Repeated measures logistic regression and cox proportional hazards

[Novice2]

Hi All, 

I have two questions (don't know if I should start a separate thread for the other, happy to do so if needed).

I have a longitudinal dataset where patients were followed up for a number of visits. At each visit they were asked 'did condition x occur in the time since last visit' ie a binary outcome (yes/no).

1) I am planning to do a competing risks cox proportional hazards model. However, I have a covariate which is related to the outcome. How would I take account of this in the coding? Further, the covariate has a time-specific function ie its value drops in the first few weeks, then stays stable. Would I need to introduce a spline?

2) I would like to do a logistic regression of said outcome x. Would the outcome from a repeated measures logistic regression be significantly different from standard logistic regression? Again, I think one of the predictors would be the time-varying serum marker mentioned above

Hope that makes sense, I would be grateful for any input and sample code. 

[Novice2]

Sorry I should have specified above that the time-dependent covariates are continuous in nature