Stratification in stcox vs streg

[Lorien Stice-Lawrence]

Hi,

I'm trying to understand how stratification of survival models differs between stcox (semiparametric Cox model) and streg (parametric models). In a nutshell, I don't understand why streg will let you estimate the effects of the stratifying variables while stcox does not. More details below:

I am estimating several different models either stratifying by Group, or controlling for each group's characteristics so that I can estimate and understand their effect on the hazard rate. I'm doing this both in stcox and in streg with an exponential distribution. I.e.:

streg INDIVIDUAL_Covariates,  distribution(exponential) strata(GROUP) vce(cluster GROUP)
streg INDIVIDUAL_Covariates GROUP_Covariates ,  distribution(exponential) vce(cluster GROUP)

stcox INDIVIDUAL_Covariates, strata(GROUP) vce(cluster GROUP)
stcox INDIVIDUAL_Covariates GROUP_Covariates, vce(cluster GROUP)

I have been omitting GROUP_Covariates from specifications where I was stratifying by GROUP, because they do not vary within group. Sometimes I am lazy and just leave them in because they will automatically be dropped in stcox. This is consistent with everything that I have read which says that you can't estimate the effects of group characteristics in a Cox model when stratifying by group. HOWEVER, I accidentally left GROUP_Covariates in the stratified exponential model estimated with streg, and Stata did not automatically drop the GROUP_Covariates and actually came up with estimates for their effect. I'm completely confused as to how this is possible. I am much more familiar with Cox models than with parametric survival models, but I don't understand why this would be impossible with a Cox model and possible with an exponential model. Are these spurious estimates or are they valid? In which case, does stratification with streg not "work" as well as in stcox in terms of controlling for the stratifying variable? To me, the case seems analogous to a regular regression model with fixed effects; if you include fixed effects for a group, you cannot estimate the effects of characteristics that are fixed within a group. So what's going on with streg?

Any insight would be appreciated!