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The question says it all - I'm just wondering whether Cox regression models are used to model non-linear relationships.

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    $\begingroup$ Does this answer your question? Why is polynomial regression considered a special case of multiple linear regression? Although that question is about ordinary linear regression, the principle is the same for all linear regression models like Cox models: the linearity is in the parameters to be estimated, not in the associated predictors. Polynomial and spline methods allow nonlinear terms for predictors while the model is still linear in their coefficients. $\endgroup$ – EdM Feb 22 at 20:16
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It depends on what you mean by non-linear. The Cox model can handle non-linear covariates through the use of spline terms on the covariate. See this, for example:

https://cran.r-project.org/web/packages/survival/vignettes/splines.pdf

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