I have a competing risks model where every observation starts in state 0 and ends up in either state 1 or state 2.

I have the following cumulative hazard functions for each transition to state 1 and 2.

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I am interested in finding the probability that an observation is in state 1 or state 2 at time t.

Currently, I write a for-loop where the observation starts in state 1 and then I use the hazard ratios to divvy up the proportion of the observation remaining in state 0 to either state 1 or state 2. This seems cumbersome, and I was wondering if there's a closed form approach for this.

  • $\begingroup$ transition 1 and transition 2 means that they end up in state 1 and 2 respectively? $\endgroup$ – peteR Feb 14 '19 at 20:01
  • $\begingroup$ Is your question on just how to use R code? I think it's to go on stackoverflow.com but you need data and a reproducible example. No need to use hazard ratios or statistical models for what you describe; plus, they could be wrong. Use an empirical estimator instead. $\endgroup$ – AdamO Feb 14 '19 at 20:04
  • $\begingroup$ @peteR you are correct $\endgroup$ – JoeBass Feb 14 '19 at 20:14
  • $\begingroup$ @AdamO sorry, I shouldn't have put R in the title. I removed it. It's more fundamental than code... It's "given that I have a discrete non-parametric cumulative hazard function for a competing risks model, how do I determine the probability that an observation is in state 1 or state 2 at time t in closed form" $\endgroup$ – JoeBass Feb 14 '19 at 20:16
  • $\begingroup$ @Joe is it a subdistributional hazard function? $\endgroup$ – AdamO Feb 14 '19 at 20:19

The for-loop is basically performing numeric integration of the cumulative (subdistribution) hazard function which is exactly what you have to do to obtain time-specific risk predictions of event 0->1, or 0->2 or still being in 0 having occurred at a specific time.


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