I have two groups of patients who underwent a surgery using method A or method B. The first group are patients who were operated in 1980's and 1990's only with method A. The second group are patients operated recently with mostly method B, but also in some cases A. In addition to that, I have various variables about patients (gender, age, medical indicators, etc.) that capture the pre-operation medical history and types of symptoms that patient developed.
The goal of the study is to compare the "effecitveness" of methods A and B in terms of patients' survival times after operation.
Somewhat different patients (in terms of age, gender, etc.) are operated with A and B. For example, quite some more older people were operated with B than with A. I want to used propensity score matching to balance the data.
My question is:
Does it make sense to estimate propensity scores (method ~ age + gender + ...) and use them for creating a matched dataset for further analysis (e.g. Cox regression)?
In particular, is it a problem that for patients in the first group method B was not yet available, so none of them could potentially received the alternative treatment?