I’ve been practicing parametric survival analysis using the notebook in the docs but am confused when it comes to predicting the survival curve for a new data point.
The method in the doc draws the event times T from the posterior predictive and then, for each timepoint of interest, calculates the proportion of samples in which T > t_{i} to estimate S(t).
However, since this is a parametric model we can simply use the closed form S(t) = 1 - F(t) as we know the distribution parameters.
I tried this approach in my own notebook on a Github fork (html here if useful) and found that this method produced different estimates to the first one.
Can either method be used or is one preferred?
Secondly, what exactly is the posterior predictive? I noticed that the coefficients were the same whether I sampled them from the trace or from the posterior predictive.