Estimating an odds ratio for a variable involved in an interaction

[zihdonv19]

I'm using this example dataset to show my question, which is from: http://support.sas.com/kb/24/455.html

  data uti;
         input diagnosis : $13. treatment $ response $ count @@;
         datalines;
      complicated    A  cured 78  complicated   A not 28
      complicated    B  cured 101 complicated   B not 11
      complicated    C  cured 68  complicated   C not 46
      uncomplicated  A  cured 40  uncomplicated A not 5
      uncomplicated  B  cured 54  uncomplicated B not 5
      uncomplicated  C  cured 34  uncomplicated C not 6
      ;

I want to examine the relationship between count and diagnosis (odds ratio) using interaction term in logistic regression at each level of treatment. What I want:

Treatment	ORs (diagnosis~count)	Confidence interval
A	1.4	(1.2, 1.6)
B	1.2	(1.1, 1.6)
C	1.5	(0.8, 1.8)

For a fabricate example, the odds ratio is 1.4 at treatment A meaning that for every one count increase, the risk of being diagnosed increased by 40%.

[FreelanceReinh]

Hello @zihdonv19,

Sorry to see that your question hasn't been answered yet.

So you reinterpret the sample data from Usage Note 24455 so that COUNT is now a continuous predictor and DIAGNOSIS is the dichotomous response variable. Let's assume that DIAGNOSIS='complicated' is the event of interest.

Then, in principle, you can obtain the desired odds ratio estimates (together with 95% confidence intervals) with this syntax:

proc logistic data=uti;
class treatment / param=glm;
model diagnosis(event='complicated') = treatment count treatment*count;
oddsratio count;
run;

However, this particular dataset with only four observations per treatment group is too small to yield a reasonable result: see the warnings about quasi-complete separation etc. in the log and in the output.