How to get 95% CI for difference in Predicted Probabilities using with binary outcome and logit link

[tka726]

I am using GLIMMIX to estimate predicted probabilities of a binary outcome in 2 groups. I can get the predicted probabilities for each group (and subtract them to get the difference) but how do I compute the 95% CI for the difference of the predicted probabilities. I know that I can not use the Difference of LSMEANS as the inverse link is not linear.

PROC GLIMMIX DATA=multicenter ;
CLASS center group pt;
MODEL SideEffect/n = group / solution;
RANDOM center / solution;
LSMEANS group/ cl diff ilink;
run;

Predicted Probability for Group A is 0.2147

Predicted Probability for Group B is 0.3085.

Difference would be 0.0938, but how to get the CI of the difference?

[StatDave · Accepted solution]

If you really want to stick with a model-based approach, you can use the NLMeans macro as discussed and illustrated in this note. But since your data can be summarized simply as a 2x2 table, you could take a non-modeling approach and simply use the RISKDIFF option in the TABLES statement of PROC FREQ after setting it up to show the 2x2 table.  

[tka726]

Thanks so much! The NLMeans macro provides exactly what I need.

proc glimmix data=multicenter ;

class center group ;

model SideEffect/n = group / solution; 

random center / solution; 

lsmeans group/ e cl diff ilink;

store out=proportions;

run;

proc plm restore=proportions;

lsmeans group/e ilink diff;

ods output coef=coeffs;

run;

 %NLMeans(instore=proportions, coef=Coeffs, link=logit, title=Differences of Predicted Probabilities)

[StatDave]

I just noticed that you have a random effect in the model. You could still use the NLMeans macro in the same basic way as shown in the note. But for a non-modeling approach, your data would be arranged as a stratified 2x2 table, with one stratum for each center. So, the PROC FREQ alternative would define the stratified table and then use the COMMONRISKDIFF option. For example:

proc freq; tables center*group*sideeff / commonriskdiff; run;