In SAS what is the difference of including treatment variable in model and using the strata statement for treatment variable?

Question

Im building a Cox Regression in SAS. My code looks like this:

proc phreg data = mydata; 
   class sex hospital;
   model time*status(0) = sex hospital age bmi;
   strata treatment_variable;
run;

Now this code does not calculate a hazard ratio for treatment A vs treatment B. If I remove the strata statement and instead include the treatment_variable inside the class and model statement I get a hazard ratio for the variable. The coefficients for the other variables in the model changes slightly when I do this.

My questions are:

1. What purpose does the strata statement serve? Why not include the treatment variable in the model? Most of the time you are interested in the effect of treatment A vs treatment B when controlling for some other variables.
2. Why does the coefficients of the other variables change?

Hope my question is clear. Thanks!

Answer 1

Stratification fits separate baseline hazards to each stratum and combines their likelihoods. This can address violation of proportional hazards across the stratification variable, but the drawbacks are that you may lose a bit of estimation efficiency and, as you discovered, you cannot actually draw inference on the stratification variable.

If proportional hazards are violated for your parameter of interest (treatment) then it would make sense to look into time-dependent covariates.