Covid-19 Gambles

[JohnW2]

Well, that is how it was reported - correct or not. ... 90 days 4 cases; next day party and 1,100 cases.

Presumably that ("next day") is not what was actually reported? If so, it's not only nonsense but also 'beyond belief'. One would not expect anyone to have become test-positive the day after exposure at a party (the 'incubation period is generally about 4-5 days) - but what on earth (other than the party) could hve resulted in the sudden 1,100 infections?!

However, assuming that they reported something different from that, they were probably reporting 'true facts', but it would be nonsense to attempt to conclude anything from it other than that a lot of people got infected at a party.

However, as I said, if you are right in saying that 1,100 asymptomatic infected people suddenly appeared in a locality that had previously had virtually no cases, there would be a serious risk that cases would rise considerably, perhaps even 'dramatically', as one moved forwards from that position - so that would definitely be 'a cause for concern'.

On my hypothetical numbers; would it have been correct if five days apart (instead of yesterday and today)?

As I said, there is no sense in, and nothing to be gained by, thinking/talking about either Rt or growth rate in relation to a sudden surge of transmission due to a single, very brief, event. Because of the possible sequalae mentioned above, the important thing woulkd be to look at the growth rate over the weeks following that one-ff event.

When I said that a person cannot infect 0.2 of another person, obviously I realise that it refers to a percentage and 100 infecting 120 is possible but it is no indication of the actual numbers - it cannot be evenly spread. ... Whether 80 infected another 80 and 20 infected 40 - or any other combination - is not known unless there were a party, for example.

Sure, but it goes without saying that all of this can only be looked at in terms of averages.

Even with Rt, the figures we can estimate obviously have to be averages, since the actual number of people infected by one infected person will obviously vary considerably, depending on that person's behaviour. An Rt of, say, 3.0 means that, on average, one infected person will infect 3 others - but an infected person who comes into contact with no-one (e.g. 'isolated' from before the end of the incubation period - which is what 'test and trace' tries to achieve) will infect no-one, but a person who mixes extensively with hundreds of others after becoming infectious will probably infect an awful lot more than three people! It is, as I said, necessarily all about 'on average' ... whilst 100 people may, on average, infect 300 others, a good few will infect no-one, and a good few will infect many, depending on many factors, primarily their 'behaviour'.

Kind Regards, John.

 

[EFLImpudence]

Yes, agreed, but that is my proposition; that the Rt number is a useless statistic even more so than 'cases'.

Just report that there were 20% more 'cases' {whenever} than {whenever}.

 

[JohnW2]

Yes, agreed, but that is my proposition; that the Rt number is a useless statistic even more so than 'cases'.

As I've said and agreed, it's totally useless in relation to the effects of a single brief event. However, other than in those exceptional situations, Rt will change slowly and gradually in response to 'what is going on' (in terms of human behaviour) and is therefore useful in 'following' what is going on and attempting to predict what is likely to happen in the future.

Whether one uses Rt or growth rate is irrelevant, since (given assumptions about the average period of infectivity/transmission) mathematically interchangeable. I often do wonder whether, from the point of view of the general public, it would not have been better to stick with growth rate, since the meaning of that is pretty obvious, rather than introducing them to this concept of 'R' - which I presume virtually none of the general public had even heard of until 18 months ago.

Just report that there were 20% more 'cases' {whenever} than {whenever}.

If you divide one by the other, you will get 'growth rate' over the interval in question (well, mathematically, growth rate "plus one" - i.e. 120 divided by 80, you would give 1.50, hence 'minus 1' gives 0.50, aka 50%). However, just reporting the growth between two specific dates is of limited usefulness, since one needs a more general feel as to what is going on over time.

Having said that, the government do report such figures. We are constantly being told about, say, the percentage increase in cases/deaths/whatever "in the last week/month/whatever as compared with the previous week/month/whatever" - which sounds essentially to be what you are asking for, isn't it?

