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Covid 2/11: As Expected

The question of how much more infectious B.1.1.7 is is pretty useless without also referencing a generation time estimate. Different agencies/countries use different values for that, so the numbers for the relative R number R_B.1.1.7 / R_old they give are not directly comparable. I expanded on this in a comment a while ago.

In the meantime, the Danish SSI also published a report in which they also stress that the numbers of how much more infectious B.1.1.7 is can't be compared across countries due to in particular different generation times being used. This report is from January 21., and in it they estimate relative R to be 1.36 as of January 14. A newer report from February 3. mentions that SSI now estimates a relative R for B.1.1.7 of 1.55. The SSI uses a generation time of 4.7 days, the English PHE uses a generation time of 6.57 days.

The quoted conclusion of 37% increase in infectiousness from the original post is unfortunately a mistake, see my comment here.

Covid 2/11: As Expected

This is an estimated 37% increase in infectiousness. Compared to 50%, that’s much much better. The difference is enough to give us a puncher’s chance of things not being so bad, both buying us time and reducing how bad it is when the time comes.

Unfortunately, this is an incorrect conclusion from the data referenced in the tweet. It seems the 37% number was obtained by dividing 1.07 by 0.78, which rounds to 1.37. However, while 1.07 is the R of the B.1.1.7 variant, the 0.78 is not the R of the other variants, but the overall R (it says so right in the tweet!), which includes B.1.1.7. As B.1.1.7 is a sizable portion of total cases, it already skews overall R upwards quite a bit, and this means that the 37% number is an underestimation.

The latest conclusion from the SSI that I am aware of is, as is also mentioned in the article linked in the post, that B.1.1.7 is 55% more infectious (using the Danish generation time estimate of 4.7 days).

Covid 1/14: To Launch a Thousand Shipments

SSI (Denmark) published a new report today, that makes some of the things I talked about in the parent comment clearer.

Bilag (=Appendix) B talks about estimating the relative growth rate for B.1.1.7. On page 14 they write:

Det mest interessante er den tidslige udvikling. For hver uge øges log(odds) med 0.077 per dag. Med den nuværende lave andel af cluster B.1.1.7 svarer dette til at hyppigheden af cluster B.1.1.7 blandt de smittede stiger med 71% (95% CI: [33%, 120%]) per uge.

My translation:

The most interesting is the temporal evolution. Every week log(odds) increases by 0.077 per day. With the current low share of cluster B.1.1.7, this corresponds to the frequency of cluster B.1.1.7 among the infected increasing by 71% (95% CI: [33%, 120%]) per week.

On the next page they consider the relative contact number (=Rt) Rt_B.1.1.7 / Rt_other. They clarify that Rt is taken with respect to an assumed generation time of 4.7 days for all variants, and estimate this quotient to be

1,36 (95% CI [1,19; 1,53])

Taking this to the power of 7/4.7 to get weekly rates as I did in my parent comment we would get a weekly factor of 1.58, which is different from the 71% increase per week that they had. I am not sure how to reconcile this. They write that they are using the SEIR model (which I am not familiar with) to convert between the data they consider on page 14 and the ratio of Rt's, so this might be the reason.

Covid 1/14: To Launch a Thousand Shipments

In the former control group, Sweden is throwing out the extra vaccine doses in Pfizer vials, because we might dislike the FDA but at least we don’t have to deal with the European Medicines Agency, who are totally Delenda Est Club members:

But good news, they could soon give the go ahead to stop throwing away vaccine doses.

Just for additional information / clarification, as it seems to me this could be interpreted to suggest that EU countries, after starting vaccinations on the 2020-12-27, threw away anything left over after taking 5 doses out of a vial until some time after 2021-01-07, whenever EMA approved using the extra doses:

While I am not familiar with EMA's role in this, and also do not know how Sweden handled it, it is certainly not true that every EU country threw away what was left over after 5 doses. In Denmark it was headline news on 2020-12-28 that more doses had been vaccinated than expected the previous day, the reason being that while 5 doses per vial was expected, they usually got 6 and often even 7 doses out of each vial. These extra doses were used from the start, and this was encouraged from the relevant Danish authorities[1], see for example this article or the evening news on public television of that day.

