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I am using Cox proportional hazard model to compare the survival of two groups (treatment vs control) of patients. However, hazard rates were not proportional between the groups. Now, would it make any sense for my primary objective (comparing the two treatment groups)if I include other covariates (e.g. age, sex, ...) to the model?

I highly appreciate your valuable suggestions/comments in this regard.

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Broadly, if the hazard isn't proportional between the two groups (which I'm assuming you're encoding as an indicator variable 0/1), then the Cox model isn't appropriate.

But I would first check the complete model (treatment, age, sex, etc), and see whether the treatment effect is proportional or not (e.g., cox.zph in R, plot scaled Schoenfeld residuals), as part of the non-proportionality may be affected by the other covariables.

Then there's also the question of how much non-proportionality is ok, as essentially no real world data is going to show perfect proportionality. I don't have a good answer to that, except that cox.zph gives you p-values if that's your kind of thing.

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