**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did not specify), and weirdly, the age group for the analysis is "under 50" while it is "under 55" in sentences that do not cite data.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.

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