Essentially, I try to predict the time to default in a credit scoring context using six categorical variables with survival analysis.
To extend the basic proportional Cox model I introduce time-dependent coefficients using a step function beta(t) according to Therneau et al. "Using time depended covariates and time depended coefficients in the Cox model".
First question is: how to get the overall test for each categorical variable after applying the Cox.zph function.
The second, and currently more important question for me is:
After fitting my model based on a training set is it possible to make a prediction based on a new testset? Since I use an interaction between the covariate BS24 and the stratification by time group on the right handside of my formula (see code in link), I'm a bit confused how prediction is going to work. At the initial time t=0 I have no idea of the future particularly in which time group the new customer will be.
To compare my models I use the time depended AUC calculated by the "score" function from package riskRegression. It internally uses a prediction function but when applying it to the extended model and the new test set it says "strata(time group) not found".
When splitting my test set with survSplit the same way I did for the training set, it works and I get a nice AUC plot. But I am afraid if this actually makes sense and I don't wrongly include future information I usually don't have.