Good news from Italy! - Printable Version
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RE: Good news from Italy! - dabigv13 - 03-30-2020
One thing that would result in an earlier peak is social distancing measures. Another is if prevalence is much higher than we expect. Say instead of unmeasured cases being 10x, they are actually 20 or 30x of measured cases. This means its spreading faster than initial models predicted, and so peak will be sooner. Also total deaths lower.
I suspect both of these are true to some extent.
RE: Good news from Italy! - 2006alum - 03-30-2020
(03-30-2020, 11:05 AM)dabigv13 Wrote: One thing that would result in an earlier peak is social distancing measures. Another is if prevalence is much higher than we expect. Say instead of unmeasured cases being 10x, they are actually 20 or 30x of measured cases. This means its spreading faster than initial models predicted, and so peak will be sooner. Also total deaths lower.Perhaps, although there's no universe where the prevalence rates are approaching where more have been exposed/infected than have not. Indeed, the best modeling I've seen done recently suggests the highest rates of infection are in Italy (est. of 9.8%) and Spain (15%). Even the worst (best?) case scenario estimates for prevalence in Italy are ~1/4 of the population infected. That is a long way off from herd immunity formation:
I suspect both of these are true to some extent.
[tweet]https://twitter.com/joshmich/status/1244645729664106497?s=20[/tweet]
RE: Good news from Italy! - burger - 03-30-2020
(03-30-2020, 11:12 AM)2006alum Wrote:These Imperial College models are full of shit. They can only get those giant numbers of infected people (the %s are small, but the numbers imply millions infected in each country) if they assume a giant number of asymptomatic or very mild infections--like 10+ asymptomatics for every symptomatic. Data from places with heavy testing, like the Diamond Princess, suggest a much lower rate of asymptomatic infections more like a 1:1 or 2:1 ratio.(03-30-2020, 11:05 AM)dabigv13 Wrote: One thing that would result in an earlier peak is social distancing measures. Another is if prevalence is much higher than we expect. Say instead of unmeasured cases being 10x, they are actually 20 or 30x of measured cases. This means its spreading faster than initial models predicted, and so peak will be sooner. Also total deaths lower.Perhaps, although there's no universe where the prevalence rates are approaching where more have been exposed/infected than have not. Indeed, the best modeling I've seen done recently suggests the highest rates of infection are in Italy (est. of 9.8%) and Spain (15%). Even the worst (best?) case scenario estimates for prevalence in Italy are ~1/4 of the population infected. That is a long way off from herd immunity formation:
I suspect both of these are true to some extent.
[tweet]https://twitter.com/joshmich/status/1244645729664106497?s=20[/tweet]
So my advice is to ignore these sorts of estimates until people start doing widespread, random surveillance or, even better, testing for antibodies. And that's probably months away at best.
RE: Good news from Italy! - burger - 03-30-2020
Yeah, I just read through the methods on that Imperial college study, and there are too many problems to explain in a short post. The biggest problem by far is that they just accept the infection fatality rate of 0.66% from another study in China, and every single calculation in the entire report hinges on that estimate being correct. It's just not credible.
RE: Good news from Italy! - BostonCard - 03-30-2020
(03-30-2020, 09:56 AM)OutsiderFan Wrote: Looks like the worst is behind Italy for real now. I'm a bit perplexed how models that a couple weeks ago were showing U.S. peak would be in June, are now being replaced with ones that show peak to be April 15.
I've quoted George Box before, so I will say it again: "All models are wrong, some models are useful". Moreover, because models induce a changes in policy/behaviors, running and publishing the models will change the outcome you are trying to model.
Also, a model that doesn't update as new data comes in is probably useless.
Lastly, all these models have associated prediction intervals. Any result is merely the best guess based on the known parameters. But the parameters (R0, incubation period, etc.) are not known precisely (and can change over time), and small differences in the parameters will have brobdingnagian differences in the outcomes of the models.
