I am modelling a survival analysis over a rather long follow-up period (10 years). My exposure is time-invariant and clearly violates the proportional hazards assumptions so Cox Proportional Hazards regression models are not an option. I was wondering about alternatives to conduct my analyses. Please find below some key points:
Stratification is not possible because it is my main variable of interest that violates the assumption and I need to compare between groups
Time-varying models are not possible given the nature of my main variable of interest
I initially thought about time-partitioned model (splitting follow-up time and interacting time with my main variable of interest) but I am not sure that is a good idea because when I plot the KM curves it is all crossing - so I struggle to find a good time interval for splitting
Given these considerations I have thought about employing flexible parametric models. Howevers, from my understanding they make strong assumptions about the shape of the curve - which is something I cannot be certain of. Would a flexible parametric model with restricted cubic spline what I am looking for? But How can I define the number of knots? And how about the distribution?
Could you please provide some inputs and examples? What do you suggest?
I use Stata MP 15 as statistical software