Using contrasts in Poisson regression

Question

The question is about using contrasts in regression analysis (here, Poisson regression with robust error variance).

We have divided the participants in our sample into 6 groups, according to their body mass index at baseline (3-category variable: normal, overweight, obese) and the metabolic status at baseline.

data d.mho; set d.mho; /*2737*/
if bmi_cat2 = 1 and Met_abnorm = 0 then gp=1; /*metabolically healthy normal weight*/
if bmi_cat2 = 1 and Met_abnorm = 1 then gp=2; /*metabolically unhealthy normal weight*/
if bmi_cat2 = 2 and Met_abnorm = 0 then gp=3; /*metabolically healthy overweight*/
if bmi_cat2 = 2 and Met_abnorm = 1 then gp=4; /*metabolically unhealthy overweight*/
if bmi_cat2 = 3 and Met_abnorm = 0 then gp=5; /*metabolically healthy obese*/
if bmi_cat2 = 3 and Met_abnorm = 1 then gp=6; /*metabolically unhealthy obese*/ 
run;

We choose the "metabolically healthy normal weight" people as the reference group. In this case, is it possible to calculate the contrasts only between group 5 and 6 (metabolically healthy obese vs metabolically unhealthy obese), while keeping 'group 1' as the reference group:

proc genmod data=&data descending;
  class   id_vol  &adjust_class  &class(ref=&ref) ;
  model &outcome =    &class &adjust_class &adjust_contin / type3 dist = poisson link = log;
  repeated subject= id_vol / type=unstr modelse;
  ods output GEEEmpPEst=modcat ; 
  estimate 'MHO vs MUO' &class 0 0 0 0 1 -1/ exp;
run; 

I've also seen examples where the contrast coefficients are not necessarily integers (but couldn't understand):

estimate 'P contrast' &class -1.5 -0.5 0.5 1.5/ exp; 

Answer 1

That final contrast statement is doing a test for a linear (on the log-scale) trend across categories.