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Coronavirus - Modelling Aspects Only

The home for all non-political Coronavirus (Covid-19) discussions on The Lemon Fool
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This is the home for all non-political Coronavirus (Covid-19) discussions on The Lemon Fool
scotia
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Re: Coronavirus - Modelling Aspects Only

#503810

Postby scotia » May 30th, 2022, 4:44 pm

Correction

Moderator Message:
Now corrected in the original

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Re: Coronavirus - Modelling Aspects Only

#517776

Postby scotia » July 28th, 2022, 12:55 am

Back on the Coronavirus -General Chat - No Statistics board, Redsturgeon posted on the 26th July

https://www.lemonfool.co.uk/viewtopic.php?p=517289#p517289

Which reported "I heard today that covid deaths are up in the UK".

I responded that some of the published data may be out of date - so I have come over to this board to provide my reasoning. I'm getting back to my simple model which proposes that the deaths are proportional to the hospital admissions a period of days before. In order to get the most up to date death data , I previously used the Covid deaths by publish date. However this data became erratic as to when it was published, and now only seems to appear around once per week - so I gave up on this model. The alternative was to use the Covid deaths by registration date - but this has the disadvantage that it is not static - with updates (additions) appearing many days after the most recent values. However I thought that an entry might be reasonably static about a week after its first publication.
So looking at the most recent data extracted this evening (27/7/22) for England, there is data on both admissions and deaths by registration date up to 25/7/22. To make allowance for later updates to the deaths data, I have assumed that it would be reasonable static at 18/7/22, so I have only included deaths up to that date. And for the model I have used a multiplicative factor as 0.11, and the delay between admissions and deaths as 10 days. This fit was achieved by looking at the earlier peak around 13th April. All of the data plotted are 7-day totals - to iron out any weekly dependencies,

Image

We see that the plotted deaths are continuing to rise - but the last (blue) data point represents the week ending 18/7/22. Looking at the (red) projected deaths, based on admissions, we see that a peak is around five days later - around 23/7/22. So if we believe the model, we are probably past the peak of deaths. Now I don't expect the simple model to give precise results - given that its parameter fit is based on data around April-May, however i would be (unpleasantly) surprised if we do not see that the registered death rate has peaked around now. But given that we need to wait for around a week for registration date deaths to settle down, we probably will need to wait for at least a further week to see if my hypothesis is correct. Optimistically - I hope I am :)

I have not included Scotland in this model, since no Scottish Covid deaths data has been published since the 2nd of June.

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Re: Coronavirus - Modelling Aspects Only

#517835

Postby funduffer » July 28th, 2022, 9:47 am

Scotia,

I have followed your modelling of deaths v hospital admission for some time, and it is interesting to me that the correlating factor has changed over time.

You are now using a factor of 0.11, which I think is lower than what you started with.

I wondered if you had a record of how this factor has changed during the pandemic? My impression is it has reduced over time, suggesting that immunity due to vaccination or prior infection has blunted the deadliness of the virus, and/ or treatments have improved.

Any thoughts?

FD

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Re: Coronavirus - Modelling Aspects Only

#517856

Postby scotia » July 28th, 2022, 11:07 am

funduffer wrote:Scotia,

I have followed your modelling of deaths v hospital admission for some time, and it is interesting to me that the correlating factor has changed over time.

You are now using a factor of 0.11, which I think is lower than what you started with.

I wondered if you had a record of how this factor has changed during the pandemic? My impression is it has reduced over time, suggesting that immunity due to vaccination or prior infection has blunted the deadliness of the virus, and/ or treatments have improved.

Any thoughts?

FD


Yes - when the factor being used clearly needs updated, it signals that there has been some change in the effect of the Covid virus. My original graphs (early Dec 2020) used past data to estimate the factors - and 0.265 with a delay of 13 days seemed to fit. But as we moved from late December into January, it became obvious that these these numbers were too optimistic for the recent data, and 0.3 with an 11 day delay became a better fit. This coincided with the PM announcing that the latest variant had a higher mortality rate. However vaccines were on the way - and hopefully this would bring substantial changes - and they did! By the end of February 2021 I revised the multiplicative factor down to 0.26 to achieve a better fit to the most recent data, then down to 0.2 in early March, and further down to 0.175 by early April. By late April I was struggling to find a fit to the ever-reducing numbers, and I had moved the multiplicative figure down to 0.075 with a time slip of 23 days. The success of the vaccines had been spectacular. But moving on to May/June, the numbers began to rise again - probably due to the new Delta variant which was causing some concern. By September 2021 the mutiplicative factor had risen to 0.14 with a time slip of 11 days. In November the factor was increased to 0.15. I continued with these parameters - however by February 2022 the fit became poor - with the shapes of the death curves not following those of the admissions. By April 2022 the deaths by published dates became obviously erratic - and by the end of May I felt that there was little point in attempting to match them to the admissions data. The Scottish Covid deaths data ceased on 2nd June. The English Covid deaths by published date has become even more erratic - although it looks like it may be settling down to a once-a-week number. The English Covid deaths by registration date has continued - but the numbers it contains are subject to adjustment for a considerable time after they are first published. Hence my (previous) reluctance to use it. I'll continue to keep a watch.

