I have one concern about propensity score matching's assumption. It seems that what propensity score is doing is to say that the choice of treatment depends on pre-treatment covariates.
Suppose I am to model the effect of networking on grant proposal (binary outcome) for individual researcher, where networking ($networking$) is measured by a dichotomous variable - reputation of past coauthors ($Z$) - high (1) or low (0). There are covariates such as researchers' own reputation ($rep$) and gender ($gen$).
My question then is: given the underlying assumption that those covariate values are pre-treatment, $rep$ would be a variable that actually changes along with $Z$, which means it is NOT pre-treatment but measured at the same time as the treatment $Z$, can I still calculate the propensity score $P(Z=1|gen,rep)$?
I found this paper: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2005.00356.x but I feel like it is not the answer to my question.
Any pointers or explanations are greatly appreciated. Thank you!