Probabilities of Covid-19

 

Astrazeneca Clears the Clot

In yet another badly-kept secret, the blood-clot investigation by the EU found the Astrazeneca vaccine still safe and effective for the general population based on a cost-benefit analysis. But they also said that the vaccine may be linked to a rare type of blood clot with low blood platelets, in general but also in younger people (under 55) in particular. They will update the product information to mention this possible risk. This is exactly what I expected.

The EMA did not provide any details on the general analysis but using Spiegelhalter's calculation (referenced in my last post on this subject), it appears that about several hundred cases of blood clots should have been observed since vaccinations began in Europe, compared to 30-40 that have been documented. In the rare blood clot analysis, they disclosed two calculations, "less than 1" vs 5, and "1.35" vs 12 (expected vs observed). Both calculations ignored cases that happened in the 14 days after vaccination (presumably the first shot although the press release did not specify), and weirdly, the age group for the analysis is "under 50" while it is "under 55" in sentences that do not cite data. The number of cases among the subgroup under 50 is smaller or equal to the number of cases among under 55. Those incidence ratios are huge, even if the counts are small.

The press release has another inconsistency. Up top, it says "most of [the rare type of blood clots] occurred in people under 55 and the majority were women" and in the middle, it says "the reported cases were almost all women under 55", and then later, it says "the majority of reports involved women under 55". Logic requires that if almost all were women and under 55, then it's not just the "majority" were women but "most" were women. I hope they clarify the record.

tl;dr For the vast majority of people, blood clots caused by vaccination is not a concern (based on data up to now) but a few unlucky people under 55 may develop a rare type of blood clot after vaccination that has led to deaths. Based on clinical trial results, the vaccine would have prevented many more deaths through Covid-19 by interpolating the VE, and so they continue to recommend its usage.

 

A Different Way to Think about Vaccine Efficacy

A loyal reader, who's a doctor out there saving lives, has plodded me many times to do a back-of-the-envelope calculation. I finally did, so I'll describe it here.

In the Johnson & Johnson trial, about 2 percent of the placebo group got infected in roughly two months. (This means 98 out of 100 participants who got saline shots in the trial have not been infected within the first two months, most of whom probably haven't been exposed to the virus yet. In earlier trials, the number is even higher.) Let's round the J&J vaccine efficacy to 60% for ease of calculation. That means the infection rate of vaccinated people is expected to be cut by 60%, from 2 percent to 0.8 percent over 2 months.

It's a little easier to think in terms of 12 months so we multiply the rates by 6. The baseline rate of infection over a year is 12 percent, and vaccination brings it down to 5 percent. If we (fully) inoculate 100 people, the expected number of cases should go from 12 to 5, so there are 7 fewer cases per 100 vaccinated. Flip that number around. What it means is for each averted case, we need to vaccinate 100/7 = 14 people. 

If your glass is half full, you'd say this is actually not bad because there are many common medicines out there with far worse effectiveness. According to Stat News, 60 people must take statins for one of them to avoid a heart attack.

If your glass is half empty, you'd notice that of the 14 who got inoculated, we expect just 1 will get a real benefit. The other 13 would have the same fate after a year, whether they got the shot or not.

The catch is we can't predict which of the 14 will benefit. We know that if those 14 did not get vaccinated, they will - with certainty - not benefit. If they take the shot, they've purchased a lottery ticket with 1/14 chance of winning and 13/14 chance of breaking even.

I just portrayed that too favorably. Some of the 13 will not benefit but will get harmed by the side effects. Buying that lottery ticket brings a small chance of making your health worse. To learn more about this, read my 2010 post on Avandia, the diabetes drug, here.

 

Bonus Time

If you're still reading, here's a bit more.

The computation above is called "number needed to treat" (NNT). This number depends on the baseline rate of event.

If you live in a country with a much lower rate of cases, then the NNT is much higher. For example, if the baseline infection rate is 10 times lower, 1.2% per year instead of 12% per year, then the expected infection rate for the vaccinated is also divided by 10, thus 0.5%. So for every 1,000 people vaccinated, we would have 12 - 5 = 7 fewer cases. So the NNT is now 1000/7 = 143. This country has to inoculate 143 people to reduce the case count by 1.

The media love to talk about the vaccine's impact on the death rate. The Covid-19 death rate is even lower, more like 0.2%. Let's bump up the efficacy to 90% so the death rate among the vaccinated is 0.02%. Out of 10,000 vaccinated people, we expect 20 - 2 = 18 averted deaths. The NNT for deaths is 10000/18 = 1250 556.

 

 

 

 

 

Comments

[Michael Droy]

Last line:
The NNT for deaths is 10000/18 = 1,250.

