[R] short term Cox proportional hazard model

[Mimosa Zeus]

Dear R users, 

I need some advices on the Cox proportional hazard model fitting, as I don't fully understand the mecanism behind. 

The dataset I'm working with have individualsbwho can have very long censored or event time (can be multiple). 

For the problem at hand, I'm interested on the effect of the time dependant covariates on the survival for short term only, 

The fitting (for example coxph) seems treat the time as a whole, 
I'm wondering if there's ways to "optimize" (attributing more weight) the short term, and ignore the effet of the covariates for the long term. 

Cheers 
Mimosa