Kind Regards, John

 

[Notch7]

that the Rt number is a useless statistic

R value is an imprecise that is based on assumptions and it has a lag of upto 3 weeks.

but it’s an easily understood metric…..

 

[EFLImpudence]

Did you mean Rt?

What is an imprecise?

 

[JohnW2]

R value is an imprecise that is based on assumptions ...

Sure, but all of the estimates we are dealing with are necessarily imprecise, subject to considerable variability, noise' and potential confounding, and most rely on various assumptions - however, that is the nature of the subject.

... and it has a lag of upto 3 weeks.

I'm not sure what you mean by that, since there doesn't have to be any lag with estimates of 'R' (Re or Rt) and more than with any of the other indices we estimate. Apply 'the assumptions' (primarily concerning the period over which transmission occurs) one could, if one so wished, estimate current R from the difference in number of new cases today and yesterday (i.e. no 'lag') - but, given variability/noise etc., that would be less than ideal. You are probably referring to the note which accompanies the government's publications of estimated R and Growth Rate figures, which says:

... These estimates represent the transmission of COVID-19 2 to 3 weeks ago, due to the time delay between someone being infected, developing symptoms, and needing healthcare.

... which makes absolutely no sense to me. The 'best estimate' we can get of R or Growth Rate is surely that which is derived from the (very imperfect and imprecise) figures we have for the number of 'new cases' each day (i.e. positive tests) - regardless of if/when they develop symptoms or if they ever 'need healthcare' (which most won't). Very odd

... but it’s an easily understood metric…..

I think it's rather a case of swings and roundabouts. As I wrote earlier, Growth Rate (of daily new cases) is presumably the concept that is most easily understood, and probably most useful to those who wish to 'follow' the evolution of the epidemic, On the other hand, 'R' is a concept which not only was not understood, but had not even been heard of, by the vast majority of the general public just 18 months ago - but, once they have been taught to understand what it means, it is a useful way of getting across the concept of 'how many people an infected person will, on average, infect'.

The primary 'assumption' determinising the mathematical relationship between R and growth rate is the period over which an infected person 'transmits' and for something like Covid that will remain essentially constant. However, that parameter can vary dramatically between different diseases, so that the mathematical relationship between R and growth rate can also be dramatically different for different diseases ...

... the classic example usually cited is HIV, for which R0 is usually said to be in the range 2 - 5 - so I suppose someone has managed to work out that, on average, each infected person infects 2 - 5 others (that 'on average' must camouflage considerable variation!). If it were Covid, the 2 - 5 others (on average) infected by one person would be infected over a period of about 4-5 days, leading to a pretty high growth rate. However, with HIV, the 2 - 5 'others' might well be infected over a period of many years, such that the growth rate would be extremely small.

However, in context, the point is that R and growth rate for Covid are essentially 'mathematically interchangeable', but that they represent different ways of looking at the spread of infection.

Kind Regards, John
...

 

[JohnW2]

R value is an imprecise that is based on assumptions and it has a lag of upto 3 weeks. but it’s an easily understood metric…..

I think it's rather a case of swings and roundabouts. As I wrote earlier, Growth Rate (of daily new cases) is presumably the concept that is most easily understood, and probably most useful to those who wish to 'follow' the evolution of the epidemic, On the other hand, 'R' is a concept which not only was not understood, but had not even been heard of, by the vast majority of the general public just 18 months ago - but, once they have been taught to understand what it means, it is a useful way of getting across the concept of 'how many people an infected person will, on average, infect'. .... The primary 'assumption' determinising the mathematical relationship between R and growth rate is the period over which an infected person 'transmits' and for something like Covid that will remain essentially constant. However, that parameter can vary dramatically between different diseases, so that the mathematical relationship between R and growth rate can also be dramatically different for different diseases ... the classic example usually cited is HIV ......