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Re: Coronavirus - Modelling Aspects Only

#517969

Postby funduffer » July 28th, 2022, 4:32 pm

scotia wrote:
funduffer wrote:Scotia,

I have followed your modelling of deaths v hospital admission for some time, and it is interesting to me that the correlating factor has changed over time.

You are now using a factor of 0.11, which I think is lower than what you started with.

I wondered if you had a record of how this factor has changed during the pandemic? My impression is it has reduced over time, suggesting that immunity due to vaccination or prior infection has blunted the deadliness of the virus, and/ or treatments have improved.

Any thoughts?

FD


Yes - when the factor being used clearly needs updated, it signals that there has been some change in the effect of the Covid virus. My original graphs (early Dec 2020) used past data to estimate the factors - and 0.265 with a delay of 13 days seemed to fit. But as we moved from late December into January, it became obvious that these these numbers were too optimistic for the recent data, and 0.3 with an 11 day delay became a better fit. This coincided with the PM announcing that the latest variant had a higher mortality rate. However vaccines were on the way - and hopefully this would bring substantial changes - and they did! By the end of February 2021 I revised the multiplicative factor down to 0.26 to achieve a better fit to the most recent data, then down to 0.2 in early March, and further down to 0.175 by early April. By late April I was struggling to find a fit to the ever-reducing numbers, and I had moved the multiplicative figure down to 0.075 with a time slip of 23 days. The success of the vaccines had been spectacular. But moving on to May/June, the numbers began to rise again - probably due to the new Delta variant which was causing some concern. By September 2021 the mutiplicative factor had risen to 0.14 with a time slip of 11 days. In November the factor was increased to 0.15. I continued with these parameters - however by February 2022 the fit became poor - with the shapes of the death curves not following those of the admissions. By April 2022 the deaths by published dates became obviously erratic - and by the end of May I felt that there was little point in attempting to match them to the admissions data. The Scottish Covid deaths data ceased on 2nd June. The English Covid deaths by published date has become even more erratic - although it looks like it may be settling down to a once-a-week number. The English Covid deaths by registration date has continued - but the numbers it contains are subject to adjustment for a considerable time after they are first published. Hence my (previous) reluctance to use it. I'll continue to keep a watch.


Fascinating. In effect, this one parameter has charted the course of the entire pandemic, covering the effects of new variants and vaccines. I hadn’t realised it has been such a roller-coaster ride!

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Re: Coronavirus - Modelling Aspects Only

#519666

Postby scotia » August 4th, 2022, 12:00 am

I'm following up my previous graph with a further week of English data (extracted this evening from coronavirus.data.gov.uk) to see if last week's tentative prediction is confirmed - that the English Covid deaths (by registration date) should have peaked around 23rd July and, and are now falling. I use a simple 2-parameter model where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous.
The latest Covid hospital admissions data is dated 1st August, as is the Covid deaths by registration date. However the deaths by registration date will be subject to updates (additions) for several days, so I have only included it up to a week previous to the latest data - i.e. to 25th July. All plotted points are 7-day summations to iron-out any weekly variations.

Image

And yes - the actual Covid deaths by registration date have peaked - around the 20-21st July. And the projected deaths (from the admissions) have continued to fall - all good news. However I was a bit puzzled by the statistically significant jump in deaths a few days before the peak. So I had a look at the daily deaths by registration date for the week 16th to 22nd July. These were 157, 189, 156, 293, 205, 145, 137. The anomalously large 293 was on 19th July - when England experienced its highest ever temperature in modern times.

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Re: Coronavirus - Modelling Aspects Only

#521483

Postby scotia » August 10th, 2022, 10:25 pm

A further week of English data (extracted this evening from coronavirus.data.gov.uk). I use a simple 2-parameter model where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous.
The latest Covid hospital admissions data is dated 8th August, as is the Covid deaths by registration date. However the deaths by registration date will be subject to updates (additions) for several days, so I have only included it up to a week previous to the latest data - i.e. to 1st August. All plotted points are 7-day summations to iron-out any weekly variations.