  1. Using delivered vaccines seems to go reasonably well in Denmark as well, according to the daily report, the status today is that 88.7% of received doses have been used, though they are still assuming 5 doses per glas of the Pfizer BioNTech vaccine (two days ago they had a doses used quota of 126.1% because of this). ↩︎

Covid 1/14: To Launch a Thousand Shipments

Short version: I think it comes down to different generation times used, and the Danish reports, the English reports, as well as what the referenced tweet 1 is saying are consistent with (assuming for the moment cases of the other variants stay constant) B.1.1.7 cases increasing by something like 60% to 80% each week. I would be very happy about corrections from someone who understands this better, I am not an expert at all.

Long version:

(Note: I will think about the change in infectiousness between other, old variants and B.1.1.7 as multiplicative below.)

In interpreting these numbers I think it is highly relevant to understand what is used as a generation time. In the referenced tweet 1, it is stated that a generation time of 5.5 is used. However, PHE (Public Health England), in their first report on B.1.1.7 2 seem to use 6.57:

we calculate the week on week growth rate in both S-negative and S-positive cases by simply dividing the case numbers in week t+1 by the case numbers in week t. We correct these weekly growth factors by raising them to the power of 6.57 to ensure they can be interpreted as reproduction numbers (given the mean generation time of SARS-CoV-2).

I interpret this like this: The effective reproduction number Rt is the factor the cases multiply by in the timespan of a generation time, so here PHE uses 6.57 days, meaning with their Rt we can get the weekly increase as Rt^(7/6.57). By the way, I think they made a typo and meant "by raising them to the power of 6.57/7".

E.g. Rt for B.1.1.7 being 70% larger than for the other variants means a weekly factor of 1.7^(7/6.57) = 1.76, so if other variant's daily cases stay constant, then daily B.1.1.7 cases will multiply by 1.76 every week.

However, SSI (Statens Serum Institut, in Denmark) generally seems to use a generation time of 4.7 [1]. So where PHE would get a Rt-ratio Rt_B.1.1.7 / Rt_other of say 1.7, we would expect SSI to obtain around 1.7^(4.7/6.57) = 1.46. This obviously still corresponds to a weekly increase of around 1.76. If PHE has 1.5, then SSI should have 1.34.

Unfortunately this is all not very transparent, SSI's reports don't really make this clear, not even when they cite the PHE numbers... :(.

The latest Danish information on what Rt for B.1.1.7 is when compared to other variants current in Denmark is from a press conference two days ago (2021-01-13), see here, the important information being: SSI estimates (as of two days ago) Rt in general to be between 0.85 and 0.9, and for B.1.1.7 Rt is estimated to be 1.2.

As B.1.1.7 still is likely under 5%, and very likely not more than 10% of total cases, we can estimate Rt_other as roughly being the overall Rt, perhaps taking a value towards the lower end of the range. So with Rt_other = 0.85 and Rt_B.1.1.7 = 1.2 we would get as ratio roughly Rt_B.1.1.7 / Rt_other = 1.41. This should be interpreted with respect to a generation time of 4.7, converting it to PHE generation time of 6.57 we get 1.41^(6.57/4.7) = 1.62. Both correspond to a weekly factor of around 1.7.

It is unclear to me whether it is better to think of the change in infectiousness between other variants and B.1.1.7 multiplicatively (so assuming Rt_B.1.1.7 / Rt_other will stay roughly constant if Rt_other changes) or additively (so assuming Rt_B.1.1.7 - Rt_other). But this might be dependent on how exactly the virus spreads, how this interacts with how people behave etc... I have been thinking about it multiplicatively up to now, but if someone has data / arguments for why additively or some other model might be better I would be very interested.

  1. See for example the last line on page 11 in 3. This report, in which they explain how they estimate the contact number (their terminology for Rt) is a bit older (2020-10-23), but I have also seen this in several other reports by SSI where generation time mattered and as far as I can remember never a different value, and am fairly confident that SSI uses 4.7 days as generation time. ↩︎