Unobserved heterogeneity in Cox model I have some questions about the Cox model and unobserved heterogeneity. 
I work on a sample of firms divided in two categories: cooperatives and corporations. I want to test the influence of some variables on their survival. I test the impact of five variables on the survival. 
I read a lot about unobserved heterogeneity, and I am asking if it is pertinent in my case to test a potential unshared frailty? 
I don't want to check for an eventual cluster heterogeneity but for individual heterogeneity. in fact, I want to know if my results could be biased by an omitted variables. 
I found the coxme package but I'm not sure that I run it correctly... 
As I want to check for unshared frailty, I run 
cox1<-coxme(Surv(time,status)~ownershipstructure+size+profitability+export+(1|id)

with id= identifiant of the firm considered. 
 A: The short answer is that yes, you can do that. However, frailty models (i.e. survival models with random effects) are quite speculative when dealing only with survival data (non-shared).
The short explanation would go like this: if you do not have any covariates in the model, then the baseline hazard and the frailty would be confounded, and then the frailty can not be identified form the data. The non-shared frailty is only identifiable because there are covariates in the model. In Cox models the covariates are assumed to have proportional hazards. In a Cox model with frailty it is assumed that the covariate has proportional hazards conditional on the frailty, and non-proportional hazards unconditional on the frailty. 
In other words, if a covariate shows non-proportional hazards, this may be explained either by proportional hazards at an individual level, masked by hidden heterogeneity (that you can account for with the frailty), or by... simply non-proportional hazards, and no frailty. So it is quite difficult to say what exactly you estimate. There is a lot of literature on the topic (especially by Odd Aalen), but my general advice is that it would be useful argue why one of the explanations would be more plausible in your dataset. 
edit in response to a comment: 
The implication is that, if there is heterogeneity and if this can be modelled with a lognormal distribution and if PH holds given the frailty, then this implies non-proportional hazards at a marginal level (without frailty). 
This implies that if proportional hazards hold at a marginal level, then either there is no heterogeneity, or there is heterogeneity but the model is misspecified. 
I hope this makes it more clear. Note though that these are concepts that puzzled and still puzzle researchers in survival analysis, so it's not something trivial at all.
