# Methods of disaggregating data to smaller units?

I have a relatively straightforward question that I know poses some difficult challenges.

Let's say I have a state-level rate of X. I would like to disaggregate the state-level rate to the county-level. I realize this is can be dangerous (ecological fallacy), but I have seen some studies use the technique with a set of assumptions.

For example, if I know that each county is a certain proportion of the entire state population, I could take that proportion and multiply it by the state-level rate of X to get an (incredibly) naive county-level rate of X.

I'm trying to find more information on ways to make this approach 'less' naive, but I can't seem to get any momentum. I've tried using the terms 'disaggregating' and 'weights', but I can't seem to tap into the right body of literature.

Does anyone know of any methods/body of work that have attempted to handle this problem?