10000/18 = 555.5

[Kaiser]

MD: Thanks. Fixed.

[A Palaz]

So the NNTs are going to vary by age group

US reported death incidence by age group

<4 0.0001%
5-14 0.0002%
15-24 0.0017%
25-34 0.0073%
35-44 0.0210%
45-54 0.0596%
55-64 0.1466%
65-74 0.3595%
75-84 0.9021%
85+ 2.4335%

Also other factors in the mix such as avaliable successful therapy.

the reinfection poss ibility and length of immunity from vaccination.

[A Palaz]

But we need some the context too for year

Incidence. Incidence
All causes. Pneumonia
<5. 0.13% 0.0019%
5-14 0.02% 0.0005%
15-24 0.09% 0.0021%
25-34 0.18% 0.0072%
35-44 0.29% 0.0186%
45-54 0.54% 0.0518%
55-64 1.21% 0.1354%
65-74 2.53% 0.3254%
75-84 6.07% 0.7878%
85+ 18.01% 1.9121%

[Georgette Asherman]

If I hear another MD say "you still have a 5% chance of getting COVID with the vaccine" I will scream. Or if certain cheesy websites run articles about vaccinated people getting COVID.

An interesting statistics paper I would assign is the risk of accidents when traveling to the vaccine. In February I heard about elderly people driving in the snow 250 miles for vaccines. I felt they should have waited for something nearer. Even in New Jersey I will have to travel a total of 65 miles for the 2 trips. Friends of mine have to go south of Philadelphia.

[Michael Droy]

In the end the vaccine is treating Lockdown, not patients.
Just as Covid kills by an auto-immune over reaction, lockdown is an auto-immune over reaction to a limited threat.
Remove the threat (real or imaginary or just flu x2 for a 3 year period) and we can go back to normal.

Sure this is homeopathy - treating the patient's mind, not the body, but if it works it is worth it. And who cares if it is not scientific or if science is created for what is really just an end to stupid media relations.

[Kaiser]

MD: My view is the opposite. The vaccines are masking the effect of lockdowns. In the U.K., the vaccination campaign coincided with a lockdown, which they haven't eased till this week. Lockdowns reduce contacts, which prevents transmission.

[Kaiser]

GA: Great points. In my book, I have a quote of someone pointing out that there is a higher chance of dying driving to the airport than riding on the plane.

And yes, even in the worst cases, the case rate in the placebo groups of those trials was 2-3% so no one has 5% chance of catching Covid (within say 2 months). It is also amusing to see people assume that 100% of trial participants have been exposed to the virus. They can't seem to distinguish between a trial of a therapeutic in which everyone in the trial has the disease versus a vaccine trial in which we don't know how many have been exposed. Most of the uninfected people in those vaccine trials have simply not been exposed to the virus.

[Michael Droy]

Kaiser: Have you seen clear evidence that lockdowns have any effects?
I agree it isn't vaccines - as surely most spread comes from super spreaders and so out breaks go first through the younger non-vaccinated before elderly people get it later. In UK infections and deaths are both low, and given ever more testing infections are at extremely low levels even compared to last summer. (But if they stop lockdowns as a result, I'm happy to let them let governments/science take the credit falsely).

In the UK there is anti-body presence in some 50-55% of the population. That is surely why the natural Autumn rise winter peak and late winter collapse in infections must have happened in UK. Most of the European countries which have not fallen right off never really had a big first wave.

If it isn't enough for full herd immunity now, it certainly is enough to speed up the normal spring time collapse in infections. (the previous winter wave had a very late start).

And if we permit normal assumptions that natural immunity is a thing, or consider that T-Cell immunity might be a thing (particularly in children where no one understands why it ignores them), then that 50-55% anti-body presence might well mean something close to herd immunity.
I'm proposing this as an explanation for the collapse in UK infections, not as a guarantee of no 3rd wave or a rationale to not vaccinate.

GA: elderly travelling to get vaccines. I suspect in many cases any "legitimate" excuse to get out of the house has been grabbed. The further the better. I don't blame them.

[Kaiser]

MD: Your post illustrates the problem with every argument trying to explain the trends. In your view, it must be immunity. That requires both an assumption that immunity matters (which you explicitly did), plus an assumption that other factors such as lockdowns, masking, holiday parties and travel don't matter. Remember, the argument that there is no evidence that X matters does not justify an assumption that X does not matter. This fallacy is unfortunately also being peddled by "experts" who are saying that there is no evidence that vaccines cause rare blood clots as if that implies that they don't. In my view, a more reasonable approach is to assume all of those factors matter to some extent - and thus, a serious analysis must look at all factors in the same model, and not exclude them by assumption; or even worse, justify a single-factor analysis by an "all else equal" type stipulation.