I am currently planning an analysis, in which I try to separate the change in the level of a binary outcome into a subgroup- and a covariate-related effect.
Let's say there are three kind of treatments: "Psychotherapy", "Psychopharmaka" and "Combined Treatment" which have different levels of success, with "Combined Treatment" being most successfull. Besides the average "success rate", the patients in these treatment groups also vary in their demographics (gender, age, etc.).
Over the last couple of years, the overall proportions of these treatment groups have shifted towards the psychopharmaka-based treatments. Also, the average rates of success have changed slightly. In the analysis I try to pull apart these effects and I am wondering which methodological approach allows to answer questions of the following kind:
- If we had the same kind of patients (demographics) and the same treatment-proportions as a year ago, what would the average rate of success look like?
- How much of the underlying change in the success rate is due to the treatment-shift and how much is due to the change in the patient-demographics?
- If we had the same demographics in the psychotherapy-subgroup than a year ago (controlling for demographics), what would the success rate in that subgroup be?
The subgroups in the data make me think of mixed-effects modeling (GLMM) and the need to control for demographics makes me think of "causal modeling", such as propensity-score-matching. Maybe these two techniques should be combined? The year-over-year effects could probably just be included as a (factor) variable.
PS: I have access to about 3 to 5 years of data, with a well above 10.000 observations per year.