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I need to use parametric models to model survival data. If the PH assumption holds, I would fit the data for my two intervention groups using a single covariate for treatment effect.

I fit a Cox PH model to my unstratified data and the PH assumption seems violated (scaled Schoenfeld residuals test: p=0.001).

Can I at this point state that the PH assumption is violated and must use stratified parametric models (e.g. log-logistic, generalised gamma)? Or the test performed is specific to the Cox model and does not apply to other (fully parametric) models?

Note that the only covariate in the models is the treatment effect.

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If you fit a Cox-PH model and find that the proportional hazards assumption is violated, then you should certainly believe that fully parametric proportional hazards models will provide a very poor fit as well.

This is because a Cox-PH model fits a model with A) proportional hazards and B) any baseline distribution. If the best fit with the requirements of A) proportional hazards and B) any baseline is a bad fit, so will a model with A) proportional hazards and B) a very specific baseline.

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