# Combining survival rates for Markov model

Hello all,

I'm trying to average cancer recurrence rates across a few trials.

The issue I'm running into is that the trials are of different duration (e.g. 5 years and 8 years). The majority of recurrences happen at the beginning of the trials so adding rates won't work (because the last few years of a long trial will have no recurrences and will skew the results). Alternatively, assuming that the recurrence happens within the shortest period of time is a possible way to do it but isn't ideal. Is there a better way?

I don't have the Kaplan Mayer data so I can't combine them that way.

Thank you so much!

• Any ideas on this?

Thanks!

• I'm not sure what to do here. It's really better suited for a biostatistician than for us as modeling software people.

I think you will need probabilities if you are building a Markov model. Perhaps you can convert the rates to probabilities via RateToProb, then compare the probabilities to see how close they are and maybe blend them.

Note that this is far from perfect because RateToProb will assume fixed risk over time. Based on your description, I don't think the risk is fixed over time.

You might consider additional research to see if you can find more suitable data for your model.

• Thank you! I've been using RateToProb and think the approximation is probably reasonable for now. I do have a follow-up question however:

Let's say the whole cohort has a 5% risk of disease over 5 years. However, my Markov model has states that don't include this risk (e.g. absorption states like death or temporary states that preclude having the illness). How do I make it so that the average rate for the whole cohort remains at 5% (would require higher risk/probability at different points given the lack of risk at others)?

Thank you!

• There is no formula that can account for overall 5% risk when there are competing risks with unknown probabilities that are drawing people away from the disease risk.

You may want to start with the regular ProbToProb(0.05; 1/5) as your first entry, which will likely result in less than 5% disease if other risks reduce the cohort experiencing the disease risk.

Then you can add an extra payoff (say payoff set 3) that specifically measured disease incidence for the first 5 years. Then when you run the model, you will get the first 5 year incidence as a model output. You can then gradually increase the probability until you get the appropriate 5-year disease incidence.

For questions such as these, I recommend that you use the standard support channel via either of these methods.