If more people can help ensure we read this correctly that’s super important. If it turns out that we’re down at 35%, that’s amazingly great, and means as I noted on 12⁄24 that I think we can mostly muddle through.
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.
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.
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.
If more people can help ensure we read this correctly that’s super important. If it turns out that we’re down at 35%, that’s amazingly great, and means as I noted on 12⁄24 that I think we can mostly muddle through.
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:
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.
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.
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:
My translation:
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
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.