In Cox model: stratification (stratification age for rx) and adjustment (adjustment age for rx) are the same? stratification in cox model
Can I return to this question to clarify one moment: 
is the stratification referred here (strata(rx)), exactly what it means as "adjustment" (adjustment age for rx)?
 A: Let's say that futime = time to death (by any cause), fustat = 1 if patient died (by any cause) and fustat = 0 if patient survived by the end of a study on cancer patients. Further, let's say that age is the age of the patients at cancer diagnosis and takes two values: age = 1 for old patients and age = 0 for young patients. Finally, rx is the treatment that was recommended to them at that time, such that rx = 1 if chemotherapy was recommended and rx = 0 if radiation. We will treat 0 as the reference category for both age and rx. 
The model coxph(Surv(futime, fustat) ~ age + rx relies on a single underlying baseline hazard which reflects the risk of death (by any cause) for young patients on radiation (i.e., for patients for whom age = 0 and rx = 0). The model produces two hazard ratios: one for age and one for rx. The hazard ratio for age will compare old versus young patients with respect to the hazard of death, assuming they are on the same treatment. 
The model coxph(Surv(futime, fustat) ~ age + str(rx) is in fact a collection of two sub-models: one for patients on chemotherapy and the other for patients on radiation. Each of the two sub-models relies on a different underlying baseline hazard. In each sub-model, the baseline hazard quantifies the risk of death (by any cause) for young patients. However, this risk is assumed to be different across treatment types. Each of the two sub-models will produce a hazard ratio for age. Under the assumption of no interaction between age and treatment, these hazard ratios will be the same so it suffices to report just one of them. The reported hazard ratio will compare old versus young patients with respect to the hazard of death assuming they are on the same treatment. 
To sum up, the model coxph(Surv(futime, fustat) ~ age + rx uses a single underlying baseline hazard, corresponding to young patients on radiation. In contrast, the model coxph(Surv(futime, fustat) ~ age + str(rx) uses two different baseline hazards - one for young patients on the radiation treatment and the other for young patients on chemotherapy. Because of this, the two models will produce different estimates for the hazard ratio of age. 
Model coxph(Surv(futime, fustat) ~ age + rx reports a hazard ratio for age which is "adjusted for" rx (in other words, which compares the hazard of death among old and young patients on the same treatment). 
