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Estimating Response Probabilities for Surveys

I recently went to a workshop on adaptive treatment regimes. We were presented with a situation where they were attempting to learn about the effectiveness of a treatment to help with a chronic condition like addiction to smoking. The treatment is applied at several points over time, and can be changed based on changes in the condition of the person (e.g. they report stronger urges to smoke). In this setup, they can learn effective treatments at the patient level.

In surveys, we only observe successful outcomes one time. We get the interview, we are done. We estimate response propensities by averaging over sets of cases. Within in any set, we assume that each person is exchangeable. Not by observing response to multiple survey requests on the same person.

Even panel surveys are only a little different. The follow-up interviews are often only with cases that responded at t=1. Even when there is follow-up with the entire sample, we usually leverage the fact that this is follow-up to a familiar survey.

I'd like to see experiments where multiple survey requests are made to the same units. It would be interesting to see if you could validate model results that way. Sadly, you might need a lot of survey requests per case (n=20+). But, hey, it's all in the name of science.

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