# Poisson regression with interactions

#### bobban

##### New Member
I am investigating the risk of getting different forms of leukemia if you live near a hazardous waste site in New York state. I am working with PROC GENMOD in SAS to do regression (with negative binomial distribution) and I would like to calculate relative risks for parts of my population. Here is some information about my data.

The outcome variable is hospital discharges for acute myeloic leukemia, and it is called "discharges".
The predictor variables are:
- Agegroup (variable name is "agegr") with 4 levels (20-39, 40-59, 60-79, 80+)
- S e x (0=male, 1=female)
- Race (0=white, 1=black)
- income with 3 levels (25th-42nd, 42nd-59th and 59th-75th percentiles)
- Urban with 4 levels (1 = entire population living in rural areas, 2 = 1-50% of population living in urban areas, 3 = 50-99% of population living in urban areas, 4=100% of population living in urban areas)
- Exposure with 2 levels (0 = no hazardous waste sites in the zip code of residence, 1 = at least one hazardous waste site in the zip code)

All the predicted variables gives me 4x2x2x3x4x2 = 384 possible combinations. I have constructed a dataset in which every line represents one of these combinations with the number of discharges in that combination and the corresponding person-time for it. The LPT is the log of the total person time and is used as an offset to adjust for different ammounts of person time in the different combinations.

The code that produces my model is as follows:

proc genmod data=ana;

class race *** agegr inc urban exposure /DESC;

model discharges = *** race agegr inc urban exposure race*exposure

/DIST=nb offset=LPT LINK=log;

run;

I have put the interaction between race and exposure (race*exposure) in the model and the results indicate that the connection between the predicted number of discharges and the exposure level is different in the two races. I used the estimate statement to obtain RRs for black and white people separately with regard to exposure. To complete the analysis I would like to compute an overall RR for exposed VS unexposed regardless of race (some kind of weighted average of the different rates for the two races I suppose...). Can anyone help me with this?

Best regards
Erik