Proportional hazards assumption and time-dependent covariates Is there a way to check that the proportional hazards assumption is correct for a Cox model with time-varying covariates ?
 A: 
If we add time-dependent covariates or interactions with time to the Cox
  proportional hazards model, then it is not a “proportional hazards” model
  any longer.

See this presentation: http://ms.uky.edu/~mai/sta635/Cox%20model.pdf
or this lecture notes: http://www.math.ucsd.edu/~rxu/math284/slect7.pdf
But this is a widely known feature.
A: The answer of Serpico is true for time-dependent coefficients but not if the model uses time-dependant covariates. If this was the case, I don't know the correct answer.
A: As Serpico suggests, the Cox model with time-dependent covariates is no longer a proportional hazards model. Here is a quote from David Collett's book, Modelling Survival Data in Medical Research (2nd ed., 2003, p. 253), that may provide some further clarification:

It is important to note that in the model given in equation $h_i(t) = \exp \left\{ \sum_{j=1}^p \beta_j x_{ji}(t) \right\} h_o(t)$, the values of the variables $x_{ji}(t)$ depend on the time $t$, and so the relative hazard $h_i(t)/h_0(t)$ is also time-dependent. This means that the hazard of death at time $t$ is no longer proportional to the baseline hazard, and the model is no longer a proportional hazards model.

