Share of Omicron by Postal Number Region

[mrtassler]

Hello,

I like the idea of extrapolating the share of Omicron for each postal number region. Here's my attempt so far:

My question is how to deal with the statistical uncertainty. For this plot:

• Estimated share of Omicron for each data point is p=k/n where k is case count for Omicron and n is total sequenced cases
• Error bars are binomial with +/- zsqrt(p(1-p)/n) and z is the z-score for confidence 90%
• The data points for p are Logit-transformed and then a linear fit is performed
• The data are weighted due to their uncertainty with 1/Var(Logit(p)) as weight. For the variance of Logit(p) I used Var(Logit(p))=1/k+1/(n-k).
• The interval for the linear estimate is determined from the weighted sum of squared errors with normalized weight
• Data points were only excluded where the error is of the order of magnitude of the value itself or where p=0/p=1.

The outcome is so far comparable with your plot but with some differences here and there.

Thanks for the analysis. Looks like the share of Omicron is quite high in some regions already.

Best

Marcus Tassler

[corneliusroemer]

Very nice! Do you restrict to representative surveillance only, with reason = N?

Your approach is a bit more classical/frequentist. I use Bayesian hierarchical regression with two levels: post code area and post code of sending lab. I also fix the relative growth advantage for all of Germany.
In your case you lump all labs in one post code area together and don't do any pooling/sharing between areas.

One could use the results of my Bayesian regression and display it much more nicely for some eye candy. I was just more interested in other things.

In this notebook, I added incidences as additional predictors. Because one expects the share of Omicron to depend on the incidence that was the case when Omicron was seeded. High incidence -> low share since importations were diluted: https://github.com/corneliusroemer/desh-data/blob/main/incidence_numpyro.ipynb

[mrtassler]

Thanks!

I used N and X for this analysis to get a larger case count. A case was considered to be Omicron when the description contained the corresponding keyword so far. For the postal region I used the sending lab since I expected this to be the lab close to where the probe was taken.

The analysis doesn't include priors so far and I did not fix the growth advantage for Omicron in particular. The logistic growth is determined by the two case-exponentials for Omicron and Delta and as far as I understand at equal generation times with that by the ratio of the current R-values for them where stronger or weaker restrictions/better conditions for growth of the virus shouldn't play much of an important role in how the logistic function develops. I would have to walk through the formulas to understand if this is true if generation time is different.

Its good to see however that both approaches come to rather comparable results. Postal region 4 is an example where there are differences which should be due to the weighting with 1/Var(Logit(p)).

Will take a look at the notebook you pointed out. It sure is interesting that Omicron comes out at such a large share in some regions and case counts are still so low...

[corneliusroemer]

Do go through the formula for relative growth when there are different generation intervals, it's quite interesting to see the effect. Relatively slow growth in Germany seems to be at least partially an effect of the combination of shorter interval and low Delta growth rate. There's a preprint with some theory here: https://www.medrxiv.org/content/10.1101/2021.12.08.21267454v1?s=09

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On Wed, Jan 5, 2022, 00:09 mrtassler ***@***.***> wrote: Thanks! I used N and X for this analysis to get a larger case count. A case was considered to be Omicron when the description contained the corresponding keyword so far. For the postal region I used the sending lab since I expected this to be the lab close to where the probe was taken. The analysis doesn't include priors so far and I did not fix the growth advantage for Omicron in particular. The logistic growth is determined by the two case-exponentials for Omicron and Delta and as far as I understand at equal generation times with that by the ratio of the current R-values for them where stronger or weaker restrictions/better conditions for growth of the virus shouldn't play much of an important role in how the logistic function develops. I would have to walk through the formulas to understand if this is true if generation time is different. Its good to see however that both approaches come to rather comparable results. Postal region 4 is an example where there are differences which should be due to the weighting with 1/Var(Logit(p)). Will take a look at the notebook you pointed out. It sure is interesting that Omicron comes out at such a large share in some regions and case counts are still so low... — Reply to this email directly, view it on GitHub <#5 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AF77AQPJEFHVBXFRUG44ZVLUUN4ZNANCNFSM5LIO6ROQ> . You are receiving this because you commented.Message ID: ***@***.***>