## Vaccine Efficiency?

Recently, two vaccine companies have presented evidence that their vaccines are respectively “90% effective” and “94½% effective”. True or False: Assuming these results hold up, the chances are respectively 9 in 10 (945 in 1,000) that if you get vaccinated you won’t get Covid? If you said True you are both woefully mistaken and doubtless far from alone. The articles report that the same large number of people got the vaccine and a placebo and of the first 95 people to show up with the disease 90% (94½%) came from the group that didn’t get the vaccine. In other words, if you got the disease the chances are 9 in 10 you didn’t get the vaccine. That is not the same thing as: if you got the vaccine the chances are 9 in 10 you didn’t get the disease.

Hypothetically — to make the arithmetic easy, but not unrealistically — suppose the number of volunteers in each group was 10,000 and of the first hundred people to get the disease 10 got the vaccine and 90 the placebo. Thus 90% of the infected folks came from the placebo group and it is reported that the vaccine was “90% effective”. If 90% effective means that 90% of vaccinated people didn’t get the disease and 10% got the disease, we have to look at the fraction of people who got the vaccine and also got the disease, which was 10 divided by 10,000 or .001, i.e., .1%, one tenth of one percent, not 10%.

Suppose, now, in an alternative experiment the experimenters had waited longer, until they had, not 100 but 1,000, infected volunteers and the same ratio of vaccine-to-placebo held: 900 infected volunteers from the placebo group and 100 from the vaccinated group. Then the fraction of people vaccinated who got the disease would be 100 divided by 10,000 or .01 or 1%, ten times as great as in the earlier experiment with only 100 infected volunteers, despite the ratio of vaccinated to placebo volunteers in the infected group remaining the same. The ratio of vaccinated to unvaccinated people in the infected group bears no direct relation to the probability that vaccination prevents infection. In the words of the drug companies, the vaccine would be 90% effective in both experiments, whereas nether experiment suggests anything like what most people would take “90% effective” to mean. The drug companies are evidently very good at creating vaccines and disastrous at talking about them.

1. ### Andrew Usher said,

November 18, 2020 @ 8:14 pm

Though they're doing that math rather loosely, it is true – and would be equally so in both your hypothetical cases – that fewer people got the disease if they were vaccinated. If we assume, as you did, that the groups are of equal size then we may conclude that it reduces the chance of acquiring the disease by 8/9 (not 9/10, but it's almost the same) .

Of course their are many other questions and issues with vaccines and their effectiveness, but these claims aren't _just_ BS (assuming they are true).

k_over_hbarc at yahoo.com

2. ### Ambarish Sridharanarayanan said,

November 18, 2020 @ 8:15 pm

> The drug companies are evidently very good at creating vaccines and disastrous at talking about them.

I think they're very good at talking about them in the context of their overall goals.

3. ### Martin said,

November 18, 2020 @ 8:26 pm

The reported effectiveness rate basically echoes industry lingo and not what a layperson might conclude from the terminology. From the CDC website, writing about flu vaccine effectiveness: "Vaccine effectiveness is the percent reduction in the frequency of influenza illness among vaccinated people compared to people not vaccinated, usually with adjustment for factors (like presence of chronic medical conditions) that are related to both influenza illness and vaccination.

So, if you expect, or observe, 100 cases among a given population of unvaccinated people, and you see only 5 cases among a vaccinated group with comparable characteristics, that's a 95 percent reduction, or 95 percent "effectiveness".

It's really not possible to determine an effectiveness rate of the variety you suggest, which you describe as the chance that if you get vaccinated, you won't get Covid. That's because those odds are very much influenced by your behavior. If you get vaccinated, and then hole up in your basement, the chances are zero you'll get infected, so the vaccine is 100% effective for you. OTOH, if you get vaccinated and go hang out unmasked in a Covid ward, that's where the defined effectiveness comes in. If you were not vaccinated in that situation, you'd surely get Covid, 100 percent odds. But since the vaccine is 95 percent effective, your odds of catching Covid drop to 5 percent.

