I am developing a negative binomial regression model that investigates factors impacting the death rate of animals that are fed. The number of deaths was counted over the course of a feeding season, however, the feeding season length (and therefore the number of days over which dead animals were counted) varied. Therefore, my response variable is calculated as a daily death rate: number of dead animals/population size/season length.
I suspect that death rate will be higher in longer feeding seasons due to animals being congregated for longer periods of time, increasing disease transmission. Therefore, I would like to include season length as both an independent variable and as an offset term. Is this an acceptable thing to do?