Since you want the clinic odds ratio for each sex and for each race, I assume that you want to allow for the clinic odds ratio to change in each sex and each race. If so, then you model needs to accommodate that. You could then just use the ODDSRATIO statement to get the clinic odds ratios for each combination of sex and race. But you seem to want them for sex alone and for race alone. To do that you have to be comfortable averaging over the other variable (that is, over race for the odds ratios for sex). You can do that using the SLICE statement. For example, using C, S, R for Clinic, Sex, and Race:
proc logistic plots=none;
class c s r / param=glm;
model disease(event='Yes')=c c*s c*r;
oddsratio c;
slice c*s / sliceby=s diff oddsratio cl;
slice c*r / sliceby=r diff oddsratio cl;
run;
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