4. ### Josh said,

November 18, 2020 @ 8:51 pm

The good news is that the efficacy statistics reported in the press are more logical than you feared: they aren't measuring the fraction of the COVID cases in the placebo group vs. the vaccine group but the expected reduction in disease if one takes the vaccine relative to if one doesn't take the vaccine.

For example, today the Times reported that in Pfizer's latest numbers from its vaccine trials, the efficacy is said to be 95%. That's because so far, 162 members of the placebo group have contracted COVID, compared with 8 members of the vaccine group, for a reduction of (162-8)/162 or 95%.

If there was confusion in the initial reporting, I wonder if it resulted from the fact that Moderna's first interim analysis came from 95 cases—90 in the placebo group, 5 in the vaccine group—and some journalist assumed the 94.5 efficacy statistic came from (95-5)/95 rather than (90-5)/90, since these numbers are so close.

I'd be curious to see the press reports that got the story wrong, if you can still dig them up.

5. ### Andrew Usher said,

November 18, 2020 @ 9:12 pm

Then even my criticism is wrong, and yes, that is logical. It's quite expected that journalists would bungle statistical concepts; they do it all the time, as with everything science-related.

6. ### Amber Music said,

November 18, 2020 @ 9:41 pm

The assumption is that the placebo and vaccine groups are generally similar so that for the 1000 people in the placebo group infected there are 1000 similar events in the vaccine group who were in situations that would have infected them if they didn't get the vaccine. Since only 100 of the vaccine group got it, the vaccine prevented 90% of infections. Or the vaccine is 90% effective. As a mathematician, it seems straightforward and accurate to me.

7. ### Julian Hook said,

November 18, 2020 @ 10:22 pm

The post is certainly correct in its assertion that a lot of people don't understand vaccine efficiency statistics. Unfortunately the post itself compounds the problem by misstating what those statistics mean. Josh has it right in the comment above: it refers to the expected reduction in the probability of infection among those who get the vaccine.

8. ### Gregory Kusnick said,

November 18, 2020 @ 10:29 pm

If some fraction F of cases are in the placebo group, then Josh's formula gives the effectiveness E as follows:

E = (F – (1 – F))/F = 2 – 1/F

For F = 1/2, this gives E = 0, which is what we expect: an even split means the vaccine had no effect. Conversely, F = 1 (all cases in placebo group) gives E = 1, i.e. completely effective at preventing cases in the vaccine group.

So it follows that for F near unity, E is approximately equal to F; thus the confusion.

9. ### Tim Rowe said,

November 18, 2020 @ 11:51 pm

Surely most people would read it as their chance of catching the virus with the vaccine is 1/10 of the chance of catching it without? This seemw like a disengenuous attempt to discredit the scientific success.

10. ### eub said,

November 19, 2020 @ 1:35 am

"Assuming these results hold up, the chances are respectively 9 in 10 […] that if you get vaccinated you won’t get Covid?"

Without regard to whether you're exposed? Why would this be a typical or useful reading? The implication of this reading is that a 90%-effective vaccine results in a 10% chance of getting Covid even if you never leave your basement.

The actual meaning is strictly better than this. A 90% risk reduction means, in effect, that if you *would* have gotten the disease, you get a 90% chance of dodging it.

11. ### A1987dM said,

November 19, 2020 @ 2:59 am

@Tim Rowe:

Most *reasonable* people would read it that way, but not everybody is reasonable and plenty of people interpreted it to mean that 10% of people who vaccinate will catch COVID.

12. ### IMarvinTPA said,

November 19, 2020 @ 7:28 am

Why isn't it just:
(Number of vaccinated who got sick)/(Number vaccinated) = Effectiveness rate?
and
(Number of unvaccinated [placeboed] who got sick)/(Number unvaccinated) = Control rate?

Those numbers I could compare and make a decision from. (If they are the same number, then the vaccine isn't effective.)

13. ### Bloix said,

November 19, 2020 @ 8:19 am

I don't understand why this is so difficult.

