exact logistic regression output

[sophia_SAS]

Dear SAS users,

Can you help with interpreting the exact logistic regression output?  Using the "Friendship" example from the SAS website below (also attached), is it correct to say the following based on the below exact conditional tests output?  The variable "recovered" is the outcome.

There is an association between friendship and recovered, when controlling for diagnosis (p=0.0004). However, the association between diagnosis and recovered was not significant when accounting for friendship (p=0.5055).

Could I also say friendship was associated with recovered, independent of diagnosis? 

http://support.sas.com/documentation/cdl/en/statug/67523/HTML/default/viewer.htm#statug_logistic_exa...

Thanks! 

[StatDave · Accepted solution]

That statement seems reasonable. Since the model assumes no interaction between friendship and diagnosis, the effect of friendship (as measured by the parameter estimate) is the same at either diagnosis. But the test and estimate for friendship adjust for the presence of diagnosis in the model, not independently of diagnosis. Probably, friendship would still be significant if diagnosis were removed from the model, but not necessarily.