I've come across a situation that I haven't had to deal with before and I've reached an impasse.

Problem

Patients in a health system are routinely monitored for a lab value important for diabetes management (A1c). When A1c reaches a particular level (higher than normal) a nurse reaches out to the patient to discuss medication and other proper treatment strategies. There is no natural control group, but we have A1c values for all patients over a number of months prior to the contact and after the contact. We would like to test the hypothesis that the intervention positively affects A1c (brings it down toward normal).

My thoughts

Initially, I thought that an interrupted time series would work since this intervention started at a particular calendar date, and we have information about the entire cohort. However, individuals were contacted over a 2-year period, so this will not work.

Then, I thought that longitudinal modeling, with some kind of linear spline function. However, I'm concerned about the fact that enrollment / inclusion in the study (intervention) is based on the outcome. There is also substantial autocorrelation in each patient's series.

While there is no natural control group, one could use individuals for whom contact was attempted, but did not engage. I'd imagine that some kind of propensity score would be needed in that case.

Any citations or suggestions are appreciated.