I have worked on a project for a risk calculator for two common conditions related to old age. The calculator is based on the estimates of two survival analysis models: competing risks for the first condition a 'plain' Cox PH for the second one.

Both models have 1 time dependent covariate (TDC), which has been accounted for in the specification.

Now the point: the calculator will rely on the regression coefficient estimates and on the baseline hazard values at time points t1, t2, t3 (to estimate cumulative incidence risks as a risk score).

For ease of use, I will provide in the formula for the calculator  baseline hazards 'adjusted' by the impact of the TDCs, e.g I will use the cumulative sum (up to times t1, t2, t3)  of the following product:

baseline hazard values * exp[ TDC slope estimate * TDC value * f(elapsed time) ].

This is formally correct (formula wise). However, in order to explain the formula in plain language to the users, can I say that my t1, t2, t3 baseline hazards values have been updated/adjusted in relation to the time dependent covariate impact?

Is this a formally correct definition of what, in practice, a TDC adjusted Cox PH (and competing risks) accomplishes?