Interpreting hazard ratios in stratified models

Question

I am unsure how to interpret hazard ratios from cox-proportional hazard models that include 1 or more stratified terms.

For example, say I run a cox regression with treatment as a covariate and stratified by sex. If the model returns a HR of say 2, is this to be interpreted as the treatment-HR over men and women (all levels of the stratified variable)? Is not the point of stratification that we expect different hazard ratios across the strata?

Thank you

Answer 1

In a Cox proportional hazards model, specifying strata allows for different baseline hazards between the strata, in your case for men versus women. If you specify the following model in R:

coxph(Surv(time,status) ~ treatment + strata(sex))

then you get a single hazard ratio for treatment, which is taken to be the same for both sexes. Differences between sexes in outcome with this model depend on the different baseline hazards, not on different hazard ratios.

If you are interested in different effects of treatment depending on sex then you need to include an interaction term (indicated by ":" below, as in R). For example, you could specify:

coxph(Surv(time,status) ~ treatment + strata(sex) + treatment:strata(sex))

to get an interaction term representing how treatment-related hazard differs between sexes. This formulation allows both for different hazards between sexes and for different baseline hazards for the sexes.

Using strata for sex does not model a relationship between sex and outcome except via the different baseline hazards. If you specify:

coxph(Surv(time,status) ~ treatment + sex + treatment:sex)

you would get hazard ratios of treatment and for sex, plus an interaction term, but with the same baseline hazard assumed for both sexes.

Answer 2

The interpretation would be (as written in a medical journal)

"The hazard ratio of the outcome comparing treated to untreated individuals of the same sex"

The interpretation is the same as with covariate adjustment, stratification requires more power, and handles more general cases such as non-proportional hazard functions between men and women (adjusting for treatment).