The placebo and vaccine groups are set up to be as similar as possible.
In the Pfizer trial, there were 162 cases in the placebo group. The presumption is that in any similar group of the same size, there would also be 162 cases. But instead, in the vaccinated group, there were eight cases. Therefore, we can conclude that the vaccine prevented approximately 154 cases. 154/162 = 95%.

In the same trial, there were nine "severe" cases in the placebo group and one severe case in the vaccinated group. So we can conclude that the vaccine prevented eight severe cases, more or less. 8/9 = 89%.

In the Moderna trial, there were 90 "symptomatic" cases in the placebo group and five in the vaccinated group. Therefore the vaccine prevented about 85 symptomatic cases. 85/90 = 94.4%.

14. ### Jerry Friedman said,

November 19, 2020 @ 9:46 am

IMarvinTPA: What are you going to do with those numbers that doesn't give you the same answer of 95% or so?

The problem with using the number of people in the study as the denominator is that presumably not all of them were exposed to covid-19.

15. ### linda seebach said,

November 19, 2020 @ 9:54 am

If the drug companies are reporting their vaccine trial results in the same mathematical language customarily used in reports of other medical trials, which is apparently the case, your comment that they are "disastrous at talking about them" is unfair, and seemingly intended to create suspicion that they are trying to mislead.

16. ### Kristian said,

November 19, 2020 @ 9:57 am

If I sold an amulet that is 90% effective at preventing shark attacks (let's assume it's for real), I don't think people in general would think this means that with the amulet your chances of not getting attacked at 9 in 10 and your chances of getting attacked are 1 in 10.

Of course lots of people are very bad at math or allergic to math, so especially if they're asked a loaded question ("does it mean your chances of getting attacked with the amulet are 1 in 10?"), many people will probably say yes without thinking about it.

I agree with the general principle that statistical reporting is often confusing and it's often much clearer to be told what happened in the experiment (e.g. after X weeks x% of the vaccinated group had been infected and y% of the placebo group).

17. ### Bloix said,

November 19, 2020 @ 10:15 am

"The problem with using the number of people in the study as the denominator is that presumably not all of them were exposed to covid-19."

You don't use the number of people in the study as the denominator. The number of people in the study is not used at all in calculating the efficacy. You use two numbers: the number of people infected in the control (placebo) group and the number infected in the vaccinated group. That's it.

"it's often much clearer to be told what happened in the experiment (e.g. after X weeks x% of the vaccinated group had been infected and y% of the placebo group)."

You don't use the percentage of each group that is infected to calculate the efficacy.

It's true that all the information you might want to know is not captured in the single data point that is the effective rate. There's a lot more information that can be gathered and presented in various ways.

But effective rates are useful, easy to calculate, easy to present, easy to grasp, and easy to compare with other studies. The press has reported them accurately. There's nothing stupid or nefarious going on here, and it's incomprehensible that people are unwilling to take the five minutes necessary to understand why this is so.

18. ### ardj said,

November 19, 2020 @ 10:28 am

I take Bloix's point. But the question of equal exposure to the evil virus is a fair one. It seems to me that the only way to be sure of a reasonably accurate rate would be to deliberately expose test groups to the virus and keep control isolated, just as experimental subjects are infected with 'flu (if I recall correctly).

19. ### Rose Eneri said,

November 19, 2020 @ 10:36 am

I have not been keeping up with news on the vaccine trials, but from what I've read here it seems that none of the trials discussed is of a "challenge" type. In other words, the people getting the actual vaccine are not subsequently intentionally exposed to the COVID virus. It seems to me that a challenge trial is the only way to establish real and true effectiveness.

Of course, challenge trials require strict controls and a sufficient number of willing, informed study participants.

November 19, 2020 @ 10:47 am

@ardj: In principle, yes, you can expose people to the virus and in some sense that would reassure you that you were getting an accurate assessment of the effectiveness of the vaccine. But the dubious ethics of deliberately exposing people to something that might kill them suggests that it makes more sense to unleash the power of statistics on large samples instead. I believe the Moderna test had 30,000 participants, equally divided into a test group and a placebo group (and further equally divided between women and men, with a controlled age distribution, etc.). Assuming the samples were well chosen, it seems pretty unlikely that there were nine times as many members of the placebo group who were then exposed to the virus compared to the number of members of the test group who were exposed.