Image

I think it is now clear that the registered deaths, and their prediction from hospital admissions are now falling in synchronism from a peak around 20-21 July. The anomalously large jump in registered deaths a few days before the peak was due to the significantly large daily deaths (293) on July 19th (when England experienced its highest ever temperature in modern times). The downward step after the peak is the result of this 19th July figure dropping out of the 7 day total.
Currently all good news. I'll keep a watch, and if there is any upturn in the data, I'll publish further plots.

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Re: Coronavirus - Modelling Aspects Only

#528742

Postby scotia » September 8th, 2022, 11:31 pm

Here's a 4 week update of the Covid data model. It uses a simple 2-parameter model where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous.
The latest Covid hospital admissions data is dated 5th September, as is the Covid deaths by registration date (extracted this evening from coronavirus.data.gov.uk). However the deaths by registration date will be subject to substantial updates (additions) for several days, so I have only included it up to a week previous to the latest data - i.e. to 29th August. All plotted points are 7-day summations to iron-out any weekly variations. I have increased the range of data plotted - so that the earlier peak remains displayed.
Image
As I commented last month it is clear that the registered deaths, and their prediction from hospital admissions are now both falling from a peak around 20-21 July, and they are now approaching the lows of early June. And further booster vaccinations for us oldies are on their way. :)

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Re: Coronavirus - Modelling Aspects Only

#528856

Postby Julian » September 9th, 2022, 1:53 pm

scotia wrote:Here's a 4 week update of the Covid data model. ...

Thanks for keeping this going. Unsurprisingly (I suppose) given where we are in the pandemic this "Coronavirus Discussions" sub-forum is not very active at the moment so it's nice to see your analyses still ticking along.

- Julian

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Re: Coronavirus - Modelling Aspects Only

#531896

Postby scotia » September 23rd, 2022, 6:11 pm

I had intended to wait for a further 4 weeks before publishing the latest data, but the ONS have reported that the Covid infection rates have increased (in the week to 14th September) for the first time since the middle of July, so I thought it may be worthwhile looking at the model output, two weeks on from the last submission.
The model uses a simple 2-parameter model where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous.
The latest Covid hospital admissions data is dated 19th September. The deaths by registration date will be subject to substantial updates (additions) for several days, so I have only included it up to the 12th September. All plotted points are 7-day summations to iron-out any weekly variations.

Image

It appears that the hospital admissions, and hence the projected deaths, are now showing a slight increase. It has been suggested that the infection rate increase as reported by the ONS may be related to the return-to-school. And presumably this has been passed on to older relatives who end up as hospital admissions and potentially deaths. I also wonder if we will see a further upward blip due to the large crowds at the Queen's funeral.
Our 5th vaccination is due on Wednesday.

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Re: Coronavirus - Modelling Aspects Only

#533743

Postby scotia » September 30th, 2022, 4:40 pm

It was reported today that Covid infections are rising - with the biggest weekly increase since the summer. So I thought it may be worth looking at the model output, only one week since the last data.
A simple 2-parameter model is used where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous.
The latest Covid hospital admissions data is dated 26th September. The deaths by registration date will be subject to substantial updates (additions) for several days, so I have only included it up to the 19th September. All plotted points are 7-day summations to iron-out any weekly variations.

Image

I'm afraid we are seeing a rise in projected deaths, but the more worrying aspect is the significantly steeper gradient in this rise than in the fall to the recent lowest point. It's difficult to understand why. I have not heard of any new variant - so it is probably down to social effects - return-to-school, more indoors gatherings, large public gatherings, and a more relaxed approach to wearing masks. It could also be partly due to the reducing protective effect of the vaccines - which hopefully will be remedied by the latest round of boosters for us oldies.

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Re: Coronavirus - Modelling Aspects Only

#535610

Postby scotia » October 7th, 2022, 12:14 pm

Given the rising infection trend, I thought it may be worth looking at the model output, only one week since the last data.
A simple 2-parameter model is used where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous.
The latest Covid hospital admissions data is dated 3rd October. The deaths by registration date will be subject to substantial updates (additions) for several days, so I have only included it up to the 26th September. All plotted points are 7-day summations to iron-out any weekly variations.

Image

The hospital Covid Admissions (and hence projected deaths) are still rising strongly, but possibly the gradient is no longer increasing. Maybe there will be better news next week.

