# Competing Risks Likelihood in each State

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.

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.

• transition 1 and transition 2 means that they end up in state 1 and 2 respectively? – peteR Feb 14 '19 at 20:01
• 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. – AdamO Feb 14 '19 at 20:04
• @peteR you are correct – JoeBass Feb 14 '19 at 20:14
• @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" – JoeBass Feb 14 '19 at 20:16
• @Joe is it a subdistributional hazard function? – AdamO Feb 14 '19 at 20:19