hi Andrei
well, you're actually treating people so stop apologizing!
thanks for the links.
there are some statisticians on here so hopefully someone can let me know
if I've got this point wrong.
Greg
> Hi Greg,
>
> Thanks, I hadn't seen that paper, it looks interesting. I'm rapildy
> running out of time though, and I feel like your math skills are about
> 15 light years ahead of mine ;-) I am just a humble clinician after all,
> with epidemiological training and hence some basic awareness of maths
> beyond numbers (using Xs and Ns and those kind of things).
>
> This graph from Pueyo's latest article strikes me as being perhaps
> tangentially related:
>
> * https://miro.medium.com/max/7104/1*WGCbwDAHS1KwXGKoEydLUA.png
>
> The article being:
>
> *
> https://medium.com/@tomaspueyo/coronavirus-the-hammer-and-the-dance-be9337092b56
>
> Pueyo provides his calculations:
>
> *
> https://docs.google.com/spreadsheets/d/1uJHvBubps9Z2Iw_-a_xeEbr3-gci6c475t1_bBVkarc/edit?usp=sharing
>
> Advanced maths right there!
>
> Best wishes,
>
> -- Andrei
>
>
> On Sat, Mar 21, 2020 at 10:10:32PM -0000, Greg Dropkin wrote:
>> Facundo, anyone
>>
>> please let me know if I've got this right.
>>
>> The table Facundo sent yesterday cites this paper by Verity et al (see
>> ref
>> 12 in the Imperial College report):
>> https://www.medrxiv.org/content/10.1101/2020.03.09.20033357v1.full.pdf
>>
>> I think that the last para on p7 of this paper is enough to reject the
>> assumption that the distribution of length of stay is exponential.
>>
>> "We similarly estimated the mean time from onset-to-recovery using data
>> on
>> outcomes in 169 cases reported outside mainland China. We obtain a
>> slightly longer duration for the onset-to-recovery distribution of
>> 22.6days (95% crI 21.1-24.4days) and CV of 0.33days (95% crI
>> 0.30-0.37days)(Figure 2)."
>>
>> Figure 2 is on p.15
>>
>> CV = 1 for exponential distributions. I also think CV is dimensionless,
>> so
>> not sure why they find 0.33days rather than 0.33. But anyway, it's not
>> 1.
>>
>> As they seem to be fitting gamma distributions:
>>
>> with shape a and rate b, mean = a/b and var = a/b^2 so CV = a^(-1/2).
>> So for their data, a ~ 9 and b = a/mean ~ 9 / 22.6 ~ 0.4
>>
>> A gamma distribution with these parameters has a probability density
>> very
>> like the red line in Fig 2 (B).
>>
>> Greg
>>
>>
>> > hi Andrei, all
>> >
>> > one of the key assumptions in the SEIR model as implemented on Alison
>> Hill's site, is that the length of stay in the E or I compartments is
>> exponentially distributed. This is key to the formulas implemented in
>> the
>> > code.
>> >
>> > On the other hand, Wikipedia
>> > (https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology)
>> mentions that an Erlang distribution might be more appropriate.
>> >
>> > Or it might be something else entirely.
>> >
>> > Alison Hill's site includes current clinical references on the Sources
>> tab, which I've not read yet.
>> >
>> > Does anyone know if any of the empirical evidence on COVID-19 sheds
>> any
>> light on the distribution of length of stay in any of the compartments?
>> >
>> > e.g. presumably the raw data would include how long each patient spent
>> after developing symptoms, before recovery or progression to severe
>> status.
>> >
>> > thanks
>> >
>> > Greg
>> >
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>
> --
> Andrei Morgan MRCPCH, MSc, PhD (Epidemiology / Neonatology)
> https://www.andreimorgan.net
>
> Honorary Clinical Lecturer,
> Department of Neonatology,
> Institute for Women's Health,
> University College London
>
>
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