In general Poisson data consists of a pair of numbers (y,n), where y is
the event count for the unit and n is the size of the unit. The Poisson
MLE is sum(y)/sum(n). A general example is county level data where y is
the number of events (rare cancer) and n is the county size. Two
special cases are where n==1 for all cases and the mle=mean(y), or where
y==1 for all subjects and n= observation time until the first event,
where mle=1/mean(n).
My preferred way to fit the distribution is
glm( y ~ offset(log(n)) + other covariates, family=poisson)
because of the mature printout,standard errors, residuals, etc. The
other covariates are optional of course. If n=1 for all observations
the offset can be omitted.
Terry Therneau
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