Agreed, when using the "deaths / (deaths + recoveries)" formula, recoveries being under-reported is possible and would skew the CFR upward. But also, if deaths are under-reported in the same proportion as recoveries, then it would not affect the CFR.

I suppose one way to reduce uncertainty is to examine a cohort of patients and follow it meticulously. To do that, we can look at the 99-patient case study published in The Lancet yesterday: https://www.thelancet.com/journals/lancet/article/PIIS0140-6... 11 died, 31 were discharged, and 57 remain in the hospital. This suggests a CFR of 11/(11+31) = 26% The assumption epidemiologists make when they use this formula is that the 57 still in the hospital have the same chance of dying as those who already died in the hospital.

...that's not the assumption epidemiologists make. For the very simple reason that there are many "just so" stories you can tell about those still in the hospital - are they sicker, and thus there longer? Are the secondary cases, which in the case of MERS had a much lower CFR?

This is a very straightforward application of survival analysis, and those still in the hospital are "censored" observations - we know their outcome takes place in the future, but we're not sure when.

There are methods for calculating things like CFR in the presence of censoring, which will change based on what type of model you're using.

Assigning 50% chance of death to any patient remaining in the hospital when calculating mortality rate would be nuts, I can only thank the epidemiologists for not publishing the number.

Not 50%, you misunderstand me. I edited my comment to clarify. What I meant is out of those who came out of the hospital (either dead or recovered), 26% died. So those remaining in the hospital are assumed to have a 26% chance of dying.

Another way of looking at probabilities, out of the 57 patients left in the hospital:

If 0 die (ie. all recover), the CFR is 11% (11 deads, 88 recovered)

If 15 die (26% of 57 still hospitalized), the CFR is 26% (11+15=26 deads, 73 recovered)

If 57 die, the CFR is 69% (11+57=68 deads, 31 recovered)

So the CFR bounds are 11-69% and if the trend on remaining patients continue it should be 26%.

Looking only at hospitalized populations creates severe selection bias when applied to the question people want answered here, namely "If I get nCOV, what's my chance of dying?" Only the most severe cases a physician sees end up hospitalized, and only the most severe cases within the general population end up being seen by a physician and confirmed as nCOV. You've already got two levels of selection bias (with an unknown percentage passing through each filter) before reaching the denominator in your numbers.

Not only that, but Wuhan's hospitals and health care system in general seem to be overwhelmed.

In other places that are better prepared and which have more resources the outcomes will likely be better, in worse prepared places with fewer resources the outcomes will likely be worse.

Let's keep that in mind before we extrapolate from Wuhan to the rest of the world.

Correct there is a bias. However even when comparing the coronavirus to the seasonal flu (hospitalized patients only), the coronavirus still looks much more severe:

Only 7% of hospitalized flu cases died in 2018-2019 (34 157 out of 490,561): https://www.cdc.gov/flu/about/burden/index.html The coronavirus would thus appear to be 4 times more deadly (26%.)

Or the hospitals are more overwhelmed now, so only the sickest patients are being admitted.

I suspect that “chance of dying” varies based on treatment, and that treatment in an overwhelmed Wuhan hospital is likely not the same as treatment as, say, the first patient in France to get the disease.

"I suspect that “chance of dying” varies based on treatment, "

I doubt this. WHile this may be true for a known disease, we have to ask, how much can the hospital do in this cases? It is a little bit like HIV in the beginning. Watch them die?

Interestingly, China is trying HIV medications on the infected.

One of the main causes of death of the new coronavirus seems to be Acute Respiratory Distress Syndrome (ARDS). This can be treated fairly effectively with ventilation, but such treatment would obviously require a bed, ventilation system, and attentive nurses, at the very least. It's easy to imagine how these requirements may currently not be met for all patients with ARDS symptoms in Wuhan.

For more info on ARDS and treatment in the context of the current pandemic, see this informative explanation: https://www.youtube.com/watch?v=okg7uq_HrhQ