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I'm trying to understand the difference in a Cox model between adding a single categorical covariate like sex = {male, female} and doing stratification by it. I'm not saying about such trivial thing like "you won't get estimate for it when stratyfing. I know it.

I have an example. I have an experiment with men and women, both treated with some drug.

Using sex as a covariate

The baseline hazard is common for both males and females. It makes sense, if I know, that - without a drug - both males and females are at equal risk of something. When I treat them with a drug, males may respond to the treatment differently than males, thus I may get different hazard rates.

So I allow each group to develop own survival curve only affected by the covariate, because they start from the same hazard.

The model would be (pseudolanguage): survival(time, event) = f(drug * sex); * means an interaction

Using sex for stratification

The baselines are now different for both males and females. It makes sense, if I know, that - without a drug - they both are at different risks, as the sex affects that (for example different hormones). The drug may also work differently for them, but they have different baseline risks from the very beginning.

So I allow each group to develop own survival curve not only affected by the covariate, but also by starting from different hazards.

The model would be (pseudolanguage): survival(time, event) = f(drug) separately for males and females.

I think the choice depends on the research question and prior knowledge about the process, whether it is more likely to have equal hazards or different hazards even without the treatment (just because of the nature of the sex).

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  • $\begingroup$ You are getting the main points, but "without a drug males and females are at the same risk" is not correct. There can be a sex effect in the model independent of the effect of drug. This sex effect can either be multiplicative in the hazard rate (proportional hazards holds for sex) or not (where you would need to stratify by sex, introduce a time x sex interaction, or switch to a different model whose assumptions may be better met). $\endgroup$
    – Frank Harrell
    Commented Apr 8, 2021 at 11:40
  • $\begingroup$ Thank you very much for the answer. I complicated it unnecessarily. I only tried to catch the difference between the need for stratification (different baselines and different evolution of the survival curves) and adjusting for a covariate (same baseline - as Cox assumes, it cancels, then it's affected only by the covariate). Because I don't know if in my analysis I should rather stratify or adjust. For example I saw an article, where pairs of KM curves were "facet_wrap" by some categorical variable. Now I'm not sure if these comparisons are adjusted for this variable or stratified by. $\endgroup$
    – FordTaurus
    Commented Apr 8, 2021 at 11:48
  • $\begingroup$ I'm trying to figure it out, because the pairs of KM curves "facet_wrapped" by the categorical covariate is reported along with HR. And the HR could be calculated either with stratification or adjustment. I saw that the formula uses something like ~ A + B, which gives to factors without interaction. A makes the pair of curves, B is used for facet_wrap. $\endgroup$
    – FordTaurus
    Commented Apr 8, 2021 at 11:51

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A sex-stratified model doesn't need to treat the strata "separately for males and females." A model written:

Surv(time, status) ~ drug + strata(sex)

combines information across both strata. The model finds a single hazard associated with drug that identically affects both stratum-specific baseline hazards.

You can combine your two approaches by specifying an interaction of drug with the strata:

Surv(time, status) ~ drug * strata(sex)

That allows both the baseline hazard and the effect of drug to differ with sex. But that doesn't mean that the analysis is separate between the strata, if other covariates not involved in stratum interactions are in the model. Information on covariate effects is shared between strata so far as possible, providing increased power.

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  • $\begingroup$ Perfect comment! That was the missing part to me! Stratified method looks at all the stratified sub-groups, constraining the fitting to have the same effect, and then the sub-fits are combined together to give the final coefficients, calculated "with respect to all the sub-groups", right? It's like "democratic analysis over sub-groups" :) $\endgroup$
    – FordTaurus
    Commented Apr 11, 2021 at 12:07
  • $\begingroup$ @NigolloSamani that's correct for predictors that aren't involved in interactions with the strata. If you specify an interaction of a predictor with the strata, as in my last example, then that predictor is evaluated separately within each stratum. $\endgroup$
    – EdM
    Commented Apr 11, 2021 at 15:37

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