The reporters at the NYT have no idea how fatality rates are calculated. Those are not fatality rates. They are just confirmed dead divided by confirmed cases, which is a number that really only has relevance once the virus has stopped spreading (clearly not the case here).
The calculations of fatality rates are very complicated, when dealing with incomplete, inaccurate information. The best guestimates, though, have to at least take into account the median time between diagnosis and death (it takes far more than this to get anywhere useful, but it is at least a starting point). Then, you can take confirmed deaths and divide by the number of deaths “that many” days ago. It is by no means perfect, but at least gets you closer to an accurate, meaningful number. (And don’t forget that the time between diagnosis and death changes drastically from area to area, and over time).
As far as the discrepancy between the areas, it can be explained by a huge number of factors. In all likelihood, though, it is because the gap from confirmation to death is wildly different. For example, in an area like a foreign country where the virus hasn’t taken hold yet, people tend to get tested much earlier (no backlog of cases, many people caught by screening, no testing backlog, etc.), and also tend to live longer, even if they eventually die (access to more doctors, ICUs, equipment, etc.). These factors can dramatically effect the time from diagnosis to death (by quite a number of days), and this increased gap can cause a wildly different deaths/confirmed ratio, even if nothing else is different.
The calculations of fatality rates are very complicated, when dealing with incomplete, inaccurate information.
I would replace "complicated" with "uncertain". The math is not all that complex compared to that used for analysis of many other things (say, a "crumple zone" in the front end of a car) which can go into astounding (to most people) detail. A modern computer can crunch through dozens of things like variable time until death in different regions, etc. No problem. Variance in input data can be handled by multiple simulations. So, it is no problem to generate lots of outputs, but, the problem is that if one is guessing wildly at the inputs, one gets a wide range of outputs. There is then no way other than, perhaps, experience or intuition, to know which output is likely "good", therefor the great uncertainty. "GIGO", if you will.
This is only a minor quibble over "semantics", I suppose. :-)
As far as the discrepancy between the areas, it can be explained by a huge number of factors. In all likelihood, though, it is because the gap from confirmation to death is wildly different. For example, in an area like a foreign country where the virus hasn’t taken hold yet, people tend to get tested much earlier (no backlog of cases, many people caught by screening, no testing backlog, etc.), and also tend to live longer, even if they eventually die (access to more doctors, ICUs, equipment, etc.). These factors can dramatically effect the time from diagnosis to death (by quite a number of days), and this increased gap can cause a wildly different deaths/confirmed ratio, even if nothing else is different.
Well, yes, but your example runs counter to the data from China vs. other countries fitting that example. A longer gap is not going to give you a lower fatality rate when a sometimes fatal disease is spreading. To the contrary, early detection resulting in many more survivors usually trumps a somewhat longer gap, even when a disease is spreading, unless the spread vs. gap is truly explosive. The exception would be if a disease had a very high mortality rate that did not respond to treatment or if effective life-saving treatment was not available. Then, early detection might not help the victims.
(I'm not disagreeing with you in general here, or about "gaps" in general - I just think you used the wrong example.) ;-)
Assuming the data is close to correct, Hubei's fatality rate is IMO most likely explained by, initially the health care system's inability to respond quickly enough to a new breakout (could any?), and later by lack of capacity for serious and critical cases (even with early detection, perhaps?) Gap variances could be in play, and obviously, more could be going on as well. In that too, we are in agreement.