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Re: Coronavirus - Modelling Aspects Only

#535858

Postby Julian » October 8th, 2022, 11:57 am

One significant change sometime in August was hospitals stopping routine Covid-19 testing for all admissions. Aparently hospitals in the UK (or just England?) no longer routinely do a Covid-19 test on admission unless a patient is displaying symptoms that might be Covid-19 so presumably the numbers now are showing fewer hospital infections than they would have been showing had this change not come into effect since anyone in hospital who has an incidental asymptomatic infection will no longer show up in the hospital admission data. (I'm assuming your hospital admission data is all admissions who test positive, i.e. it includes not only people admitted because of a C-19 infection but also people admitted with, or presumably subsequently contracting, a C-19 infection.)

- Julian

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Re: Coronavirus - Modelling Aspects Only

#535963

Postby scotia » October 8th, 2022, 8:35 pm

Julian wrote:One significant change sometime in August was hospitals stopping routine Covid-19 testing for all admissions. Aparently hospitals in the UK (or just England?) no longer routinely do a Covid-19 test on admission unless a patient is displaying symptoms that might be Covid-19 so presumably the numbers now are showing fewer hospital infections than they would have been showing had this change not come into effect since anyone in hospital who has an incidental asymptomatic infection will no longer show up in the hospital admission data. (I'm assuming your hospital admission data is all admissions who test positive, i.e. it includes not only people admitted because of a C-19 infection but also people admitted with, or presumably subsequently contracting, a C-19 infection.)

- Julian

I think your assumption on admissions is correct - but the precise descriptive text for hospital admissions on coronavirus.data.gov.uk is not easy to find. There is an interesting note from the 22nd September indicating that Scotland has adopted a changed policy :-
Public Health Scotland have changed the definition of patients admitted to hospital and are no longer reporting admissions using the existing definition. The new measure is intended to reflect "community-acquired" COVID-19 and therefore is not comparable to the measures in use in the other three nations, so has not been included in dashboard reporting.

Notice the text "existing definition" - presumably that would clarify the current position in England - but I can't find it.

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Re: Coronavirus - Modelling Aspects Only

#536214

Postby vrdiver » October 10th, 2022, 8:32 am

scotia wrote:
Public Health Scotland have changed the definition of patients admitted to hospital and are no longer reporting admissions using the existing definition. The new measure is intended to reflect "community-acquired" COVID-19 and therefore is not comparable to the measures in use in the other three nations, so has not been included in dashboard reporting.

Does this mean that Scotland will no longer report Covid cases where the infection was contracted in hospital? If so, would you expect to see the ratio of fatalities to admissions rise, as there would be associated deaths but no corresponding admission?

VRD

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Re: Coronavirus - Modelling Aspects Only

#536277

Postby Julian » October 10th, 2022, 12:35 pm

vrdiver wrote:
scotia wrote:
Public Health Scotland have changed the definition of patients admitted to hospital and are no longer reporting admissions using the existing definition. The new measure is intended to reflect "community-acquired" COVID-19 and therefore is not comparable to the measures in use in the other three nations, so has not been included in dashboard reporting.

Does this mean that Scotland will no longer report Covid cases where the infection was contracted in hospital? If so, would you expect to see the ratio of fatalities to admissions rise, as there would be associated deaths but no corresponding admission?

VRD

It's an interesting question. I can see the logic behind your thinking. It has me wondering how the testing for hospital-acquired infections is handled. Presumably as soon as someone in hospital starts exhibiting new symptoms(*) that could be indicative of Covid-19 (C-19) they get tested so that appropriate treatments can be considered (Paxlovid, Remdesivir, various monoclonal antibodies etc) but with such a wide range of symptoms now associated with C-19 I wonder how many infections might be missed due to lack of tests and if someone dies without having been tested would a posthumous test be done or would, in many cases, the death certificate assume that the primary cause of death was something else? It's all getting very complicated.

Also, I've seen quite a lot of discussion recently on excess deaths in places like the USA and particularly the UK where non-Covid related excess deaths are running well above average. That is manna from heaven for the most ardent anti-vaxers who of course immediately jump to the conclusion that it must be vaccine-related, seemingly without any attempt to consider other possibilities. There are many non-vaccine-related possible explanations for the excess deaths that we are seeing right now and the possibility of a hospital-acquired SARS-CoV-2 infection fatally exacerbating whatever other condition a patient was admitted for, but that C-19 infection not being picked up because an in-hospital test wasn't done for some reason, might be another partial explanation to add to that list.

- Julian

(*) By definition they will always be new symptoms that emerged whilst in hospital because, as I understand the new procedures (and admittedly that is not very well!), had those symptoms been extant at time of admission the patient would have been tested for C-19 at the point of admission.

