I'm working with a survey that uses a rolling data collection format (i.e., there are multiple waves of sampling and initial contacts). I'm trying to develop a model to predict how likely a sample member is to respond to the survey within 7 weeks from today. Predicting whether a respondent who is first contacted today will respond within 7 weeks is fairly straightforward - just a basic propensity model predicting response within seven weeks of initial contact. However, predicting whether a case that's been in the field for several weeks already will respond in the next 7 weeks is more difficult.
My question is how do I take into account that the probability of response changes based on how long the case has been a nonrespondent (i.e., a respondent's initial probability of response may have been .75, but if they're still a nonrespondent after 4 weeks, they'll probably remain a nonrespondent)? I could just include the amount of time the case has been in the field as a variable in the propensity model, but I'm not sure if that's the appropriate way to handle it. It seems like this may be a situation for survival analysis, but my knowledge in that area is limited.
Any suggestions of an approach, model, or previous research I should consider would be much appreciated.
