One of the assumptions of the Rubin causal model is positivity which, for an individual $i$, a set of covariates $X$ and a treatment assignment indicator $Z_i$, is often expressed as $0 < P(Z_i | X) < 1$.
The situation I’m in is as follows:
As newer treatments are approved and adopted over time, older treatments may fall out of use. This may be for economic or administrative reasons, rather than through safety or efficacy concerns. So effectively the old treatments, while still approved, are no longer used, though in theory it might still be possible to prescribe them, hence in theory $0 < P(Z_i | X) < 1$. In practice though I can see in the data that there are no prescriptions after certain dates for some of the older treatments.
(In fact it is more complicated than that because these types of switchover to new treatments are different in different regions due to independent prescribing rules throughout the regions of the country whose data I’m looking at).
So although the study data may cover a number of years, there is in effect limited overlap in terms of time when all treatments are available and actually used, with earlier patients not having had access to the not yet available new treatments. But the later patients all being put on the newer treatments with the old treatments no longer prescribed.
I would have thought that this must be quite a common occurrence and that many published analyses who use causal methods (propensity scoring or inverse probability weighting etc) in observational studies must have faced this issue.
My questions then are:
- Can this type of situation be handled within the causal analysis framework or similar type of analysis? For example, try to use causal methods to achieve covariate balancing and continue from there – so it won’t be a true causal analysis as such but as “causal” as possible given the data.
- And if there is some literature on this subject, could someone give me some guidance to any references regarding this type of situation?
Any guidance/help appreciated.