I’m posting to ask for references regarding causal inference with treatment effect modifiers in the context of a comparison of treated group vs untreated group.
The context is an analysis to estimate the effect of lipid lowering treatment on LDL-cholesterol (as % reduction from baseline) using routine health care data from diagnosis of familial hypercholesterolaemia (FH) to 2 years follow-up. We will focus on the patients who were not treated before the FH diagnosis. We will compare the patients who were treated after the FH diagnosis with those who were not treated.
Clearly, patients who were not treated are likely to be different from those who were treated in characteristics that affect the outcome (% reduction in LDL cholesterol from the FH diagnosis baseline) and the decision to treat.
The issue is that some of the confounders are only relevant for the treated group. Specifically, characteristics that affect adherence will affect the decision to treat and the LDL-cholesterol reduction, but will not affect the LDL-cholesterol reduction in the untreated group. These characteristics are effect modifiers (i.e. interaction effect) but not prognostic (i.e. main effect).
Hence my questions are:
- Should the characteristics that predict the treatment decision and the LDL-cholesterol reduction but only in the treated group be included?
- Is propensity score matching the appropriate technique for this situation?
I understand that this is quite a complex area, so I’m not expecting a fully thought out answer. I would be grateful if anyone could direct me towards good papers about this topic.
Thank you very much in advance!