My case is that previously it's assumed that the counts of events follows a negative binomial distribution, and the annualized exacerbation rate is 1 with a dispersion parameter of 1.5, and all 500 patients will be followed up for 1 year. But due to some operation reasons, the follow-up period have to be shorten from 1 year to around 0.5 year for each patient. My understanding is that the annualized exacerbation rate is still 1, just including 0.5 year as a offset variable when doing the NB regression (correct me if I am wrong). My question is will the dispersion parameter be impacted due to the fact that the followup period become shorter? (I have to do some simulation using R, i need to know how should the dispersion parameter as well as the mean of the NB distribution be setup).