# Change in transitional probability and tunnel states

I have a markov model with three states -- Pre-cancerous, Cancerous and Death --annual cycle length and 100 cycles. The cohort start at Pre-cancerous state. Probability of transitioning from Cancerous state back to Pre-cancerous state is 0.3 after one year in the Cancerous state, with an annual relative reduction of 7% thereafter. I use the following approach to input this probability.

I set Tunnel max=100 for Cancerous state, and write the transitional probability as:

if(_tunnel=1;0.3;(0.3*(0.93^(_tunnel-1))))

Is this the correct approach for the given scenario? Thank you!

## Comments

Belinda OrmeMahip

I have a couple of comments and suggest that if you need further assistance the best place for this correspondence would be via the support channel. To do this, in the Help Centre you just submit a Support Request.

The use of _tunnel is for counting the number of continuous cycles in a given state. So, if the cohort moves back to pre-cancerous the _tunnel counter will rest to 1. It seems as though the relative reduction should be accumulated on a continuous basis so I don't think your approach of using tunnels will work.

The best approach for this type of model would be to use a patient level model where you can track the history of each patient and record the number of years they are in the Cancerous state using trackers. You can use this tracker to impact the transition probability (as you have suggested in your formula already).

Andrew MunzerOne thing to consider is whether the probability continues to drop after 40 or more cycles. It may be that at some point the probability stabilizes and no longer changes.

Note that tunnel states add implied states in the model. If you set tunnel max to 100, there will actually be 100 Cancerous states in the model at run time. If you don't need that many states, you should reduce the tunnel max value.

Of course, that may not be possible.

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