21. ### Kenny Easwaran said,

November 19, 2020 @ 10:56 am

The last two comments I see, from ardj and Rose Eneri, are both suggesting that some sort of "challenge trials" would be needed to establish an accurate estimate of efficacy. While challenge trials would certainly be faster, and give you larger numbers of cases to calculate more precise numbers from, the challenge trials *wouldn't* tell us what we *actually* care about, which is how much the vaccine protects people in ecologically valid conditions, including actual real-world types of exposure and the actual real-world mix of viral variants that are going around. Challenge trials would presumably involve one specific strain (so there would be worries about whether some of the different variants or strains in circulation might have mutations that get around the protection of the vaccine), and challenge trials would presumably involve one particular method of administration (perhaps our body fights off infections more or less effectively when it comes in through the nose or through the eye or on a droplet or in a deeply-inhaled aerosol). Furthermore, it could be that the challenge is done in a way that exceeds the protection from the vaccine, so that nearly everyone in both groups gets infected – that might make us think the vaccine isn't effective, but with these ecological trials we can see that in real-world conditions, you are 20 times more likely to get infected if you don't have the vaccine than if you do.

22. ### Paul Kay said,

November 19, 2020 @ 12:19 pm

Something several commenters have pointed out, starting with Andrew Usher, which I failed to see, is that the meaningful notion of efficacy apparently intended by the vaccine makers is not — as I had assumed — about the probability that one will get the virus if one takes the vaccine but rather the relative probabilities of infection with the vaccine to infection without the vaccine. My arithmetic was okay but my understanding of the intended interpretation of "efficacy" was wrong. So my characterization of the drug companies' definition of efficacy as "disastrous" was altogether unjust. Under the apparently intended definition of efficacy, an efficacy of 90% holds in every one of the following conditions: (a) probability of infection is 9% without vaccine and 1% with vaccine, (b) probability of infection is 4.5% without vaccine and .5% with vaccine, (c) probability of infection is .9% without vaccine and .1% with vaccine, … "Efficacy" doesn't tell you what your chances are with the vaccine, it tells you how much better your chances are with the vaccine than without. This is probably a concept of interest to many people in deciding whether to seek vaccination. It also makes sense of earlier statements of various experts that vaccines with efficacies as low as 50% would be acceptable.

23. ### Kristian said,

November 19, 2020 @ 12:43 pm

Vaccines build herd immunity at a certain point anyway, so they don't have to be completely effective to protect everyone.

24. ### Bloix said,

November 19, 2020 @ 1:19 pm

The point is not whether any individual will benefit from the vaccine. The point is that we need to drive the reproduction ratio below one. If the reproduction ratio is less than one, the virus eventually dies out. If it is greater than one, the virus spreads exponentially. The math for this is very simple, and it's the same as the math for a nuclear reaction or for the extinction of the woolly mammoth.

You can drive the reproduction ratio down by a rigorous regime of social distancing, prohibitions on travel, closure of restaurants, bars, churches, and schools, and contact tracing of infected persons combined with strict quarantining of exposed persons.

Or you can do it by making the virus less infectious. That is what a vaccine does – it makes people less susceptible to infection. To stop a pandemic, it doesn't need to be 100% effective, it just needs to be effective enough, either by itself or combined with other public health methods, to drive the reproduction ratio lower than one. It's nice if the vaccine is so effective that any individual can be pretty sure that he or she won't get sick, but that is not the point. The point is to break the chain reaction-like nature of the disease's spread. Knowing the effective rate provides the information needed in order to determine whether the vaccine will be able to do this, and if so, how fast it can do it.

One would think that after nine months of this shit, these simple facts would be common knowledge on the level of "the world is round."

