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Should I do some transformation of continuous variables in accelerated failure time model? In PH model it is needed and martingale residuals are helpful there. I know that PH and AFT models are equal sometimes, so should I look for a transformations when I using AFT model too? If yes, how to find them?

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If I understand correctly, you are concerned about continuous variables might have non-linear effects, e.g. quadratic or logarithmic.

If you have a clear idea about the functional effect of the variable (e.g. quadratic), transform the variable.

Otherwise it is preferable to use semi-parametric methods (ideally penalized splines) that will estimate the functional shape of the covariate effect from the data.

Example using survival package:

library(survival)
mod <- survreg(Surv(time, status) ~ pspline(age), data = lung)
termplot(mod)

Created on 2019-04-27 by the reprex package (v0.2.1)

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