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.
— 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