I have a dataset that includes a random sample of individuals who are currently in a relationship in the United States. I also have data on the date that they met their partner and the date that they considered themselves in a romantic relationship.
I was planning on doing an event history analysis to compare different types of relationships (IV) and the time it takes for them to transition from meeting --> relationship (DV). In other words, for each year they know each other, what is the risk that they will enter a relationship.
However, someone recently pointed out to me that since I do not have information on all of the people that they have met in their lives, I am in a sense sampling on the dependent variable. Since everyone in my sample is in a relationship, there is no censoring and everyone experiences the event (relationship entry) once.
So, my question is basically this: Can I use some sort of event history analysis (Cox model, discrete time, etc.) OR am I really only able to do a t-test comparing the outcomes for each group?