Is the concept of "doubling time" meaningful in the context of Covid19?
There has been much discussion of "doubling time" in the context of Covid19. Whether or not this application of a concept derived from exponential growth is applicable in the Covid19 context might be questioned. As wikipedia points out:
In practice eventually other constraints become important, exponential growth stops and the doubling time changes or becomes inapplicable.
(...) While using doubling times is convenient and simple, we should not apply the idea without considering factors which may affect future growth.
link: https://en.wikipedia.org/wiki/Doubling_time
Back on 20 April 2020, New Jersey Governor Murphy tweeted:
LOOK: The rates by which the numbers of new #COVID19 cases are doubling have significantly SLOWED.
Just a few weeks ago, in some areas of the state cases were doubling in a matter of days.
Now we’re seeing those rates slow to where we can measure them in the numbers of weeks.
link: https://twitter.com/GovMurphy/status/1252301088960794632
AND
https://www.phillyvoice.com/new-jersey-coronavirus-new-covid-19-patients-stabilizes-hospitalizations-covid-19/
But four days later on April 24, the "doubling rate" was up [meaning "doubling time" was shorter]:
Murphy says the time it takes for the number of positive cases also got shorter, particularly in the southern part of the state. Murphy wants to see the so-called doubling rate moving in the other direction.
link: http://newjersey.news12.com/story/42047015/positive-covid19-cases-surge-past-100k-gov-murphy-signs-order-to-help-renters
On 3 May 2020, Scott Gottlieb talked about "doubling rate" on Face the Nation:
MARGARET BRENNAN: So these federal social distancing guidelines expire this week. It's a-- a different story state to state over what's opening up. But you tweeted this week that you saw some worrying-- worrisome signals, specifically, when it comes to hospitalization rates. What is the direction of the epidemic?
SCOTT GOTTLIEB: Well, when you look across the country, it's really a mixed bag. Certainly cases are falling in the Tri-State region around New York City. But when you back out what's happening in New York, and New York is really driving a lot of the national statistics because it was such a large outbreak, around the nation, hospitalizations and new cases continue to rise. So there's about twenty states where you see a rising number of new cases: Illinois, Texas, Maryland, Indiana, Virginia, North Carolina, Tennessee have a lot of new cases on a daily basis. And so while mitigation didn't fail, I think it's fair to say that it didn't work as well as we expected. We expected that we would start seeing more significant declines in new cases and deaths around the nation at this point. And we're just not seeing that.
MARGARET BRENNAN: This morning Doctor Deborah Birx was on another network, and she said our projections were always that we would see between a hundred thousand and two hundred and forty thousand Americans' lives lost due to the virus. On Monday of this week, the President said it's probably sixty to seven-- seventy thousand dead. The week before, he said fifty to sixty thousand. Are these White House numbers reliable at all?
SCOTT GOTTLIEB: Well, the White House was looking at the IHME model out of Washington State. And that model initially showed at the high end two hundred and fifty thousand deaths and a base case of a hundred thousand. But it's come down since then to about seventy thousand. It's starting to creep back up when you look at the updates of that model over the last two weeks. I think we have to look out to what's going to happen by the end of June. It's really hard to predict beyond June where this goes because we could have large outbreaks or it could become quiescent in the summer. But I think when you look out to the end of June, it's probably the case that we're going to get above a hundred thousand deaths nationally. I think the concerning thing here is that we're looking at the prospect that this may be a persistent spread, that while the doubling time has come down dramatically to about twenty-five days. So the amount of days it takes for the epidemic to double in size is about twenty-five now, from day-- days or less than a week at the outset of this epidemic. We may be facing the prospect that twenty thousand, thirty thousand new cases a day diagnosed becomes a new normal and a thousand or more deaths becomes a new normal as well. Right now we're seeing, for about thirty days now, about thirty thousand cases a day and two thousand deaths a day. And if you factor in that we're probably diagnosing only one in ten infections
Apart from whether New Jersey COVID19 data fits models such as the logistic function, one might question whether or not incomplete data from symptomatic patients gives an accurate picture if at least some asymptomatic patients can transmit the disease to others.
