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Clark and Nick
The case fatality rate in different countries is all over the place. Here is an article that discussed the reasons why this is so. As Clark says, the case fatality rate always improves with time presumably because you always diagnose the more severe cases first as milder cases may escape attention and you will also get better at treating a disease that you become more familiar with in time. Of course there are many other demographic factors, as discussed in that website referred to above:
Between countries, case Fatality rates vary significantly, and over time, which suggests considerable uncertainty over the exact case fatality rates.
1. The number of cases detected by testing will vary considerably by country;
2. Selection bias can mean those with severe disease are preferentially tested;
3. There may be delays between symptoms onset and deaths which can lead to underestimation of the CFR;
4. There may be factors that account for increased death rates such as coinfection, more inadequate healthcare, patient demographics (i.e., older patients might be more prevalent in countries such as Italy);
5. There may be increased rates of smoking or comorbidities amongst the fatalities.
6. Differences in how deaths are attributed to Coronavirus: dying with the disease (association) is not the same as dying from the disease (causation).
But also I think that the overall mortality can only be ascertained after widespread testing and also after the end of the epidemic, or at least the first wave of the epidemic.