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I'm a student who still learn survival analysis. So I checked PH assumption in my data using Schoenfeld residuals, log log survival plot, and time-dependent covariates; and my main predictor (i.e. smoking) violate PH assumption. However, before checking PH assumption I did Cox PH regression just to see whether smoking has interaction with other variables (as what was found in other studies) and I did found smoking has significant interaction with other variables. I plan to use Extended cox, but could not figure out what to do with the smoking variable (as it is interact with time, as well as other variables). Any help is much appreciated. Thanks!

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I am not sure which statistical package you are using, but as far as I know there is no difference in Cox and extended-Cox models. In R there is no technical difference between this:

model.coxph1 <- coxph(Surv(t1, t2, event) ~ smoking + cov1 + cov2, 
                      data = data)

And this:

model.coxph1 <- coxph(Surv(t1, t2, event) ~ smoking + cov1 + cov2 +
                      smoking:cov1, data = data)

If after the interaction smoking still violates the proportional assumptions, you can create an interaction with time, or stratify it based on the pattern you see in the Schoenfeld residuals. For examples in R see Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Model by Therneau (creator of the survival package) for further explanations.

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