I am not a medical researcher, but I don’t see anything wrong with the general methodology of epidemiological research. When it comes to guns, it’s a data problem, not a methodology problem.
The methodology is straightforward. You hypothesize that eating cheeseburgers causes heart disease. You randomly assign a sample of people into two groups. Group A eats cheeseburgers and Group B doesn’t. You sample the post-burger incidence of heart disease. You also measure a lot of controlling factors like the person’s weight, medical history, exercise habits, general eating habits, etc. You estimate a logistic regression that predicts the quantitative increase in the probability of heart disease based on eating cheeseburgers, all other f actors constant.
There’s no reason this can’t be similarly applied to the risk of bad outcomes from possessing firearms, provided data on the relevant controlling factors can be collected. But the problem is, how do you measure maturity, responsibility, common sense, good habits, etc. in addition to gun safety experience, knowledge, safe handling practices, etc. It would be an impossibly expensive effort to measure such qualities, hence it isn’t generally done.
So, when some medical researcher tries to infer something about my risk of accidents or death from my possession of firearms, I will discount their conclusions because they don’t know what really influences my behavior.
“Always liked me a sidearm with some heft.” Boss Spearman in Open Range.