I have a dataset spanning two years which consists of individuals entering some process. Once they have entered this process I want to predict the number of days they will remain in this process based on some set of covariates. There are some charateristics of the data which lead me to doubt whether my current approach is correct.

First, the time that an individual remains in the system is known. That is, there is no right censoring, since an average duration is only a couple of weeks and the data is not entirely up to date. As a result I decided not to use survival models as censoring of data is the main reason for using this class of models as far as I know.

Second, I thought of using count models such as a Poisson model or Negative Binomial regression model. Although my dependent variable fits the description of data normally used in Poisson and NB models, that is, integer and non-negative numbers, I'm not sure if it is entirely correct. The part of which I'm not sure is the following:

In many papers the data is described as: 'We model the number of occurences per individual over a specified period of time.' In my case, individuals can enter the process multiple times and the counts are consecutive. I'm not following a group of persons over the same period of time and try to model how many days in that period, consecutive days or spread out, an individual is in that process.

Can someone tell me if this would give any issues in my analysis?

Any insights provided would be of great help!