Still no surprises. The U.S. now stands at 34 new cases per 100K population per day, down 41 percent in the past seven days.
COVID-19 hospitalization and deaths are falling much more slowly than reported new cases. My best guess remains that recent growth in home testing has created a divergence between reported new cases and new hospitalizations and deaths. But there’s no way to prove that directly, and that implies that there is a very large volume of home testing going on.
Data source for this and other graphs of new case counts: Calculated from The New York Times. (2021). Coronavirus (Covid-19) Data in the United States. Retrieved 2/19/2022, from https://github.com/nytimes/covid-19-data.” The NY Times U.S. tracking page may be found at https://www.nytimes.com/interactive/2020/us/coronavirus-us-cases.html
Hospitalizations and deaths
New COVID-19 hospitalizations peaked within a day of the peak in new cases. That said, while daily new cases are now just 14% of the peak rate, daily new COVID-19 hospitalizations remain at about 38% of their peak.
Source: Calculated from CDC COVID data tracker data. Mortality rate is deaths divided by new cases from two weeks earlier.
Accordingly, if I plot the apparent case hospitalization and case mortality rates for Omicron, they are rising. Nearly 7% of officially-diagnosed COVID-19 cases are ending up in the hospital, and about 0.6% of those new cases end up dying. The apparent case hospitalization rate is no different from what it was under the far-more-virulent Delta strain.
Source: Calculated from CDC COVID data tracker data. Mortality rate is deaths divided by new cases from two weeks earlier.
The lines above are nearly parallel. The simplest way to explain that would be a reduction in reported cases (the denominator in those rates) as a fraction of actual, true cases. Plausibly, that could be due to an increase in home testing in the past month or so, diverting positive cases out of the official statistics. Alternatively, maybe so many people are “done with COVID” that any COVID-like symptoms are just being shrugged off as likely to be a cold or the flu. Again resulting in fewer positives in the official statistics.
In any case, the most plausible explanation of the bottom graph is that we’re now missing a chunk of cases out of the official counts, cases that were not missing in the past. The alternative explanation — that somehow Omicron has gotten a lot more virulent and nobody noticed — doesn’t really seem plausible.
A new rule of 9 for figuring the odds
I like to figure the odds when I assess the risks of various activities. For COVID, that means estimating the likelihood that I’m going to run across somebody who is actively contagious.
In the past, I’ve used different multipliers to convert the official new-case count into some estimate of the fraction of the population that is likely to be contagious at any given time. You have to account for two factors:
- Ratio of true cases to officially reported cases.
- Days that each true case is walking around infectious, before symptoms set in.
This makes the heroic assumption that if you have COVID-19 symptoms or test positive, you will have good sense to isolate yourself and not spread COVID-19. The “good sense” clause tells you that not every American is going to do that.
In the past I’ve used an estimate of the ratio of true cases to reported cases of 2 to 1. That was based on CDC seroprevalence data. Now, with this latest round, I’m going to bump that up to 3 to 1, as a nod to the additional cases that now seem to be missing from the official case counts.
For Omicron, I used an average of three days of being infectious before symptom onset, acknowledging Omicron’s generally faster progress. (In the past I had used an estimate of four days.) I guess I’ll keep that.
Given that — a guess of three actual cases for every official one, a guess of three days’ average period of infectiousness before symptom onset — my new rule estimating risk of exposure is “multiply by nine”. Take your currently reported new cases per 100,000 per day and multiply by nine to get an estimate of the number of persons (per 100K) walking around in an infectious state.
Example: Today, per the New York Times, Fairfax County is seeing 14 new cases per 100K per day. I then estimate that:
Percent of population infectious = 9*(14/100,000) = 0.00123 = 0.126 percent. Or roughly one person in eight hundred.
From that, for any count of the number of people you will interact with out side the home, you can estimate the likelihood that nobody you interact with is infectious.
You can so that for (e.g.) a church service, a classroom, a gym, an office, or similar. This really doesn’t address the odds of getting infected. It’s just an estimate of the likelihood that you are sharing that space with someone who is infectious.
The statistical calculation is simple. The likelihood that nobody in a crowd is infections is the likelihood that the first person isn’t, times the likelihood that the second person isn’t, …. , times the likelihood that the last person isn’t.
For example, if I go to a gym in Fairfax County, and there are typically 30 people in the workout room I use, the likelihood that nobody in that room is infections would be (1 – 0.00126)*(1 – 0.00126)* … *(1 – 0.00126) or (1 – 0.00126)^30 = 96%. (Where ^ is “to the power of”.)
My conclusion is that at the current new case rate, in Fairfax County, when I go to the guy, there’s a 96% chance that nobody in the workout room is infectious with COVID-19. In other words, right now, in Fairfax County, in that room with 30 people, there’s a 4 percent chance that somebody in that room is infectious.
If I then go to the gym once a week for 52 weeks, what are the odds that, at some point, I’ll never be in the same room as an infectious individual? That’s just the odds for any one day, 52 times, or 0.96^52 =0.12. There’s only a 12 percent chance that I’ll make it through the entire year without being in the same room as an infectious individual.
All of this assumes that all persons are equally likely to be walking around in an infectious state. And it assumes that all persons are equally susceptible to infection, if exposed to COVID-19. Neither of those is a great assumption, particularly when (e.g.) vaccination plus booster is reasonably effective at avoiding infection.
That said, this basic calculation gives me some crude handle on the relative risk that I am taking.
In reality, this week my wife and went fully back to the gym, using the weightlifting and cardio equipment. (Up to now, we had only been walking a track, which was by-and-large unused, in addition to being located in a large open space.) I looked at that 4 percent risk, and then factored in:
- Being vaccinated and boostered.
- Wearing an N95 mask (yes, you can run on a treadmill in an N95, it’s not a problem).
- Not getting very close to anybody else in the gym.
- Going mid-morning when it’s almost 100% an elderly crowd.
I vaguely figured that the odds of infection were small enough to be ignored. Or, at least, were small relative to the health consequences of not getting adequate exercise.
And, as a sub-finding, it is perfectly possible to run on a treadmill while wearing an N95.
FWIW, here’s the arithmetic, in tabular form. Look up your local new case rate, accept my nine-fold rule as being roughly correct, assume that everybody you meet has the exact same area-average likelihood of being infected, and you get the following table of risks:
Source: Arithmetic.
Think of the the 250-size group as being the size of a typical church service. Even if new cases are down to 20 per 100K per day, there’s about a one-third chance (36%) that a typical 250-person church service would have at least one person who is actively infectious with COVID-19. And if you were to hold services for a year, it’s effectively certain (100%) that you’re going to have at least one infectious person attend for at least one of those services.
The point of this is not to make people afraid. The point is that risk is unavoidable.
But, risk has always been unavoidable. You just didn’t pay it much attention.
Every year, you have faced some risk of hospitalization or death from flu. You probably never gave that a second thought. And I will continue to hold that up as my standard for a generally acceptable level of health risk.
And so, I continue to mask up wherever signs suggest that. In particular, I continue mask up in stores as a courtesy to the cashiers. I might only come close to a handful of people grocery shopping. But I’d guess the average grocery store checkout clerk is exposed to a hundred people in an eight-hour shift, and they work that shift five days a week.
The upshot is that when I grocery shop, I’m reading my odds off the “group of 10” column above. For that same experience, the grocery store cashier is reading from the “group of 100, repeated 52 times” column. I’d guess that, even now, a typical grocery store cashier in Fairfax County is exposed to an infectious individual about once a week on average. Given that I can’t buy groceries unless the stores are open and running, the least I can do is wear a decent mask while I’m there.
