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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: enter image description here

It's a good fit to my eye, and here is the individual's estimated survival curve (exp of the negative of the above )

enter image description here

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:

enter image description here

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?

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The bottom plot is simply saying that lifetimes often vary from the median. This is inherent in the first two plots. That is, the person in the plot has a median of about 10, but he/she also has about a 20% chance of dying before 5, and about a 20% chance of making it past 20.

If curves for other people are similar, then the bottom plot agrees with the top 2.

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  • $\begingroup$ I find this disappointing -- I was hoping for more correlation between my prediction and actual observed values, similar to other forms of regression (I'm thinking least sq. for example). Do you think using the expected lifetime, instead of the median, would produce desired results? $\endgroup$ Nov 3 '13 at 5:31
  • $\begingroup$ The correlation isn't 0 in the bottom plot. But to get a stronger correlation you'd have to have some steeper descent in the survival curve. Or add covariates. $\endgroup$
    – Peter Flom
    Nov 3 '13 at 10:39
  • $\begingroup$ Thanks for the advice. I just needed a second pair of eyes on this to push me in the right direction =) $\endgroup$ Nov 3 '13 at 14:26

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