25. ### Trogluddite said,

November 19, 2020 @ 3:10 pm

I think that Paul Kay's follow-up post highlights that the initial problem was linguistic rather than statistical (as one would hope on LL!). There is no shortage of words which have precise scientific or technical definitions differing from their everyday meanings, and the word "effective" can be ambiguous even in everyday speech, since we have to know what effect is anticipated. It should have been obvious from the outset that this word might present a problem of interpretation for some lay readers (especially those with little patience!)

Either the drug companies' press officers or the journalists presenting the results to the public should have summarised them using jargon-free language comprehensible to any reasonably bright citizen – as several previous posters have demonstrated is easily done. While I agree that lack of familiarity with statistics is a common problem, this case seems more a matter of poor science journalism which makes no effort to help lay readers comprehend jargon which is, perfectly reasonably, beyond their expertise (though, of course, "scientists say: [cut'n'paste]" keeps down costs!)

26. ### Ross Presser said,

November 19, 2020 @ 5:10 pm

So Paul Kay's followup comment properly gives the industry-specific meaning of "efficacy":

> "Efficacy" doesn't tell you what your chances are with the vaccine, it tells you how much better your chances are with the vaccine than without.

Several other words were used in the blog post title, the blog post body, and in comments. Do any of them have different industry-speciific meanings? Are any of them used as exact synonyms for Efficacy?

* Efficiency
* Effective
* Effectiveness

27. ### Jerry Friedman said,

November 19, 2020 @ 5:16 pm

Bloix: "The problem with using the number of people in the study as the denominator is that presumably not all of them were exposed to covid-19."

You don't use the number of people in the study as the denominator.

Yes, I was explaining to IMarvinTPA why not (or one reason why not, if there's more than one).

28. ### Ross Presser said,

November 19, 2020 @ 5:24 pm

I thought of an analogy … not perfect, but it points out the necessary distinction.

For "being exposed to virus" think "car accident".
For "getting disease" think "being injured in accident".
For "vaccine" think "wearing seatbelt".

If you are in a car accident, wearing a seatbelt makes it less likely that you will be injured. It says nothing about how likely you are to be in a car accident, nor does it say anything about how many people wearing seatbelts will still be injured.

The way this is not a perfect analogy is that car accidents are not communicable diseases; having an injury does not cause other people to have accidents, and wearing a seatbelt does not prevent you from causing accidents.

29. ### Mark P said,

November 19, 2020 @ 5:37 pm

Bloix, your comment is the first time I have seen it explained that the primary goal of a vaccination is not to protect the vaccinated but rather to break the chain of infection, and that the effectiveness is expressed in those terms. I suspect that most people, in fact, the overwhelming majority of people, think that the point of a vaccination is to protect the vaccinated, and that as a secondary effect, the infection rate will drop. They will see an effectiveness and think it means that it refers to a level of individual protection. I have not seen or heard it explained as you did, so expecting me and the rest of the non-epidemiologists to have figured that out is probably unfair.

30. ### Gregory Kusnick said,

November 19, 2020 @ 5:48 pm

If this comes down to a disconnect between the technical definition of efficacy and its everyday, common-sense meaning, what should we take the common-sense meaning to be?

We all know people who, in the face of the pandemic, continue to shake hands, hug, congregate in groups without masks, and go out to parties and crowded bars. Suppose for the sake of argument that 10% of those people end up getting sick. Does common sense then tell us that behaving recklessly is 90% effective at preventing disease? Clearly not, yet this is exactly parallel to the calculation that Paul originally proposed as "what most people would take '90% effective' to mean".

31. ### Rachael Churchill said,

November 19, 2020 @ 6:04 pm

Mark P: No, you were right the first time, the effectiveness does refer to how effective the vaccine is at protecting the vaccinated individual. Bloix's point was that you don't need that effectiveness (at protecting the vaccinated individual) to be 100% in order to break the chain of infection and drive R brie 1.

32. ### Josh said,

November 19, 2020 @ 6:34 pm

@Ross Presser: Excellent question. There is indeed a difference in industry terminology between studies of vaccine "efficacy" and vaccine "effectiveness."

Studies of vaccine "efficacy" are randomized controlled trials under ideal conditions.

