conclusions Only modest differences in vaccine effectiveness were noted with the delta variant as compared with the alpha variant after the receipt of two vaccine doses. Absolute differences in vaccine effectiveness were more marked after the receipt of the first dose. This finding would support efforts to maximize vaccine uptake with two doses among vulnerable populations. (Funded by Public Health England.)
pfortuny 5y ago
Exactly the same as “x% of automobile deaths were not using the safety belt”… What happens when everybody uses it?
- deleted 5y ago
  [deleted]
- jonnycomputer 5y ago
  Fair point.
mmastrac 5y ago
The calculations running over hospitalization numbers tend to show that vaccines are ~85% effective in preventing hospitalization, usually by showing the reduction in N/100k cases.
- jonnycomputer 5y ago
  That is what I've seen as well.
deleted 5y ago
[deleted]
jcelerier 5y ago
> Trivially, and to make the point, if 100% of people are vaccinated, then 100% of hospitalizations will be among the vaccinated I mean, that's still scary, people were hoping for exactly 0% of covid-related hospitalization if you're vaccinated
- throwaway894345 5y ago
  I'd be more concerned that 100% of people are vaccinated and that's still not enough to stop transmission.
- jonnycomputer 5y ago
  I can't argue about what general public thought; but I think the epidemiological consensus even before we had experience with these vaccines is that vaccine effectiveness wouldn't be 100%--based on our experience with other vaccines. Instead, we rely on population effects to do the work. If susceptibility to infection is above some point in the general population, then infections become a self-sustaining cascade through social networks (of course, the composition and structure of that network also matter--I'm simplifying). But if you can push susceptibility lower enough, the infections will not cause self-sustaining cascades. This is, btw, why I consider anti-vaxxers (in the before times) as free-loaders who relied on those around them being vaccinated to protect them.
  - nradov 5y ago
    Anti-vaxxers won't be effectively protected long term by those around them being vaccinated. The Delta variant is sufficiently contagious that there will be no significant herd immunity effect. All of us can expect to get exposed eventually. https://www.businessinsider.com/delta-variant-made-herd-immunity-not-possible-astrazeneca-developer-2021-8 https://www.businessinsider.com/delta-variant-made-herd-immu...
    - jonnycomputer 5y ago
      I think this is why I didn't include the covid-anti-vaxxers in that mix; they're more like covid fatalists. Absent a vaccine, covid-fatalism--the idea that you will get it eventually--is not insane. Lots of simulations show you can flatten the curve with various measures, but the area under the curve ends up being the same in the long run; or at least that's my lay person understanding of it. Not getting everyone sick at once keeps everything getting overwhelmed at once ... but long sustained restrictions have costs too. But all that logic is really thrown out the window with widespread availability of effective vaccines.
baxtr 5y ago
Agree 100%. A friend of mine shared the article this morning and I basically said the same. By itself the 60% is a meaningless number and says nothing about the vaccine efficacy. > An embarrassing failure for science.org Yes. Looking at the author's bio, you would expect a more nuanced comment and not this kind of fear mongering. Meredith Wadman Meredith joined Science as a staff writer in September 2016, after covering biomedical research and its politics from Washington, D.C., for 20 years. Her current beat includes biology research, policy, and sexual harassment . She has been a staff writer for Nature and a contributing writer at Fortune. She has also written op-eds for The Wall Street Journal, The New York Times and The Washington Post. Her first book, The Vaccine Race: Science, Politics and the Human Costs of Defeating Disease, was published by Viking (U.S./Canada) and Transworld (U.K.) in February 2017. Meredith earned her B.A. in Human Biology at Stanford University and began medical school at the University of British Columbia in her native Vancouver. She completed her medical degree as a Rhodes Scholar at the University of Oxford in the United Kingdom, and earned a master’s of science at the Columbia University Graduate School of Journalism.