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Re: Coronavirus - Modelling Aspects Only

#537129

Postby scotia » October 14th, 2022, 12:19 am

Given the rising infection trend, I thought it may be worth looking at the model output, only one week since the last data.
A simple 2-parameter model is used where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous.
The latest Covid hospital admissions data is dated 10th October. The deaths by registration date will be subject to substantial updates (additions) for several days, so I have only included it up to the 3rd October. All plotted points are 7-day summations to iron-out any weekly variations.

Image

And it looks like good news. I speculated last week that the lessening gradient of the projected deaths (i.e based on the 10 day previous admissions) may herald a peak, and this seems to have occurred. Hopefully next week we will see a continuing downward trend.
And the reason? Possibly the new round of vaccinations, or the back-to-school effect now dampening down. or-or-or-or :?

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Re: Coronavirus - Modelling Aspects Only

#537145

Postby Itsallaguess » October 14th, 2022, 6:24 am

scotia wrote:
And it looks like good news. I speculated last week that the lessening gradient of the projected deaths (i.e based on the 10 day previous admissions) may herald a peak, and this seems to have occurred. Hopefully next week we will see a continuing downward trend.

And the reason? Possibly the new round of vaccinations, or the back-to-school effect now dampening down. or-or-or-or :?


If we go back and look at your great chart from July, and incorporate that earlier peak into your current two-peak chart, we get something like this -

Image

Now clearly, there's a huge number of variables and influences going on over that longer period, but generally, might we simply be looking at the life-cycle of a 'novel dangerous virus' during a period where it moves from being 'novel' to being 'coped with', and 'managed', and where we'd perhaps rightly expect that over time, those peak-oscillations will modulate lower and lower until eventually the virus becomes 'background noise' like all the others?

I suppose what I'm trying to do with the above extended chart is turn your question around, and instead of asking 'Why is it doing this?', perhaps instead asking 'Why wouldn't we expect it to be doing this?'...

Cheers,

Itsallaguess

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Re: Coronavirus - Modelling Aspects Only

#537147

Postby servodude » October 14th, 2022, 6:41 am

Itsallaguess wrote:
scotia wrote:
And it looks like good news. I speculated last week that the lessening gradient of the projected deaths (i.e based on the 10 day previous admissions) may herald a peak, and this seems to have occurred. Hopefully next week we will see a continuing downward trend.

And the reason? Possibly the new round of vaccinations, or the back-to-school effect now dampening down. or-or-or-or :?


If we go back and look at your great chart from July, and incorporate that earlier peak into your current two-peak chart, we get something like this -

Image

Now clearly, there's a huge number of variables and influences going on over that longer period, but generally, might we simply be looking at the life-cycle of a 'novel dangerous virus' during a period where it moves from being 'novel' to being 'coped with', and 'managed', and where we'd perhaps rightly expect that over time, those peak-oscillations will modulate lower and lower until eventually the virus becomes 'background noise' like all the others?

I suppose what I'm trying to do with the above extended chart is turn your question around, and instead of asking 'Why is it doing this?', perhaps instead asking 'Why wouldn't we expect it to be doing this?'...

Cheers,

Itsallaguess


I was thinking something very similar (and not just because the curves look like a very familiar second order response)

I think earlier in this thread I talked about establishing/validating a model then watching the model parameters change over time as a way of quantifying the big picture. It's relatively common in multi modal or adaptive control and helps acknowledge that you're not simply looking at a time series.
In simple terms it's trying to work out the how/why/when to the what we see.
And to that end why and "why not" are the same (just in different directions :) )

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Re: Coronavirus - Modelling Aspects Only

#537259

Postby scotia » October 14th, 2022, 12:19 pm

Due to overwhelming public demand :D , I'll post 12 months of model data
A simple 2-parameter model is used where the Covid deaths, by registration date, are predicted as being 0.11 times the Covid hospital admissions of 10 days previous. These two parameters were selected to provide a reasonable fit to the peak in deaths around the middle of April (around point 180 in the graph below). I am surprised at how well this fit has given reasonable agreement from around the middle of February (around point 120) to the present.

Image

Looking at the earliest data in the late autumn of 2021, the shapes of the projected and actual deaths are in reasonable agreement, but the projected deaths are clearly an underestimate. It would appear that the Covid variant at that time (Delta) was more virulent than Omicron which replaced it as the dominant strain.
Also looking at the very steep rise in projected deaths from around point 75 - this corresponds to Admissions data from 21st December. Could this be Party, Party, Party :shock:
And repeating what we noticed earlier, the hottest day in England produced an anomalous step upwards in Covid deaths.
All other analysis welcome :)


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