Sample Selection in Experiment

[Patrick Button]

I am working on a proposed project where my me and my co-authors are measuring access to healthcare services, namely, who gets appointment offers from doctor's offices and how long is the wait for the appointment if an appointment is offered. We will be randomly assigning prospective patients who will differ on different characteristics (e.g., gender, race, reason for visit) to call physician offices and request the next available appointment. We will then log the offered appointment without actually booking it.

We are trying to determine what kind of selection model will allow us to analyze the joint decision of offering the prospective patient an appointment, and offering them a specific appointment time.

So here is the data we will have:

1. Indicator variables for assigned characteristics. To keep the example simple, consider us randomly assigning prospective patients who are non-minority or minority to doctor's offices, so MINORITY = 1 if the prospective patient is a minority.
2. Indicator variable for if an appointment was offered or not (APPT_OFFER)
3. Offered different appointment times when offered an appointment (captured by days from call to appointment). This is WAITDAYS, where WAITDAYS is set to be missing if no appointment is offered (APPT_OFFER = 0).

We are concerned that running separate regressions for each outcome in isolation is problematic, since they are jointly determined. So there would be issues with doing the following:

probit appt_offer minority
reg waitdays minority

So we believe that this requires a selection model or something similar, perhaps along the lines of a Heckman sample selection. We aren't exactly sure what model(s) would make sense here and if the literature has evolved since I read about this issue way back in grad school, so we were hoping to pick the brains of some better econometricians.

Thank you for any and all feedback. It is greatly appreciated.

(Stack Overflow cross-post: https://stackoverflow.com/questions/...xperiment-data)

[Clyde Schechter]

I'm not an econometrician, I'm an epidemiologist. So this advice may not fly in your discipline. But my instinct would be to approach the waiting time differently. I would use a non-parametric survival analysis (log-rank test), where I would represent not being offered an appointment as an infinite waiting time (which, operationally, I would code as a very large waiting time, beyond the range of actually observed waiting times among those who were offered an appointment).