Studies of vaccine "effectiveness" are observational studies carried out in real-world conditions.

33. ### Andrew Usher said,

November 19, 2020 @ 11:02 pm

To Bloix's comment:
Yes, that is how it is technically expressed. But if we have seen anything from the progress of this disease, it is that the model of a constant reproduction rate has failed pretty dramatically. The many (and still uncertain) real-world factors behind it can't be summed up in one number we can manipulate at will, except in imaginary models.

We can absolutely predict that a vaccine of reasonably high effectiveness will retard infections compared to no vaccine, but making any quantitative predictions beyond that is foolish. The only thing we've absolutely known through the whole course is that it _will_ fall below 1 at some time because of immunity, regardless of current trends. Contrary to the scaremongers' deceptions, it can not increase indefinitely no matter what we do or don't do.

34. ### Philip Taylor said,

November 20, 2020 @ 6:30 am

Andrew, could you clarify what "it" is in your final clause : "it can not increase indefinitely no matter what we do or don't do" ? Is "it" the R-value ?

35. ### Sean Purdy said,

November 20, 2020 @ 6:53 am

I have no expertise in statistics or epidemiology, but my understanding of “90% efficacy” in the news reports was definitely NOT that the vaccine would reduce my chances of getting covid to 10% – because my chances of getting covid are also dependent on how prevalent it is in the population and how many people I have transmissably risky contact with.

So the big news for me was that this could very quickly reduce the incidence of covid in the population. Having greater protection as an individual was secondary to this – and would not be something I would rely on without the population-scale effect. A 10% chance of getting this disease is still far too high for my liking.

(I know this restates points above from Bloix and others, but it’s one layman’s answer to the question in the OP.)

36. ### Andrew Usher said,

November 20, 2020 @ 8:14 am

Philip Taylor:
If you must make it precise, the it could mean the rate of new infections, or the number currently infected. Though of course it's also true of the R-value itself, that's a higher level or sophistication than would be directed at the general public.

Now to be similarly technical, what is "a 10% chance of getting the disease"? We can only measure that over a relatively short time period, and that depends on your behavior as much as anything. From the first day I her enough about this disease to understand it, I assumed that my chance of getting it (some time) was close to 1

37. ### Philip Taylor said,

November 20, 2020 @ 9:01 am

" it's also true of the R-value itself, that's a higer level or sophistication than would be directed at the general public" — that is an interesting assertion. In the UK, we (the lay public) hear or read about the current R value in various parts of the country on a daily basis, and are therefore presumably assumed to understand it; is the same not true in the United States ?

38. ### Philip Taylor said,

November 20, 2020 @ 9:10 am

… and to address your later point ("From the first day I heard enough about this disease to understand it, I assumed that my chance of getting it (some time) was close to 1") — that too I find interesting, because I have always assumed that the probability of my contracting Covid-19 was close to zero. Only 0.75% of the world population (approximately) have contracted Covid-19 since the first reported case, and at that rate it would have to remain circulating in the population at the current rate for more years than I expect to live before the probability of my contracting it exceeded 0.5

39. ### Riikka said,

November 20, 2020 @ 9:43 am

Iis even more complicated. The effectiveness of the vaccine may not have anything to do with stopping the transmission:

It is not yet clear whether or not the vaccine could protect against coronavirus infection or simply against developing symptoms once you are infected.

“If it’s stopping infection then, by definition, it should be stopping transmission from one person to another,” said Hunter. "If you don’t get the infection because you’ve been immunised you’re not going to infect me anyway. But, if what you’re getting is an asymptomatic infection, there is still the risk potential that you could infect me, although it will almost certainly be a lot lower than if you are actually clinically ill.”

40. ### Thomas Hutcheson said,

November 20, 2020 @ 10:15 am

I do not understand the criticism. Surely one would not want the reported interim results to depend on the arbitrary cut-off point of the number of people in the subsample.

