What is the difference in interpretation of the effect estimates in a Cox model stratified by sex vs. with a random statement for sex? Thanks.
In a stratified Cox model, the baseline hazards functions from the different strata are unrelated.
In contrast, using a random effect implies that the baseline hazard functions are proportional to each other.
A detailed comparison of these two modelling strategies are provided in
- Glidden, D. V. & Vittinghoff, E. (2004). Modelling clustered survival data from multicentre clinical trials. Statistics in Medicine 23, 369–388.
- Munda, M. & Legrand, C. (2014a). Adjusting for centre heterogeneity in multicentre clinical trials with a time-to-event outcome. Pharmaceutical Statistics 13, 145–152.
That being said, gender is not a random effect.