Is there any way that one could explain the following?

San Marino has the most total deaths per million and a CFR of 1.8%.

Bosnia and Herzegovina is currently 8th for the most total deaths per million but it has a CFR of 3.8%.

Case-fatality ratio – is the proportion of deaths from a certain disease compared to the total number of people diagnosed with the disease for a particular period.

Does this mean that in B&H way more people who get the disease end up dying from it, but somehow San Marino ended up on the first place in relative death cases despite the much lower CFR?

I just am wondering if there is a mathematical / scientific explanation for this. Like for example because San Marino has a smaller population? Perhaps there is something I am missing.

The data is taken from here: https://en.wikipedia.org/wiki/COVID-19_pandemic_death_rates_by_country

If this is the wrong stack exchange, please let me know so I can move the question.

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    When countries with populations as small as San Marino's are compared with non-tiny countries, all kinds of weird things can happen. – BrenBarn Mar 25 at 23:11

San Marino is, from an epidemiology perspective, effectively a city in Italy. It's also quite small (just over 30,000 people), and the total number of deaths there from your source is 80. This is a tiny sample compared to the other countries on that list.

Italy is also quite high on that list. ~175 deaths vs ~237 deaths per 100,000 is certainly in the same ballpark. From the statistics posted by the NY Times, there are several regions in Italy that have higher death rates than San Marino, for example:

Valle d'Aosta, 333

Lombardy, 299

Friuli Venezia Giulia, 262

Emilia-Romagna, 259

Emilia-Romagna is particularly relevant, because this is the region of Italy that most surrounds San Marino (Marche is the other, with 166 deaths per 100,000). So really, there is nothing unusual about San Marino relative to the region of Italy it is located in; it falls right between the rates for the broader regions that surround it.

You can expect CFRs to be strongly influenced by three factors: demographic susceptibility (for example, an older population), testing (CFR goes down if you test extensively and find more asymptomatic/mild cases), and actual medical care.

Let's start with testing, because in many ways this is the "least interesting" factor: it reflects something with the data rather than anything "real" about the CFR.

From worldometer, San Marino has done 1.5 million tests per 1 million residents, with 132k cases/mil, 29 tests per case. Bosnia and Herzegovina have 234k tests per 1 million residents, with 49k cases/mil, less than 5 tests per case. Of course expressing these in #s/million is a bit funny for San Marino, which is far from having 1000000 residents, but at least these numbers can be compared with other places.

Using Italy again for comparison, Italy had 791k tests per million and 57k cases per million, about 14 tests per case, with a CFR of 3.1%, falling between the other two countries on both measures.

These numbers suggest that there was less overall less testing in Bosnia and Herzegovina vs San Marino, which you'd expect to show up as a higher CFR (fewer mild cases in the denominator).

Does this mean that in B&H way more people who get the disease end up dying from it, but somehow San Marino ended up on the first place in relative death cases despite the much lower CFR?

A more thorough statistical analysis would be required to discover smaller measurable differences between countries, but the basic anomalies you point out do not seem unusual when these influential factors are considered. The simplest explanation is that San Marino is a small enclave in a severely impacted region of Italy. The deaths per population there are not unusual for local region. The differences in CFR are most easily explained by differences in testing that influence the number of mild cases included in the CFR calculations.

The other big factor in how many deaths per population is in how many actual cases per population there are. We can't know this number exactly, only estimate from assumptions about how many cases are tested positive, but the numbers suggest that probably more people in San Marino (along with the adjacent regions of Italy) were infected, so more people there died. An older population could have also contributed slightly.

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