I’ve been at Duke and in academic research for a little more than three years. There are two important categories of helpful questions that I always need to think about:
- “What exactly are you counting and are you counting what you think you are counting?”
- “What, exactly, is your denominator?
We need to ask these questions when we think about COVID-19 right now as we know two things about it. First, we are still in an exponential growth phase of infection spread where success at this point is merely slowly the exponent of the growth function in the United States at this time.
22 days from 100 cases to 100,000, because that’s how exponential growth works when left unchecked.https://t.co/Lytl2cz0Ph pic.twitter.com/RdpaRRKjqD
— Justin Wolfers (@JustinWolfers) March 27, 2020
Right now, it seems like the US is seeing a doubling of cases every two to three days. Some of this is a function of testing starting to come online picking up lower acuity cases, but a lot is probably new cases.
The other thing that we know is about COVID 19 is that there is a significant lag between infection and symptoms and then symptoms to hospitalization for the people who are hit the hardest by the disease.
Annals of Internal Medicine## estimated the time from infection to detectable symptoms was a median of 5 days.
After symptoms were detected in China, hospital admissions were usually happening a median of seven days for all hospitalized patients and eight days for patients who went to an ICU.
If we can safely add up median time from infection to symptoms and then symptoms to hospitalization, that sums to a back of the envelope span of 12 to 13 days. In the United States, that translates to between 4 and 6 doubling cycles. Most of the people who are presenting ICUs were infected by the time significant social distancing started in the United States. The ACC basketball tournament was still being played in front of 8,000 fans on March 12. New York City public schools were still open on March 15. Spring Break and Mardi Gras were in full swing.
From a March 12, 2020 Lancet article**, a very good point is made about death rates as a function of time infected:
However, these mortality rate estimates are based on the number of deaths relative to the number of confirmed cases of infection, which is not representative of the actual death rate; patients who die on any given day were infected much earlier, and thus the denominator of the mortality rate should be the total number of patients infected at the same time as those who died…
All of this is a long way to say that I am extremely perplexed by this following tweet:
FWIW: New York now has a pretty large sample size of coronavirus cases. And, so far, the hospitalization rate is between 13 and 15 percent. The ventilator rate is under 4 percent. These are, so far!!, better than worst fears.
— Dan Goldberg (@DanCGoldberg) March 28, 2020
If this is Total Hospitalizations/Total Cases or Total Ventilation/Total Cases, then we have a huge timing problem as most cases (50%) are cases that happened in the past doubling and 87.5% of the cases are from individuals who were infected in the past three doublings. People who have been infected in the past two or three doubling cycles are (at this time) extremely unlikely to be already dead, already ventilated or already hospitalized.
The CDC has a good summary of the complete case outcome from Diamond Princess where there was a effectively a single infection event and significant follow-up:
Among 3,711 Diamond Princess passengers and crew, 712 (19.2%) had positive test results for SARS-CoV-2 (Figure 1). Of these, 331 (46.5%) were asymptomatic at the time of testing. Among 381 symptomatic patients, 37 (9.7%) required intensive care, and nine (1.3%) died (8). Infections also occurred among three Japanese responders, including one nurse, one quarantine officer, and one administrative officer (9). As of March 13, among 428 U.S. passengers and crew, 107 (25.0%) had positive test results for COVID-19; 11 U.S. passengers remain hospitalized in Japan (median age = 75 years), including seven in serious condition (median age = 76 years).
In that case the denominator does not have time variation and the Case Fatality Rate (CFR) is not complete as there are still people in the ICU who could quite plausibly die, but there has been enough time to establish a somewhat reliable number.
When we see reporting that is a function of division, we always need to ask what are we counting, and are we counting what we think we are counting and finally are we using the right denominator?
## DOI: 10.7326/M20-0504
** Lancet Infect Dis 2020 Published Online
March 12, 2020 https://doi.org/10.1016/S1473-3099(20)30195-X
New Deal democrat
Here’s a little “good” – actually, “less bad” – news. For the past three days in a row, the US has added about 20,000 new infections daily. The exponential *rate* of growth has slowed from about 35%/day during the first three weeks of March, to a little over 20%/day for the last 6 days combined, to a little under 15%/day yesterday.
