How to apply a probability based on time since entering that transition health state
I am creating a Markov Model for a cost-effective analysis of various colon cancer chemotherapy treatments. The cohort entering the model has just had surgery for colon cancer, and there are 6 Markov nodes, each for a different chemotherapy treatment.
I am trying to apply a different transition probability from alive to death from colon cancer for patients who have a cancer recurrence.
The health states in each Markov node in our tree are: Disease Free, Recur 0-2 Years, Recur 2-3 Years, Recur >3 Years, Death from All Causes, and Death from Colon Cancer. The three "Recur..." health states are to divide the patients by the time since initial surgery that they experience a recurrence, since each of these 3 intervals has a difference probability of death after recurrence.
In each of the "Recur..." health states, the patient either dies from all causes, dies from colon cancer, or lives with cancer post-recurrence (returning to this same recurrence health state). For example, in the "Recur 0-2 Years post-surgery" health state, the patient will either:
- Die from All Causes (go to Death from All Causes health state)
- Live with colon cancer post-recurrence (return to Recur 0-2 Years health state)
- Die from Colon Cancer (go to Death from Colon Cancer health state)
Within this "Recur 0-2 Years" health state, I am trying to apply a transition probability for death from colon cancer based on the time since the recurrence, essentially, a probability dependent on the time that a patient has been in this health state. So for example,
- from 0-6 months from the time of recurrence, p_death_colonCA = 0.4
- from 6-12 months from the time of recurrence, p_death_colonCA = 0.5,
etc. for 6 month intervals.
I attempted to do this using a table with probability values for each 6 month interval post-recurrence, applying the table to tunnels. The table of death probabilities goes from 0-66 months post-recurrence, or 11 intervals, so I set the tunnel max = 11, and
p_death_colonCA = t_death_colonCA_recur_0-2years[_tunnel],
but I do not think that this applied the tunnels correctly.
Is there a method to apply this table of probability values that differ for each 6 month interval based on the time since entering this health state, rather than by stage? If the only way to do this is by using tunnels, since this is a cohort analysis, am I applying the tunnels incorrectly? How do you set each of the 11 tunnels in this case to be equivalent to 6 month intervals?