Estimates/Odds Ratio for 2-way interaction of binary (0,1) predictors in Proc Logistic.

[NMB82]

I have a significant interaction that I want to explore further. I'm not the best with contrast coding and most of the examples I'm finding are either 3-way interactions or those with all class variables or a combo class/continuous. Here are the basics of my model:

ODS RTF;
ODS GRAPHICS ON;
PROC LOGISTIC DATA=work.data1 DESCENDING SIMPLE PLOTS=ALL;
  CLASS  a (REF='0') b (REF='0') / PARAM=reference ;
  MODEL  y = a b c d c*d / EXPB CL INFLUENCE ;
  ODDSRATIO c / AT(d = 0 1) CL=WALD;
  ODDSRATIO d / AT(c = 0 1) CL=WALD;
  CONTRAST 'c=1 & d=0' c 1 d 0 /ESTIMATE = PARM E;
  CONTRAST 'c=1 & d=1' c 1 d 1 /ESTIMATE = PARM E;
  CONTRAST 'c=0 & d=0' c 0 d 0 /ESTIMATE = PARM E;
  CONTRAST 'c=0 & d=1' c 0 d 1 /ESTIMATE = PARM E;
  UNITS / DEFAULT=1;
  OUTPUT OUT=Results;
RUN;
ODS GRAPHICS OFF;

For this model, y is binary (0,1), a and b and both categorical with numerous levels, and c and d are continuous binary (0,1) variables. What I want is to get estimates/odds ratios for all levels of the interaction, which is p<.01. I don't think this code is correct, but I have a feeling I'm close. Any advice would be appreciated! 

[FreelanceReinh]

Hello @NMB82,

Your ODDSRATIO statements are correct. Option "CL=WALD" is the default, though, hence redundant. Also redundant are the UNITS statement (unit 1 is the default) and three of the CONTRAST statements: The third is trivial, the first and the fourth repeat the results for the parameters of c and d.

From the ODDSRATIO statements you already get the odds ratios (and pertinent confidence limits) for (c,d)= (1, 0) vs. (0, 0), (1, 1) vs. (0, 1), (0, 1) vs. (0, 0) and (1, 1) vs. (1, 0), all adjusted for a and b. The second CONTRAST statement suggests that you're also interested in the odds ratio "(1, 1) vs. (0, 0)", but for this you would need to use the ESTIMATE=EXP option and to insert the interaction term c*d 1 into the list of effects and values. You can get both the estimate (here: of the sum of the estimates for c, d and c*d) and the odds ratio (i.e. the exponentiated estimate) with a similar ESTIMATE statement. Here's an ESTIMATE statement that in addition (just for completeness and as another example) includes the remaining odds ratio "(1, 0) vs. (0, 1)":

estimate 'c=1, d=0 vs. c=0, d=1' c 1 d -1,
         'c=1, d=1 vs. c=0, d=0' c 1 d 1 c*d 1 / e cl exp;

[StatDave]

You don't need any of the ODDSRATIO or CONTRASTS statements. You can get all possible pairwise comparisons of the four C*D levels using a single LSMEANS statement:

PROC LOGISTIC DATA=work.data1;
  CLASS  a (REF='0') b (REF='0') c d / PARAM=glm ;
  MODEL  y(event="1") = a b c d c*d;
  lsmeans c*d / ilink cl diff oddsratio;
  run;