# Discontinuation rate by distribution

I have a patient cohort with a treatment discontinuation rate of 22% that is most likely within the first year of treatment. I know I can spread the 22% evenly across the year with ProbtoProb. However, is there a way to do a similar adjustment based on a distribution of time to event? For example, using the a mean time to discontinuation distribution to spread the 22% over the first year of treatment rather than evenly across all stages in the first year.

• You can create a time-to-event distribution with fixed risk by converting then annual probability to a rate then creating an exponential distribution. However, I am not sure if that will fit well within your model.

Note that if you just use the ProbToProb function, different portions of the cohort or simulated patients will discontinue at different times over the year.

• I'm not sure I explained the issue clearly. 22% of patients will discontinue treatment due to an adverse event in the first year. The model assumes after the first year, the risk is 0 (data suggests this is reasonable). The development of adverse events is technically weighted around 6 weeks with most people developing the issue within 4-8 weeks. I created a normal distribution using the data in the literature (it should probably be a beta distribution). I don't have the stats knowledge to generate the beta dist parameters with the limited data I have and a normal distribution is better than spread evenly throughout the year.

Does that make sense?

• If you were running a Discrete Event Simulation, then the distribution would be used directly. However, if you have a Markov model, you need a probability for the event.

You could use the ProbToProb to calculate the probability for the first year along with an if function to set the probability to 0 after the elapsed time.

If you are running Microsimulation even for a Markov model, you could sample the time of the event, then compare the current _stage to the sampled time. However, this will not work for Markov Cohort analyses.