This is a general statistics question about Poisson Regression. I have age-adjusted and crude rates for opioid mortality for the period 2014-2016. I want to use Poisson regression, but I am not sure if this is the right statistical analysis for the type of data that I have. Now, I am not that well verse when it comes to statistics, so I was hoping someone could give me some advice on how to proceed. I know that Poisson regression use models count, but I believe you can model mortality rates too. My dependent variable would be the age-adjusted or crude rates, while my independent variables would consist of socio-economic indicators such as low educational attainment, poverty, unemployment, occupation, median household income as percentages pulled from the American Community Survey 2013-2017.
After doing a little bit of research, I realized that I need to use an offset if I am trying to model mortality rates. An example I have crude rates for opioid mortality for 100 counties in North Carolina. My dependent variable would be my death counts for each county for 2014-2016, while my offset would be the total population at risk for the study period (2014-2016).