I'm using cox regression model to study the association of variable A with coronary heart disease. One of my covariates (variable B) has a clear non-linear relationship with predictor (Variable A), assessed by scatter plots; linear regression. My question is that does this cause any violation if the Schoenfeld residuals of the cox-model are fine? I'm using R.
This is an interesting question which has been studied. An number of useful things have been discovered by that research. Some of which are in articles from the attached google search. The short answer is that it can be a problem but I suggest you look at these attached results and see how they impact your own situation. Best wishes, David Booth
Therneau and Grambsch use a simple approach based on martingale residuals for assessing the functional form. Plot the martingale residuals from an intercept-only model (in R: resid(coxph(Surv(t,d)~1))) against the predictor values. Adding a LOESS curve is helpful in determining the functional form. Heavy censoring and collinearity can affect the usefulness of this approach. There is an example of how to do this in Therneau & Grambsch (2000). Modeling Survival Data: Extending the Cox Model. Springer.
Thank you Timo Törmäkangas , your comment was very usefull. I also thought that maybe I should plot martingale residuals, but I wasn't sure. I found this very usefull:
http://www.sthda.com/english/wiki/cox-model-assumptions
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