check the following link

https://www.statalist.org/forums/forum/general-stata-discussion/general/1421887-how-to-do-when-log-linearity-is-not-checked-in-cox-models

The best I can say is who knows what will happen if you go ahead ahead. That depends on the data. My advice is to consult a good biostatistician. Best, D. Booth

Hi Chukwudi,

When the assumptions are not met then the model would be invalid and there'll be loss of power. Are your independent variables continuous? If so you may try to transform them into categorical variables using plausible cut-off values and then add to the model. For example instead of adding age as a continuous variable you might categorize it as age =65 then continue with the analysis. This might help with the PH assumption. As for the non-linearity, the same applies or you can do some transformations (like log, sqrt, etc.) on your independent variables and then run the analysis.

We have explored this situation and results are published in our recent paper; which provides alternatives when PH assumption is invalid:

Effects of Proportional Hazard Assumption on Variable Selection Methods for Censored Data:

https://doi.org/10.1080/19466315.2019.1694578

Another alternative is to use nonparametric and semiparametric models and you may find these two papers useful in those directions:

Efficient Sieve Maximum Likelihood Estimation of Time-Transformation Models

Article Efficient Sieve Maximum Likelihood Estimation of Time-Transf...

Nonparametric regression models for right-censored data using Bernstein polynomials: Article Nonparametric regression models for right-censored data usin...

Hope you find these citations useful for your work.

There are many ways to check the assumptions and then remedies are also suggested. These can be found in books like Klein and Moeschberger. In pharma industries, I have seen that they generally perform separate (technically speaking stratified) Cox modelling when there is a possibility of violation of PH assumption (e.g. stratification by site). I would also suggest you to see " Stensrud, M. J., & Hernán, M. A. (2020). Why Test for Proportional Hazards?. Jama, 323(14), 1401-1402." where they are raising question whether we really need to be worried for this assumption!!!

You have to stratify or extend the classical Cox regression model to accommodate the covariates that violate the PH assumption...