The best way to use these things is not as a prediction of the future, but as a bookend for possible scenarios. The far end (worst case) is probably 80% infection rate, 2+% mortality for Covid-19 patients plus spillover effects to patients with other diseases who can't get treatment.
Most likely scenario is the one the President outlined today: 5% of the population gets infected in the acute period and 100,000 - 200,000 dead (1% mortality).
Optimistic scenario is that the measures undertaken slow the pandemic faster and more effectively than we think, and we are looking at 1 million infected and 10,000 dead.
BC
(03-30-2020, 11:05 AM)dabigv13 Wrote: One thing that would result in an earlier peak is social distancing measures. Another is if prevalence is much higher than we expect. Say instead of unmeasured cases being 10x, they are actually 20 or 30x of measured cases. This means its spreading faster than initial models predicted, and so peak will be sooner. Also total deaths lower.
I suspect both of these are true to some extent.
Social distancing usually results in a later peak, not an earlier one, unless social distancing is enough to cause Reff to drop to close to 1 or lower. As Reff comes down from 3 (or 2.5), the curve flattens and is delayed.
You can play around with the effect of social distancing in this online SEIR model:
http://gabgoh.github.io/COVID/index.html
AS R(t) drops from an R0 of 2.2, the peak moves back until you get R(t) gets down to 1.28, and then it starts to move back in.
BC
RE: Good news from Italy! - OutsiderFan - 03-30-2020
This modeling "only" arrives at 84,000 total deaths in U.S.
I've looked at the numbers projected for the various states and all seem small to me, but this comes from the University of Washington, which has done a lot of good work on this pandemic.
http://covid19.healthdata.org/projections
RE: Good news from Italy! - burger - 03-30-2020
(03-30-2020, 12:56 PM)OutsiderFan Wrote: This modeling "only" arrives at 84,000 total deaths in U.S.
I've looked at the numbers projected for the various states and all seem small to me, but this comes from the University of Washington, which has done a lot of good work on this pandemic.
http://covid19.healthdata.org/projections
I read through the methods, and this isn't even a model. It's a curve fitting exercise*. They are simply fitting a normal (bell-shaped) curve to the death counts. There are past examples (like HIV) where fitting this kind of curve gave wildly misleading results. I would put zero stock in these predictions.
*curve fitting is fine for describing the distribution of past events, but it's useless for prediction.
RE: Good news from Italy! - OutsiderFan - 03-30-2020
(03-30-2020, 01:11 PM)burger Wrote:(03-30-2020, 12:56 PM)OutsiderFan Wrote: This modeling "only" arrives at 84,000 total deaths in U.S.
I've looked at the numbers projected for the various states and all seem small to me, but this comes from the University of Washington, which has done a lot of good work on this pandemic.
http://covid19.healthdata.org/projections
I read through the methods, and this isn't even a model. It's a curve fitting exercise*. They are simply fitting a normal (bell-shaped) curve to the death counts. There are past examples (like HIV) where fitting this kind of curve gave wildly misleading results. I would put zero stock in these predictions.
*curve fitting is fine for describing the distribution of past events, but it's useless for prediction.
Never heard the term "curve fitting" before, but it makes sense.
Has anyone seen any model for the U.S. and U.S. states that they would put any stock in at all? Anything with projections that have closely lived up to reality? Caveat being we have no real idea what reality is other than deaths and hospital admissions. The reports some countries haven't even counted deaths of people outside hospitals certainly doesn't help.
RE: Good news from Italy! - Goose - 03-30-2020
(03-30-2020, 01:11 PM)burger Wrote: I read through the methods, and this isn't even a model. It's a curve fitting exercise*. They are simply fitting a normal (bell-shaped) curve to the death counts. There are past examples (like HIV) where fitting this kind of curve gave wildly misleading results. I would put zero stock in these predictions.
*curve fitting is fine for describing the distribution of past events, but it's useless for prediction.
