When evaluating the effect of a continuous covariate that changes from one wave to the next, (in this instance, the relationship between a continuous health index score and mortality risk) do I need to indicate that the covariate varies with time via the stcox, tvc(option), or does Stata automatically do this? While previous posts touch on this, I have seen contradictory answers. Example below for clarification.

Sample Cox regressions:

#1: stcox female age index_score

#2: stcox female age, tvc(index_score)

The first regression shows a much stronger effect of a one unit change in the index score on mortality risk than the second.

Thank you