41. ### david said,

November 20, 2020 @ 10:50 am

Vaccine efficacy has been well defined for more than a century.
https://en.wikipedia.org/wiki/Vaccine_efficacy

95% efficacy is very high. The FDA said they would consider anything over 50% and the highest efficacy mentioned in the wikipedia article is 79%.

42. ### James Wimberley said,

November 20, 2020 @ 4:03 pm

A challenge trial has been approved for the Imperial College vaccine in the UK. The purpose a such trials is to get statistically significant results faster. The Phase 3 non-challenge trials seem to use 150 cases as the benchmark for this, and need 30,000 participants or so. If it's the same number of cases for a challenge trial, where both vaccine and placebo groups are deliberately exposed to the virus, the number and time needed are much less. Guess that the infection rate from deliberate exposure is 50%, and the vaccine benchmark is >50% effective, the trial only needs 1200 participants and one month. But – a big but – it is plainly unethical to create >150 cases of a potentially lethal disease in order to cross-check the statistical results of a properly conducted Phase 3 trial. Furthermore, the volunteers for a challenge trial are all young and very healthy. I suppose you can't ethically find out the differential efficacy in more vulnerable old people.

43. ### Andrew Usher said,

November 21, 2020 @ 1:02 pm

Philip Taylor:
No, to my knowledge, the R-value is not normally used in American reporting. If they want to use that concept they may say 'cases are doubling every X days/weeks', which is probably more meaningful both to laymen and to doctors – of course they'll only report when cases are rising.

As to the probability of contracting the disease: you say 0.75% of the world population has. Well, we know that's an underestimate, because most cases are undiagnosed, and some are totally asymptomatic. Further that figure includes parts of the world where spread has been extremely low or zero, contrary to the case in the US, the UK, and the rest of Europe. The actual number of Europeans (and also Americans) that have been infected is probably not under 10%, and will continue to rise.

Is that alarming? Only if you want it to be. Our governments and media generally want it to be.

44. ### Kaleberg said,

November 23, 2020 @ 12:27 am

Another way of thinking of 90% effectiveness is that in the face of a postulated infectious exposure to the virus, one has a 10% chance of being infected if one has been vaccinated but a 90% chance of being infected if one has not been. The idea is that one wants a rate of likelihood of infection independent of the rate of exposure. That's why the endpoints are a certain number of infections, not a certain period of exposure.

BTW How many people, besides me, love the way they describe letting the experimenters look at the data as unblinding it? Note that they don't unblind the experimenters. They unblind the data. People say "love is blind", but I never hear about a romance breaking ending with an unblinding, or perhaps I don't hang out with enough medical researchers.

45. ### Philip Taylor said,

November 23, 2020 @ 8:54 am

"Another way of thinking of 90% effectiveness is that in the face of a postulated infectious exposure to the virus, one has a 10% chance of being infected if one has been vaccinated but a 90% chance of being infected if one has not".

I don't think that that is true. 90% effectivness tells us nothing at all about the risk of being infected or otherwise — all it tells us is that if vaccinated, one is 90% less likely to be infected that if one were not. That is all.

46. ### Andrew Usher said,

November 23, 2020 @ 7:38 pm

Right; I don't know what Kaleberg was spinning off. I don't need to ask why you ignore my last message; no one else resists indoctrination on this issue.

47. ### Philip Taylor said,

November 24, 2020 @ 6:33 am

Andrew — I am not 100% certain that "I don't need to ask why you ignore[d] my last message" refers either to me or to "Is [the fact that the actual number of Europeans (and also Americans) that have been infected is probably not under 10%, and will continue to rise] alarming?" but assuming that the answer to both is "yes", then I did indeed choose to ignore it because it seems to me that no matter whether or not "our governments and media generally want it to be [alarming]", it is alarming and that is simply an undeniable fact — as undeniable as the facts that the earth is not flat, that it rotates around the sun, and that all species arose through the mechanism of evolution rather than through creation or divine intervention.

48. ### Andrew Usher said,

November 24, 2020 @ 6:44 pm

I don't think that whether something is 'alarming' is a matter of fact; at least, it's not a fact about the virus as your comparisons would suggest.