Looking back at what I wrote yesterday, I think there's a consequence of what I wrote that I perhaps did not stress enough, as regards the suggestion that R is "an easily understood metric".

For a start, as I said, I would say that 'growth rate' is much more generally understood that 'R' - not the least because, as I said, anything which the general public 'understand' about R is essentially what that have learned in the past 18 months, since very few will even have heard of it before that.

Furthermore, for nearly all purposes it's actually growth rate which really matters since it is an estimate of a direct measure of how rapidly a virus is spreading (i.e. how rapidly an outbreak/epidemic is developing) - and, in fact, as far as I can see, real-time estimates of R are necessarily derived mathematically from the growth of observed case numbers, on the basis of the 'assumptions' mentioned by Notch.

In as much as those 'assumptions' (about the average duration of the period of transmission by an infected person) will remain constant for any particular virus, I suppose that, once one has got used to it, there's no real problem with using R as a surrogate for growth rate, but I must say that I personally don't really see the point, when the latter is what most of us are actually interested in.

The potential problem with R only really arises if one tries to use it for comparing two different diseases, because those 'assumptions' which determine the relationship between growth rate and R can differ dramatically between diseases, as I illustrated with Covid-19 vs. HIV.

In particular, one needs to avoid the mistake of thinking that a high, or very high, R necessarily translates to a high, or very high, growth rate ... an R of 2.0 would, for a disease like Covid, correspond roughly to a growth rate that could be expressed as "doubling every 4-5 days" (which most would probably regard as 'very fast') whereas the same R for HIV might correspond to (just pulling something or of the air) a growth rate of "doubling every 4-5 years" (which most would probably regard as 'extremely slow').

For what it's worth, I can say that in virtually all the analysis I do, I work with estimates of growth rate and, although I could if I wanted to, almost never bother converting them to Rt figures.

Kind Regards, John

 

[plugwash]

Where R does seem relevant is in seeing how much change one needs to "turn the corner". If R is 1.2 then a relatively small change could turn the corner from cases growing to cases shrinking, if R is 10 then even cutting it by a factor of four will only slow growth down.

 

[Swwils]

https://www.medrxiv.org/content/10.1101/2021.06.28.21259420v2

Possibly helpful for you JohnW2.

Comparisons now will start to get tricky as studies will be based in alpha / delta or include long tails of data from much earlier.

For instance studies including data from vaccinations in January are likely to be different than those from just this May.

 

[JohnW2]

Where R does seem relevant is in seeing how much change one needs to "turn the corner". If R is 1.2 then a relatively small change could turn the corner from cases growing to cases shrinking, if R is 10 then even cutting it by a factor of four will only slow growth down.

Whilst that's true, it's no less true if one thinks in terms of growth rates - and I'm inclined to think that the latter would probably make the contrast you mention even more apparently/dramatic ...

As I have illustrated, for Covid-19 infection, an R of 1.2 corresponds to a growth rate of about +4% per day (roughly "doubling every 18 days"). In contrast, an R value of 10 would correspond to a growth rate of about +180% per day (roughly, "doubling every 17 hours").

I would think that the dramatic difference between "doubling every 18 days and "doubling every 17 hours" would be even more immediately apparent than the difference between R values of 1.2 and 10 - as would the point that a lot less had to be changed to move the situation to "never doubling" (in fact, reducing) in the former case than the latter.

The two approaches are obviously mathematically equivalent, but I would think that, for most of the general public, the growth rate approach is probably the more 'immediately interpretable'. However, since I'm used to having to look at R values, I cannot personally be sure how the 'general public' would view the situation.

Kind Regards, John

 

[JohnW2]

https://www.medrxiv.org/content/10.1101/2021.06.28.21259420v2
Possibly helpful for you JohnW2. .... Comparisons now will start to get tricky as studies will be based in alpha / delta or include long tails of data from much earlier. ... For instance studies including data from vaccinations in January are likely to be different than those from just this May.

