IANAD (I am not a doctor). However, common sense tells you that "cause of death" is impossible to pin down in all cases, because you don't have the counterfactual ("if they did not have COVID, would they have died anyway?"). The official "cause of death" is quite often "congestive heart failure" but that's just the last thing that happened to them.
For that reason, "excess deaths" is about the best we can do, being an aggregate number. We don't need to decide if they died "of COVID" or "with COVID." We have a distribution of the number of deaths, there's no issue of whether someone is dead or not, and it has a mean and SD.
It's also common sense that, whatever other variables you bring in, "persons per household" is a primary variable. Sustained contact with an infected person just has to be a prime cause of the spread of a communicable disease. "Population density" is probably a weaker proxy for that.
For that reason, "excess deaths" is about the best we can do, being an aggregate number. We don't need to decide if they died "of COVID" or "with COVID." We have a distribution of the number of deaths, there's no issue of whether someone is dead or not, and it has a mean and SD.
It's also common sense that, whatever other variables you bring in, "persons per household" is a primary variable. Sustained contact with an infected person just has to be a prime cause of the spread of a communicable disease. "Population density" is probably a weaker proxy for that.