Goodness of fit to poisson distribution for monthly rates

[simkinm2]

I have monthly data for events for which I'd like to ensure a good fit for monthly rates to a poisson distribution.  The data looks like this:

Month           Number_of_events        Patient_days       Events rate per_1000_patient_days

Jan2016             125                                 500                                250

Feb2016             150                                 523                               286.80

etc.....

I am plotting the monthly rates on a control chart and want to ensure I am meeting the assumption that the underlying distribution is a poisson distribution, otherwise the control limits I've calculated are not valid.  I believe I need to use proc genmod to model number_of_events and use the log of patient_days but want to make sure I am not missing anything.  Any advice is greatly appreciated!

[PGStats]

What have you tried so far?

[simkinm2]

I've tried something like this:

data a;

set a;

log_pt_days= log(patient_days);

run; 

proc genmod data = a;

model number_of_events/ dist = poi offset = log_pt_days;

run; 

[PeterClemmensen]

There are plenty of articles on fitting Poisson distributions like

http://blogs.sas.com/content/iml/2012/04/04/fitting-a-poisson-distribution-to-data-in-sas.html

http://sasnrd.com/fit-discrete-distribution/

[StatDave]

See this note.