Many thanks - I'll look at it properly when I have some moments. I have a feeling that I've seen it, or reference to it, before, but I am currently seeing (and in many cases rapidly forgetting!) so many papers that I'm not certain!

Having looked at just the abstract, one first reaction occurs to me. In practical terms, all that really matters to us now (in UK) is the delta variant. As far as I can tell, this paper relates to Canadian data up to May 2021, and they appear to have estimated, amongst other things, protection that the viruses provide against delta. However, that was a point in time when we had seen little delta in the UK - so (although I didn't think this was the case) I have to wonder whether delta was perhaps much more prevalent in Canada (than in the UK) at that time? Maybe reading the full paper will clarify this for me!

However, and maybe this was your main point, although we currently have little interest (in the UK) in anything other than delta, this paper does give insights in the ability of vaccines to provide useful protection against variants that had not yet emerged at the time the vaccines were developed.

Kind Regards, John

 

[EFLImpudence]

I would think that the dramatic difference between "doubling every 18 days and "doubling every 17 hours" would be even more immediately apparent than the difference between R values of 1.2 and 10 - as would the point that a lot less had to be changed to move the situation to "never doubling" (in fact, reducing) in the former case than the latter.

The two approaches are obviously mathematically equivalent, but I would think that, for most of the general public, the growth rate approach is probably the more 'immediately interpretable'. However, since I'm used to having to look at R values, I cannot personally be sure how the 'general public' would view the situation.

Either way, the point I made is still valid.

I.e. Rt and growth rate are the product of what has already happened. They are only a general (likely) indication of what might happen in the future if things stay the same. They cannot be confirmed, if that is even worth doing (we were correct yesterday), until it has happened (tomorrow) - especially for 'cases' which depend on the number of tests.

Even the 'doubling every X days' has been wrong more often than correct.

 

[JohnW2]

Either way, the point I made is still valid. ... I.e. Rt and growth rate are the product of what has already happened. They are only a general (likely) indication of what might happen in the future if things stay the same. They cannot be confirmed, if that is even worth doing (we were correct yesterday), until it has happened (tomorrow)

I don't really understand what point you are making.

Anything based on real-world data is imprecise, subject to variability etc. and (since we don't have crystal balls) inevitably relates to "what has already happened".

You are surely not suggesting that we should not bother looking at any estimates of the rate of rise (or fall) of Covid infections (as 'R', growth rate or whatever), because the only data we have relates to "what has already happened" and therefore may not be accurate in relation to "what is about to happen", are you? In order to make 'management decisions', we need to have some handle on 'what is going on' and 'what is likely to happen as we move forward', even if they are only imprecise estimates.

I think what may be confusing you a bit is that, in order to discuss the concepts (and the relative merits) of R and growth rate, we have done so very simplistically. Although growth rate does represent an estimate of average percentage change (increase or decrease) in infections from day to day, the estimated figures you will see published are nothing like as crudely estimated as by dividing today's number of cases by yesterday's number.

Rather, the published estimates are the result of sophisticated modelling, based one one or more of measures such as positive tests, hospital admissions, deaths, random testing of the community etc., and taking many other factors (and 'assumptions') into account. In fact, the range of figures published by the government are the result of modelling by at least half a dozen different academic modelling groups, using different models. If you are interested, you can read a bit about this (here) .

... so, the estimates you see are much more complicated than "today's figures divided by 'yesterday's", and are obviously imperfect, but they are the 'best available" estimates of R and growth rate (albeit somewhat 'stale' by the time they are published).

However, to simply see "what is happening", in real time, it is essentially adequate to just look at plots of the daily data, smoothed in some way (e.g. by weekly 'moving averages') in order to get rid of the considerable day-to-day variation which otherwise makes the graphs difficult to 'read'. That approach avoids the appreciable lag period (2-3 weeks) before modelled R and growth rate estimates become available.

Kind Regards, John