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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!

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You do need pre-treatment variables. Using post-treatment wrongs can lead to enormous problems - unless you have a perfect model for how treatment affects the variable, I which case you could back calculate the pre-treatment scores.

Let's assume getting a grant increases reputation a lot. After getting a grant all recipients have way higher reputation than those that did not. In such a case, the propensity score would put a lot of emphasis on reputation, but you have know idea whether it was already different pre-treatment or whether there was not such much of a difference pre-treatment.

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  • $\begingroup$ Thanks for your reply but I feel like your understanding of the problem is not what I meant to say. My emphasis is not on $Y$ (outcome) but more on $Z$ (treatment) and $rep$ (one of the control, candidate reputation). Specifically, my point is $rep$ is not measured after the grant decision but instead, measured at the same time as $Z$ (the treatment). In other words, the covariates are not pre-treatment but at-the-same-time-as-treatment. How could this affect PSM? Thanks! $\endgroup$ – Zhiya Dec 29 '18 at 5:12
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    $\begingroup$ The main worry is always that something could have been (If indirectly affected by treatment - e.g. "We gave him a grant, so we better rate him a bit better on reputation." would be a very short term way to do this. If there is no risk, at all, of this or any other influence of treatment on the reputation score, then using the reputation score for the propensity score is fine. $\endgroup$ – Björn Dec 29 '18 at 14:37

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