I'm using artificially generated hazard curves (that is, I know the true hazard curve) and Aalen's additive model to fit the covariates. For example, below is an individual's hazard curve and my estimate of it:
It's a good fit to my eye, and here is the individual's estimated survival curve (exp of the negative of the above )
Again, this looks fine to me. What happens next though is odd. To make predictions of individuals' lifetimes, I use the median of the survival curve (the intersection of the curve and 0.5). I then plot this prediction against the observed value, and what I was expecting to see was a high correlation between the two, instead I see this:
This seems very wrong to me. A few questions I have:
Is using the median correct? Intuitively I see nothing wrong with it, but my results suggest otherwise.
Is predicting lifetimes just too noisy of a challenge and this is indeed that best I can do?
Has anyone experienced something like this before?