I am fitting a simple negative binomial regression model with (Yearly cancer death ~ Offset (Size of population) + Age + Household income). I used the offset term because I want to compare the yearly cancer death risk in various cities with different population size.
However, because the Size of population is used as an offset term, only regression coefficients for Age and Household income are available in the results. If I also want to predict the number of yearly cancer death of a population size 200,000 with known age and household income, is there any way I can acquire this piece of information from the model?
Or should I fit another negative binomial regression with (Yearly cancer death ~ Size of population + Age + Household income), where the Size of population is no longer an offset term, to get the answer?