In practice eventually other constraints become important, exponential growth stops and the doubling time changes or becomes inapplicable.
(...) While using doubling times is convenient and simple, we should not apply the idea without considering factors which may affect future growth.
link: https://en.wikipedia.org/wiki/Doubling_time
Back on 20 April 2020, New Jersey Governor Murphy tweeted:
LOOK: The rates by which the numbers of new #COVID19 cases are doubling have significantly SLOWED.
Just a few weeks ago, in some areas of the state cases were doubling in a matter of days.
Now we’re seeing those rates slow to where we can measure them in the numbers of weeks.
link: https://twitter.com/GovMurphy/status/1252301088960794632
AND
https://www.phillyvoice.com/new-jersey-coronavirus-new-covid-19-patients-stabilizes-hospitalizations-covid-19/
But four days later on April 24, the "doubling rate" was up [meaning "doubling time" was shorter]:
Murphy says the time it takes for the number of positive cases also got shorter, particularly in the southern part of the state. Murphy wants to see the so-called doubling rate moving in the other direction.
link: http://newjersey.news12.com/story/42047015/positive-covid19-cases-surge-past-100k-gov-murphy-signs-order-to-help-renters
On 3 May 2020, Scott Gottlieb talked about "doubling rate" on Face the Nation:
MARGARET BRENNAN: So these federal social distancing guidelines expire this week. It's a-- a different story state to state over what's opening up. But you tweeted this week that you saw some worrying-- worrisome signals, specifically, when it comes to hospitalization rates. What is the direction of the epidemic?
SCOTT GOTTLIEB: Well, when you look across the country, it's really a mixed bag. Certainly cases are falling in the Tri-State region around New York City. But when you back out what's happening in New York, and New York is really driving a lot of the national statistics because it was such a large outbreak, around the nation, hospitalizations and new cases continue to rise. So there's about twenty states where you see a rising number of new cases: Illinois, Texas, Maryland, Indiana, Virginia, North Carolina, Tennessee have a lot of new cases on a daily basis. And so while mitigation didn't fail, I think it's fair to say that it didn't work as well as we expected. We expected that we would start seeing more significant declines in new cases and deaths around the nation at this point. And we're just not seeing that.
MARGARET BRENNAN: This morning Doctor Deborah Birx was on another network, and she said our projections were always that we would see between a hundred thousand and two hundred and forty thousand Americans' lives lost due to the virus. On Monday of this week, the President said it's probably sixty to seven-- seventy thousand dead. The week before, he said fifty to sixty thousand. Are these White House numbers reliable at all?
SCOTT GOTTLIEB: Well, the White House was looking at the IHME model out of Washington State. And that model initially showed at the high end two hundred and fifty thousand deaths and a base case of a hundred thousand. But it's come down since then to about seventy thousand. It's starting to creep back up when you look at the updates of that model over the last two weeks. I think we have to look out to what's going to happen by the end of June. It's really hard to predict beyond June where this goes because we could have large outbreaks or it could become quiescent in the summer. But I think when you look out to the end of June, it's probably the case that we're going to get above a hundred thousand deaths nationally. I think the concerning thing here is that we're looking at the prospect that this may be a persistent spread, that while the doubling time has come down dramatically to about twenty-five days. So the amount of days it takes for the epidemic to double in size is about twenty-five now, from day-- days or less than a week at the outset of this epidemic. We may be facing the prospect that twenty thousand, thirty thousand new cases a day diagnosed becomes a new normal and a thousand or more deaths becomes a new normal as well. Right now we're seeing, for about thirty days now, about thirty thousand cases a day and two thousand deaths a day. And if you factor in that we're probably diagnosing only one in ten infections
Apart from whether New Jersey COVID19 data fits models such as the logistic function, one might question whether or not incomplete data from symptomatic patients gives an accurate picture if at least some asymptomatic patients can transmit the disease to others.
posted by Lawrence B. Ebert at 3:22 AM
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