# test of difference (equivalence) between pairs of hazard ratios derived from two models

I have two stratified cox proportional hazards regression models each restricted to data on men and women, respectively. Both models have the same covariates and the data on men and women come from the same database. I would like to see whether I could compare the hazard ratios (HR) in any fashion for a given covariate derived from these two models.

For example. Among men the HR (95% CI) for covariate A is 0.75 (0.60 - 0.90) whereas among women the HR (95% CI) for covariate A is 0.60 (0.40-0.80). Is there a way to test for equivalence between these two HRs?

To add, I cannot run the desired model with data including both men and women because of the overarching research question and study design.

I've come across R's survcomp::hr.comp (& hr.comp2) which somehow relies on student's t-test for comparisons; though it appears that comparisons are made between different HRs from two different covariates rather than a single covariate. Otherwise all p-values = 1

Any counsel here is appreciated.