Could you please post the link you used to get that methods section?
RE: Good news from Italy! - burger - 03-30-2020
(03-30-2020, 02:58 PM)Goose Wrote:http://www.healthdata.org/sites/default/files/files/research_articles/2020/COVID-forecasting-03252020_4.pdf(03-30-2020, 01:11 PM)burger Wrote: I read through the methods, and this isn't even a model. It's a curve fitting exercise*. They are simply fitting a normal (bell-shaped) curve to the death counts. There are past examples (like HIV) where fitting this kind of curve gave wildly misleading results. I would put zero stock in these predictions.
*curve fitting is fine for describing the distribution of past events, but it's useless for prediction.
Could you please post the link you used to get that methods section?
RE: Good news from Italy! - Goose - 03-30-2020
(03-30-2020, 03:21 PM)burger Wrote:Thank you sir! After looking at what they are doing, I believe it isn't quite as bad as you say, although at the end of the day I totally agree with your conclusion. The fact they are using a Gaussian function to fit the curve has nothing to do with the "normal" distribution. It is just that this particular sigmodial function fit the Wuhan data better than any other function they tried. They did not quantify how good a fit it was, as far as I can tell. This approach makes some sense if one believes that the projected death rates predict hospitalization rates and case load, and that that curve has the same basic shape everywhere, just with different parameters. IOW, everyone is like Wuhan except with a timescale that could be stretched/shrunk or shifted ahead/retarded back. There are so many other assumptions about how these parameters are inter-related that there is almost no way their model could be correct. They have to "fit" curves to the data in Santa Clara for example only knowing the initial values. Hard to do even if the distribution will end the end look like Wuhan, and it very well may not for many reasons they aren't even aware of. There are so many differences that the idea this will be the case is hard to believe.(03-30-2020, 02:58 PM)Goose Wrote:http://www.healthdata.org/sites/default/files/files/research_articles/2020/COVID-forecasting-03252020_4.pdf(03-30-2020, 01:11 PM)burger Wrote: I read through the methods, and this isn't even a model. It's a curve fitting exercise*. They are simply fitting a normal (bell-shaped) curve to the death counts. There are past examples (like HIV) where fitting this kind of curve gave wildly misleading results. I would put zero stock in these predictions.
*curve fitting is fine for describing the distribution of past events, but it's useless for prediction.
Could you please post the link you used to get that methods section?
One thing they also did not present is a discussion of how well their methodology would have predicted results in Italy, Spain, France etc. had it been applied early on. I suspect it would not have fared well.
Curve fitting can indeed be a good method of predicting the future if you have good reason to believe that the present event will behave basically like the past event subject to factors that can be parameterized by the curve. Sometimes, there are good reasons to believe that it will, especially if there have been many "similar" events that did in fact behave that way. However, if it is an event that you have never seen before, it is a big assumption that the next such event will behave similarly.
RE: Good news from Italy! - BostonCard - 03-30-2020
Gaussian refers to the residual error, not the curve itself.
BC
RE: Good news from Italy! - burger - 03-30-2020
(03-30-2020, 07:08 PM)BostonCard Wrote: Gaussian refers to the residual error, not the curve itself.No, it's the shape of the curve. Equation on page 4.
BC
RE: Good news from Italy! - BostonCard - 03-30-2020
Sorry, I misread. you are right that the formula fit the curve. However, the formula was for a Gaussian error function, not a Gaussian function, so your post threw me for a loop.
Gaussian function ≠ Gaussian error function
Gaussian function:
![[Image: 360px-Normal_Distribution_PDF.svg.png]](https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/360px-Normal_Distribution_PDF.svg.png)
Gaussian error function
![[Image: 400px-Error_Function.svg.png]](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Error_Function.svg/400px-Error_Function.svg.png)
The Gaussian error function for a given represents the probability that a measurement value in a Gaussian function lies between those two values.