Also, there are signs that California’s new case count *may* be plateauing, especially in the SF area which was put under lockdown about 2 weeks ago.
WaterGirl
David, I find myself wondering if any of the statistics are valid anywhere in the US – with so little testing, even of people who are sick – how can we have any idea at all how many people are sick/have been sick with this?
Aren’t our numbers probably 100x higher than what is being acknowledged?
Basically, garbage in, garbage out. I will be very happy if you tell me that my concerns about this are not valid concerns.
Wag
David, as always, an interesting post. As a primary care physician in a university health care system, I’m watching the pandemic with intense interest. Your insights are always food for thought.
I have a cousin who is a math teacher in Chicago. He posted an interesting video about how to visualize the end of exponential growth I’d be interested in your thoughts about this, as well.
https://m.youtube.com/watch?feature=youtu.be&v=54XLXg4fYsc
Wag
@WaterGirl: I share these concerns. In Trump’s dreams, we would have as little testing as Russia, where there are “no” cases. Putin has held down the release of test results in Russia to an amazing extent.
zzyzx
@WaterGirl: I don’t see that as concerns. I see that as a good thing oddly enough. If we’re really only getting 1% of the infected population in our stats, then we’re getting close to the point where growth has to slow just because there is herd immunity already and it means the death rate is significantly lower than we thought.
That says a lot of good things about the odds of a secondary wave of infections if we’ve already built up a much larger herd immunity than we thought we did.
Or maybe I’m running the numbers wrong and someone can correct me.
New Deal democrat
@Wag: Thanks for this! Very informative explanation. By his metric, and per my above comment, the US may be beginning to break exponential growth to the downside.
David Anderson
@New Deal democrat: Yeah, the first three weeks of March had no organized physical distancing anywhere except for Puget Sound. The past two weeks have seen first sporadic and then wide scale but not universal physical distancing.
Washington State is seeing an Ro of 1.4 right now in some models compared to an earlier Ro 2.7 according to the NY Times (https://www.nytimes.com/2020/03/29/us/seattle-washington-state-coronavirus-transmission-rate.html)
That is still a spreading epidemic but it is one where the curve is far flatter than what we will see in Florida and Mississippi where evidently it is up to God’s Will to keep them safe from the heathen blue staters.
Wag
@New Deal democrat: Perhaps. Although I’d be more confident if we had more intensive testing from the start.
New Deal democrat
@David Anderson: If I were Gov. Cuomo, I would react to Trump and the CDC’s quarantine and advisory bits with “Oh please, b’rer fox, please don’t throw me into the briar patch!” The last thing the NYC area needs is travelers from, e.g., FL coming back into the area and re-sparking new infections.
Now that the Northeast, Midwest, and Mountain and Far West areas are generally under “stay at home” advisories, I am waiting for the next shoes to drop: (1) restrictions on incoming travel from Dixie (ex-NC and LA) and the High Plains (ex-KS); and (2) banding together to negotiate supplies.
I am also pleased that the “Sledgehammer, then Scalpel” or “China first, then South Korea” paradigm of how to proceed looks like it has gained wide acceptance in the medical community.
catclub
mardi gras date was Feb 28. That was over by march 12-15 dates you are talking about.
Mardi gras two weeks later, or the covid-19 epidemic two weeks further along and mardi gras becomes a huge mixing pot of people and virus.
wenchacha
@New Deal democrat: I saw pictures of a Brentwood public market from Saturday. Way too many people. SF may be sheltering, but not so much in LA?
catclub
We cancelled church for Mar 15 and 22nd on Thursday mar 12.
The dioceses cancelled (much more officially) on mar 13. So there was already awareness. State or city decrees were not happening.
South Mississippi is definitely not Puget Sound.
Ken
@catclub: It would be interesting to see a breakdown of responses by denomination. The Catholic church, from my limited survey, seems to have been pretty proactive, often cancelling masses before state restrictions went into effect.
zzyzx
@Ken: I assume that’s because of Italy?
