Extrapolate an Extended Cox model from 6 years to 30 without assuming a parametric distribution in R I am attempting to extrapolate a Extended Cox Model (cox model with a time-varying covariate) from 6 years to 30 years in R. Is there a way to do this?
I have thought of a mediocre way of doing this:
Plot two plots, one with the slopes from the KM curve for each year vs. time and one with the downward shifts of the KM curve for each year and fit a line for each plot. Use those lines to estimate the slopes and shifts for the years past 6. I am also not quite sure how to nicely code this in R. 
Another idea is to repeat the hazard at year 6 over and over again. This would be an extremely conservative approach, but may get the job done.
I know this may not be the "fanciest" way of doing things. But, aside from fitting a distribution, I have run out of ideas. 
 A: Some assumptions need to be made to extrapolate (far) beyond the range of the data you have. These assumptions could either be parametric models or something like repeating the hazard of the last year (or last 2 years) over and over. The latter approach is quite a strong assumption (more or less extrapolation with an exponential distribution based on the average hazard rate of the last year, if the hazard rate did not vary too much throughout the year). 
One possibility to avoid assuming one particular model and to reflect the uncertainty about the appropriate model, is to entertain a range of plausible models and to do (e.g. Bayesian) model averaging. 
Another possibility is to use information external to your main dataset, because extrapolating to 30 years from just 6 years may be very challenging unless there are reasons to believe the underlying process would not change too much (or if we know how we expect it to change). It is hard to say anything about that without knowing what the unity under risk are.
