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What are the consequences of violating the Proportional Hazards assumption in a Cox Model? I've got a Model where two factors are highly significative, but all the estimated betas associated to the levels of these factors violate the PH assumption according to the Schoenefeld Goodness of Fit test.

Here are the beta vs time plot for some of the betas:

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enter image description here

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I think it depends on who you ask.

According to this article

There are various opinions on the importance of this assumption with regard to the parameters interpretation. Some authors state that violation from it is nothing extremely problematic as in such cases parameter for a covariate for which assumption is not satisfied can be understood as ‘average effect’ over timepoints that are observed in a dataset (Allison, 1995). The others however underline the importance of this assumption (Hosmer, Lemeshow 1999) and suggest potential modification of the model if hazard ratio turns out not to be constant over time for some covariates.

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