- jonnycomputer 5y ago
  I think it must be something about the incentives of publishing.
- dkural 5y ago
  The 60% is also not adjusted for age, see here for good explanations: https://www.washingtonpost.com/outlook/2021/08/31/covid-israel-hospitalization-rates-simpsons-paradox/ https://www.washingtonpost.com/outlook/2021/08/31/covid-isra... https://www.covid-datascience.com/post/israeli-data-how-can-efficacy-vs-severe-disease-be-strong-when-60-of-hospitalized-are-vaccinated https://www.covid-datascience.com/post/israeli-data-how-can-... This is such an important point, I think it's worth including the key table here: Vaccine effectiveness vs. severe disease for younger (<50yr) = 1 - 0.3/3.9 = 91.8% Vaccine effectiveness vs. severe disease for older (>50yr) = 1- 13.6/91.9 = 85.2% But if you combine the two, you get 67.5% !!!! which is the # people have been wrongly focused on.
ldjkfkdsjnv 5y ago
I think the science always knew this, but they mislead the population because being vaccinated is still better than not. The whole vaccination thing is a white lie. We have never eradicated the flu, it mutates too fast. Same is true with Covid-19. The medical establishment has always known this, yet they spread propaganda because, again, being vaccinated is safer. The numbers about 99% effective were a lie, they knew it would mutate and that would see a drastic drop. I would argue this is a dangerous game they are playing with public trust.
- gowld 5y ago
  It's no game.The vaccine was extremely effective. After a year, a new vaccine will be needed for the new strains. Just like the flu vaccines.
- gtt 5y ago
  In my opinion science should be about Truth, the rest should be left to people and their leaders. Truth being central to the process of science is what makes science unique and allows for societies to accumulate knowledge.
- dkural 5y ago
  Could you provide a source for your 99%, given you're accusing others of lying? The numbers I have are ~96% for the Pfizer, and ~94% for Moderna. I explain this in another comment below, but even against Delta, the efficacy is actually quite high, even in the Israeli data: Vaccine effectiveness vs. severe disease for younger (<50yr) = 1 - 0.3/3.9 = 91.8% Vaccine effectiveness vs. severe disease for older (>50yr) = 1- 13.6/91.9 = 85.2% The combined number suffers from Simpson's paradox, please read more: https://www.covid-datascience.com/post/israeli-data-how-can-efficacy-vs-severe-disease-be-strong-when-60-of-hospitalized-are-vaccinated https://www.covid-datascience.com/post/israeli-data-how-can-... & please stop spreading misinformation. 96-94% to 85-91% is against a new variant is hardly a drastic drop. The vaccine is saving millions of lives globally.
- jonnycomputer 5y ago
  When we make accusations like this, its becoming to actually point to specific examples where specific individuals or organizations have done this. For example, this doesn't accord with my recollection, by my recollection is skewed in various ways.
graycat 5y ago
You make a good point about the conditional probabilities. The article also said "most". There is some relatively good data from Israel, but, still, in practice most doesn't just mean > 50% but is essentially wildly undefined. So apparently the author(s) of the article like to write with emotional adjectives instead of important numerical data. The authors were trained in belle lettre (maybe art as in communication, interpretation of human experience, emotion or VEFEEE -- vicarious escapist fantasy emotional experience entertainment) or just like to grab people by the heart, the gut, below the belt to get eyeballs for ad revenue? Whatever, when they got to most I quit reading.
inter_netuser 5y ago
indeed, strange article. It is however quite possible at this point, that the effectiveness against symptomatic infection wears off to nearly zero after 5-6 months. This seems to be the cause with both mRNA and sinopharm's inactivated virus vaccine as well.