BC
RE: Good news from Italy! - Goose - 03-30-2020
(03-30-2020, 07:49 PM)BostonCard Wrote: Sorry, I misread. you are right that the formula fit the curve. However, the formula was for a Gaussian error function, not a Gaussian function, so your post threw me for a loop.True, but as I read it, the use of this function has nothing to do with a probability distribution. It was the function that best fit the data among the alternatives they tried. They say the tried other "sigmoidal" functions, meaning S shaped curves, and liked this one the best. They did not tell us what else they tried or even how will the one they chose fit the data.
Gaussian function ≠ Gaussian error function
Gaussian function:
Gaussian error function
The Gaussian error function for a given represents the probability that a measurement value in a Gaussian function lies between those two values.
BC
RE: Good news from Italy! - JustAnotherFan - 03-31-2020
Apologies if this is a dumb question but I'm going to ask it anyway. I'm not keeping up with the conversation here as I haven't touched any of this since my undergrad days. But when you say curve-fitting do you mean just trying to find some sort of function that can be applied to the data to help explain the growth?
RE: Good news from Italy! - burger - 03-31-2020
(03-31-2020, 05:01 AM)JustAnotherFan Wrote: Apologies if this is a dumb question but I'm going to ask it anyway. I'm not keeping up with the conversation here as I haven't touched any of this since my undergrad days. But when you say curve-fitting do you mean just trying to find some sort of function that can be applied to the data to help explain the growth?Yes. The problem is that the data are the deaths so far, which are still growing quickly in most states. But there is little to no support for the bell-shaped curves they're using. It's possible that things will reach a peak and then slow down nicely, but there are still a lot of ways this could play out. Models like this one give false confidence that things are trending in the right direction when, so far at least, there is little to be optimistic about (outside of Washington maybe). That may change in the next couple of weeks in a lot of states as lockdowns start to reduce the death rates. But we have to wait and see.
RE: Good news from Italy! - OutsiderFan - 03-31-2020
Italy numbers are in for March 31:
March 21: +6,557 - 793 Dead
March 22: +5,560 - 651 Dead
March 23: +4,790 - 602 Dead
March 24: +5,249 - 743 Dead
March 25: +5,210 - 683 Dead
March 26: +6,203 - 712 Dead
March 27: +5,909 - 919 Dead
March 28: +5,974 - 889 Dead
March 29: +5,217 - 756 Dead
March 30: +4,050 - 812 Dead
March 31: +4,053 - 837 Dead
Nothing really left to say other than it's still spreading, albeit not as fast as before. Even it lockdown it appears to spread, which can only mean infections are happening when people are going grocery shopping?
RE: Good news from Italy! - BostonCard - 03-31-2020
(03-31-2020, 07:42 AM)burger Wrote: But there is little to no support for the bell-shaped curves they're using.
Again, Gaussian error function ≠ Gaussian function. It is not a bell-shaped curve; it's a sinusoidal curve. And the SEIR model would predict that a cumulative count of deaths would be a sinusoidal curve (though not, as far as I can tell, a Gaussian error function).
BC
RE: Good news from Italy! - burger - 03-31-2020
(03-31-2020, 09:49 AM)BostonCard Wrote:(03-31-2020, 07:42 AM)burger Wrote: But there is little to no support for the bell-shaped curves they're using.
Again, Gaussian error function ≠ Gaussian function. It is not a bell-shaped curve; it's a sinusoidal curve. And the SEIR model would predict that a cumulative count of deaths would be a sinusoidal curve (though not, as far as I can tell, a Gaussian error function).
BC
The model uses the Gaussian error function for the cumulative number of deaths. The curve for the number of deaths by day is just the derivative of the error function, which is a gaussian curve. That's what they're showing in the results here http://covid19.healthdata.org/projections
I'm not sure why they're modeling the cumulative deaths rather than the individual counts by day, as that is surely a far easier equation to model with no integrals involved.