0
$\begingroup$

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.

enter image description here

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.

$\endgroup$
  • $\begingroup$ transition 1 and transition 2 means that they end up in state 1 and 2 respectively? $\endgroup$ – peteR Feb 14 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 at 20:04
  • $\begingroup$ @peteR you are correct $\endgroup$ – JoeBass Feb 14 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 at 20:16
  • $\begingroup$ @Joe is it a subdistributional hazard function? $\endgroup$ – AdamO Feb 14 at 20:19
0
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.