I suspect one reason King County kicked into gear so quickly was because our death count was inflated by it hitting a nursing home, so we worried that we were further along the path than we were.
New Deal democrat
@wenchacha: Sorry, I really don’t have good knowledge about regions in CA, except that I have seen graphs w/r/t SF, which had a lockdown order early.
Exregis
At the Johns Hopkins coronavirus map site, if you click on the USA heading on the left, look at the confirmed-cases graph to the lower right and use the little arrows in the graph to get the logarithmic view, what you see is pretty much a straight line from the latter part of February to today, with maybe the tiniest lessening of the slope for the last week (as measured by the knife I was using to butter my English muffin). That indicates that we have a pure exponential growth whose exponent may have shifted just the tiniest bit down. I wouldn’t consider that possible downshift the least bit significant so far.
Of course that’s not the death rate. What we can say for sure is that the death rate is between the today’s deaths divided by today’s confirmed cases AND today’s deaths divided by today’s closed cases, where closed cases are the sum of deaths and recoveries. Or between 1.8% AND 34.6%. Every term — confirmed cases, recovered cases, and even deaths — is subject to unknown error. But given what we have and going by South Korean testing results, it sure seems as if the death rate is substantially higher than the 1% figure bandied about.
Pittsburgh Mike
This is all true, the hospitalization rate should be considered an indicator of what was going on 2 weeks ago, and the death rate is similarly a reflection of the state 3 weeks ago. And the doubling time (looking at hospitalization and death rates, not the more noisy case rates) does appear to be in the 2-3 day range.
There is a bit of good news, in that log base 2 of the US death rate is 0.263 over the last 4 days, and 0.234 over the last two days, as compared with 0.449 for the 8 days starting 3/15. So, nationwide, we’re falling behind the exponential growth rate, and indeed, the absolute number of new deaths per day seems to be leveling off now, both in the whole US and PA, where I live.
We’re still nowhere near being able to ‘open’ the economy again; doing so requires very low absolute # of cases, and either maintaining significant social distancing and better than usual hygiene, or broad testing and case tracking to catch new outbreaks. But there is a ray of hope that a path out of this situation is possible, assuming Trump doesn’t f**k it up.
Another Scott
Excellent post.
Yes, we don’t really know the denominator or the numerator (the BBC is reporting that (somewhere? The UK?) isn’t counting COVID-19 deaths outside of hospitals). More numbers are good, even if only to scare politicians and the public about how serious this is and to get people to take effective measures (stay home!, wash your hands!!).
I’ve said for a while that it’s my belief that the virus is everywhere and we should treat it as if it is.
Testing for infection really doesn’t matter when it comes to treatment (because there is no real treatment yet). (If at all possible) Stay home if you’re well. Stay home if you think you’re getting sick, stay home if you’re very sick, go to the hospital if there really is no other choice. Medical staff need an unlimited supply of PPE in order to act as if everyone they touch is infected.
What really matters for the “end” of this (if there is an end) is testing for antibodies, and the development of effective treatment (a “cure”), and development of an effective vaccine. The federal government should spend whatever it takes at the CDC, FDA, university/federal/private research labs, etc., to get those things out NOW NOW NOW. Misinformation about malaria drugs is killing people and wasting time.
Thanks again.
Cheers,
Scott.
ZeeLizzee
I was just having this convo w spouse this morning.
Connecticut is saying 1900 positives in 12000 test.
What we don’t know is how this deals with the lag between when the test is administered and when the results come back. There are instances where people got tested around the 21st/22nd and have yet to get their results. How’s THAT being accounted for?
I taught Adult Ed for a few years, and the level of basic numeracy in this country is appalling. That ignorance will surely contribute to the coming storm.
Cam-WA
@zzyzx: I think your math might be wrong. At a 1% confirmed-and-reported to actual rate, ~144,000 reported US cases translates to 14,400,000 actual cases. That’s nowhere near herd immunity. The lowest % needed for herd immunity I’ve read is 50% (which seems low, but what do I know?), which translates to 165,000,000 cases needed (half of 330,000,000 US population).