Buttons840 5y ago

p(i|v) = ( p(v|i) * p(i) ) / p(v) p(v|i) = 0.6 p(v) = 0.6 p(i) = ?; but it's high (record case counts) p(i|v) = p(i); high If Israel has a 60% vaccination rate, and 60% of those in the hospital are vaccinated, then doesn't this mean the vaccine has no effect on the chances of being hospitalized?

pgalvin 5y ago
No, because you assume that a 10 year old has an equal probability of being hospitalised as a 90 year old (for example). Israel has a low overall vaccination rate because they have a very young population. If you restrict the sample to just >50 year olds (majority of hospitalisations), then both statistics look very different.
- nradov 5y ago
  Based on CDC data a 90 year old has at least 30× the risk of hospitalization compared to a 10 year old. https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/burden.html https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/burd...
mint2 5y ago
That is why considering age is important and why interacting variables make it so easy for statistics to mislead when talking to people who are less verse or aren’t aware of the topic being studied. About 78% of those above 12 are vaccinated in Israel, and the rate is even higher for those more susceptible to the virus. Without quantifying those factors, it’s going to lead to a garbage in garbage out assessment.
jonnycomputer 5y ago
Well, the article says 78% of people 12 yo and older are vaccinated in Israel. Not sure what percent if you drop it to include everyone. 87% of those who were hospitalized were 60 or older (which doesn't match the general population). I imagine that vaccination rates are much much higher than 60% among those over 60. In the US its around 80%. But also, hospitalizations are much more likely the older you get. Moreover (and this was the point of the paper the article was discussing), the effectiveness of the vaccine may dwindle with time, and the 60+ crowd were among the first to get vaccinated. So, no, I don't think you can do so simple a calculation and conclude that. Instead of back of the envelope estimates, I think I'd just point to this study: https://www.nejm.org/doi/full/10.1056/NEJMoa2108891 https://www.nejm.org/doi/full/10.1056/NEJMoa2108891 Abstract: Background The B.1.617.2 (delta) variant of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes coronavirus disease 2019 (Covid-19), has contributed to a surge in cases in India and has now been detected across the globe, including a notable increase in cases in the United Kingdom. The effectiveness of the BNT162b2 and ChAdOx1 nCoV-19 vaccines against this variant has been unclear. Methods We used a test-negative case–control design to estimate the effectiveness of vaccination against symptomatic disease caused by the delta variant or the predominant strain (B.1.1.7, or alpha variant) over the period that the delta variant began circulating. Variants were identified with the use of sequencing and on the basis of the spike (S) gene status. Data on all symptomatic sequenced cases of Covid-19 in England were used to estimate the proportion of cases with either variant according to the patients’ vaccination status. Results Effectiveness after one dose of vaccine (BNT162b2 or ChAdOx1 nCoV-19) was notably lower among persons with the delta variant (30.7%; 95% confidence interval [CI], 25.2 to 35.7) than among those with the alpha variant (48.7%; 95% CI, 45.5 to 51.7); the results were similar for both vaccines. With the BNT162b2 vaccine, the effectiveness of two doses was 93.7% (95% CI, 91.6 to 95.3) among persons with the alpha variant and 88.0% (95% CI, 85.3 to 90.1) among those with the delta variant. With the ChAdOx1 nCoV-19 vaccine, the effectiveness of two doses was 74.5% (95% CI, 68.4 to 79.4) among persons with the alpha variant and 67.0% (95% CI, 61.3 to 71.8) among those with the delta variant. Conclusions Only modest differences in vaccine effectiveness were noted with the delta variant as compared with the alpha variant after the receipt of two vaccine doses. Absolute differences in vaccine effectiveness were more marked after the receipt of the first dose. This finding would support efforts to maximize vaccine uptake with two doses among vulnerable populations. (Funded by Public Health England.)

pfortuny 5y ago

Exactly the same as “x% of automobile deaths were not using the safety belt”… What happens when everybody uses it?

deleted 5y ago
[deleted]
jonnycomputer 5y ago
Fair point.

mmastrac 5y ago

The calculations running over hospitalization numbers tend to show that vaccines are ~85% effective in preventing hospitalization, usually by showing the reduction in N/100k cases.

jonnycomputer 5y ago
That is what I've seen as well.

deleted 5y ago

[deleted]

jcelerier 5y ago

> Trivially, and to make the point, if 100% of people are vaccinated, then 100% of hospitalizations will be among the vaccinated I mean, that's still scary, people were hoping for exactly 0% of covid-related hospitalization if you're vaccinated

throwaway894345 5y ago
I'd be more concerned that 100% of people are vaccinated and that's still not enough to stop transmission.
jonnycomputer 5y ago
I can't argue about what general public thought; but I think the epidemiological consensus even before we had experience with these vaccines is that vaccine effectiveness wouldn't be 100%--based on our experience with other vaccines. Instead, we rely on population effects to do the work. If susceptibility to infection is above some point in the general population, then infections become a self-sustaining cascade through social networks (of course, the composition and structure of that network also matter--I'm simplifying). But if you can push susceptibility lower enough, the infections will not cause self-sustaining cascades. This is, btw, why I consider anti-vaxxers (in the before times) as free-loaders who relied on those around them being vaccinated to protect them.
- nradov 5y ago
  Anti-vaxxers won't be effectively protected long term by those around them being vaccinated. The Delta variant is sufficiently contagious that there will be no significant herd immunity effect. All of us can expect to get exposed eventually. https://www.businessinsider.com/delta-variant-made-herd-immunity-not-possible-astrazeneca-developer-2021-8 https://www.businessinsider.com/delta-variant-made-herd-immu...
  - jonnycomputer 5y ago
    I think this is why I didn't include the covid-anti-vaxxers in that mix; they're more like covid fatalists. Absent a vaccine, covid-fatalism--the idea that you will get it eventually--is not insane. Lots of simulations show you can flatten the curve with various measures, but the area under the curve ends up being the same in the long run; or at least that's my lay person understanding of it. Not getting everyone sick at once keeps everything getting overwhelmed at once ... but long sustained restrictions have costs too. But all that logic is really thrown out the window with widespread availability of effective vaccines.

