How to model a covariate for age in my cox prediction model

Question

I'm currently doing a prediction model using Cox regression on a dataset coming from an ongoing clinical database and containing information about patients who all have the same genetic disease.

In it, I have several binary variables for clinical manifestations of the disease(Present/absent), a birth date, a binary variable for my outcome(present/absent), a diagnosis date for my outcome, and a date of the last follow-up.

My binary variable for the outcome is my event variable, for the time-to-event variable it's the time from when patients are ten years old to either the event or censoring.

Knowing all of that, how is an age variable in a model defined in a situation like mine, if it is used at all?

Being a genetic disease, patients are born with it, so the age of onset can't be used. The age at recruitment has no value since the database is ongoing, and patients of all ages are recruited.

Am I missing something or age cannot really be a meaningful covariate in my model?

Answer 1

If your Cox model meets the proportional hazards (PH) assumption, then using age (minus 10) as the definition of survival time directly captures the association between age and hazard.

If the PH assumption isn't tenable for some covariate in your model, then the association of that covariate with hazard changes as a function of age. In that situation you can model the coefficient for that covariate as time(age)-dependent. Sections 4.2 and 5 of the R survival time dependence vignette show how to build such models. I suppose you might then consider age to be a "covariate" also, as the "time transform" function used in that modeling defines a new time-varying covariate as the product of the original covariate times your specified function of age. I think that describing this situation as an age-dependent association of the other covariate with outcome is preferable, however.