The GENMOD analysis of the above example would be the following. No WEIGHT statement (or ZERO option) is needed. But with this modeling approach, one of the parameters - the one for the level with zero count - is infinite. For the level without the zero count, a confidence interval is provides but is wider than the intervals from PROC FREQ. The nonmodeling approach provided by PROC FREQ avoids parameter estimation and the exact analysis provides good estimates and confidence intervals for both levels.
data b;
input t c;
tr=20;
off=log(tr);
datalines;
1 0
0 10
;
proc genmod;
class t;
model c=t/d=p offset=off;
lsmeans t / ilink cl;
run;
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