Logistic regression or Poisson regression (log linear)

Greetings,

I am trying to determine which form of regression to use. The dependent
variable is binomial, meaning either 'experimental treatment' or
'control treatment.' The independent variable is either 'event
occurred' or 'event did not occur' but an event can occur more than
once (independent events) over the course of my sample unit which is
one day. The events are relatively rare. I have 244 samples/days. 10
times an event occurred once in a day. Once two events occurred in a
day, one time three events occurred in a day and one time seven events
occurred in a day.

My objective is to determine if the event occurs with the control
treatment more often than with the experimental treatment. I am not so
interested in determining if, for example, 7 events occur more often in
the control treatment vs. the experimental treatment, particularly
since this and other multiple event days happened only once. I realize
I could bin the event data into 1 or more but this seems to be
discarding relevant data that is already pretty slim.

I hope this is clear and someone may have suggestions. Thanks for your
considerations.

Ryan Silva

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