Comparing two groups of incidence rates Thank you for your time with this question.
I'm trying to answer whether an exposure is correlated to incidence of disease. I have a group of 100 counties in California,  and I have the incidence of disease among exposed people in those counties as well as incidence of disease among nonexposed people in each county.
For example, the data looks like, County A, exposed 5.6 , nonexposed 6.8, County B,  exposed 3.3, nonexposed 3.2, etc. etc. up to 100 counties in California.
I also have various sociodemographic variables for each those 100 counties. Some of these variables can be separated by exposed and non-exposed.  For example, I have median income of exposed and nonexposed, average household value of exposed and nonexposed, and percentage of exposed and nonexposed on private insurance. I also have other variables that are strictly by county, meaning there is no breakdown of exposed or nonexposed (these include things like average age of the county, % of each race and/or ethnic background, % male/female).
I am curious as to what would be the best way to actually see if there are differences in incidence rates between exposed and unexposed in California, and whether those differences are truly attributable to the exposure.
I was doing some reading, and came across propensity score matching, but notice that that's mostly used for treatment and outcome type data, instead of exposure and  incidence type data. Would something like a logistic regression to find significant covariates and then controlling for those do the trick?
Would greatly appreciate any advice here.
Thank you

If you want to compute a causal effect you need to control for confounders. The problem is, that you really need to find all confounders, otherwise your results are not reliable, and in the worst case nasty things like Simpson's paradox could happen.
Now, you mentioned covariates like age, race, and sex, for which you only have data averaged over exposed and nonexposed. That means you cannot control for them. And while I don't know the details of your scenario, I think that those covariates could easily be confounders.
In general, if you knew all the confounders and had always the data separated for exposed and nonexposed, you could use propensity score matching or regression or a mixture of both using MatchIt. Exposure can be understood as some type of treatment and incidences are valid outcomes.