baxtr 5y ago

Agree 100%. A friend of mine shared the article this morning and I basically said the same. By itself the 60% is a meaningless number and says nothing about the vaccine efficacy. > An embarrassing failure for science.org Yes. Looking at the author's bio, you would expect a more nuanced comment and not this kind of fear mongering. Meredith Wadman Meredith joined Science as a staff writer in September 2016, after covering biomedical research and its politics from Washington, D.C., for 20 years. Her current beat includes biology research, policy, and sexual harassment . She has been a staff writer for Nature and a contributing writer at Fortune. She has also written op-eds for The Wall Street Journal, The New York Times and The Washington Post. Her first book, The Vaccine Race: Science, Politics and the Human Costs of Defeating Disease, was published by Viking (U.S./Canada) and Transworld (U.K.) in February 2017. Meredith earned her B.A. in Human Biology at Stanford University and began medical school at the University of British Columbia in her native Vancouver. She completed her medical degree as a Rhodes Scholar at the University of Oxford in the United Kingdom, and earned a master’s of science at the Columbia University Graduate School of Journalism.

jonnycomputer 5y ago
I think it must be something about the incentives of publishing.
dkural 5y ago
The 60% is also not adjusted for age, see here for good explanations: https://www.washingtonpost.com/outlook/2021/08/31/covid-israel-hospitalization-rates-simpsons-paradox/ https://www.washingtonpost.com/outlook/2021/08/31/covid-isra... https://www.covid-datascience.com/post/israeli-data-how-can-efficacy-vs-severe-disease-be-strong-when-60-of-hospitalized-are-vaccinated https://www.covid-datascience.com/post/israeli-data-how-can-... This is such an important point, I think it's worth including the key table here: Vaccine effectiveness vs. severe disease for younger (<50yr) = 1 - 0.3/3.9 = 91.8% Vaccine effectiveness vs. severe disease for older (>50yr) = 1- 13.6/91.9 = 85.2% But if you combine the two, you get 67.5% !!!! which is the # people have been wrongly focused on.

ldjkfkdsjnv 5y ago

I think the science always knew this, but they mislead the population because being vaccinated is still better than not. The whole vaccination thing is a white lie. We have never eradicated the flu, it mutates too fast. Same is true with Covid-19. The medical establishment has always known this, yet they spread propaganda because, again, being vaccinated is safer. The numbers about 99% effective were a lie, they knew it would mutate and that would see a drastic drop. I would argue this is a dangerous game they are playing with public trust.

gowld 5y ago
It's no game.The vaccine was extremely effective. After a year, a new vaccine will be needed for the new strains. Just like the flu vaccines.
gtt 5y ago
In my opinion science should be about Truth, the rest should be left to people and their leaders. Truth being central to the process of science is what makes science unique and allows for societies to accumulate knowledge.
dkural 5y ago
Could you provide a source for your 99%, given you're accusing others of lying? The numbers I have are ~96% for the Pfizer, and ~94% for Moderna. I explain this in another comment below, but even against Delta, the efficacy is actually quite high, even in the Israeli data: Vaccine effectiveness vs. severe disease for younger (<50yr) = 1 - 0.3/3.9 = 91.8% Vaccine effectiveness vs. severe disease for older (>50yr) = 1- 13.6/91.9 = 85.2% The combined number suffers from Simpson's paradox, please read more: https://www.covid-datascience.com/post/israeli-data-how-can-efficacy-vs-severe-disease-be-strong-when-60-of-hospitalized-are-vaccinated https://www.covid-datascience.com/post/israeli-data-how-can-... & please stop spreading misinformation. 96-94% to 85-91% is against a new variant is hardly a drastic drop. The vaccine is saving millions of lives globally.
jonnycomputer 5y ago
When we make accusations like this, its becoming to actually point to specific examples where specific individuals or organizations have done this. For example, this doesn't accord with my recollection, by my recollection is skewed in various ways.

graycat 5y ago

You make a good point about the conditional probabilities. The article also said "most". There is some relatively good data from Israel, but, still, in practice most doesn't just mean > 50% but is essentially wildly undefined. So apparently the author(s) of the article like to write with emotional adjectives instead of important numerical data. The authors were trained in belle lettre (maybe art as in communication, interpretation of human experience, emotion or VEFEEE -- vicarious escapist fantasy emotional experience entertainment) or just like to grab people by the heart, the gut, below the belt to get eyeballs for ad revenue? Whatever, when they got to most I quit reading.

inter_netuser 5y ago

indeed, strange article. It is however quite possible at this point, that the effectiveness against symptomatic infection wears off to nearly zero after 5-6 months. This seems to be the cause with both mRNA and sinopharm's inactivated virus vaccine as well.