# Poisson regression for # of acute toxicities as outcome variable?

I have a data set of N=200 comprised of patients who either received Treatment A (N=50) or Treatment B (N=150). I have treatment toxicity outcomes (binary yes or no) across 4 domains: hematologic, skin, gastrointestinal (GI), or urinary. Patients could have had anywhere from 0 to 4 of the toxicities.

My outcome of interest is # of acute toxicity domains experienced by the patient. So this would be a "count" variable that can take on a value of 0, 1, 2, 3, or 4.

Objective: Determine if Treatment A is associated with fewer acute toxicities compared to Treatment B.

What regression model would you recommend using? I was thinking Poisson regression with robust errors since the dependent variable is a count variable, but I wasn't sure if it would be biased because by definition patients cannot have more than 4 toxicities.

This was the SAS code I was thinking of using:

proc genmod data = my_data;
class treatment id_code /param=glm;
model total_acute_toxicities = treatment confounder_1 confounder_2 /dist=poisson;
repeated subject=id_code;
run;