Using a large, cross-sectional survey of victims of violence, I am interested in testing the effect of alcohol intoxication (let's call it the 'treatment') on victims' subjective rating of the seriousness of the assault (outcome).
I have run regression analyses to explore factors associated with seriousness ratings and, as you might expect, the amount of injury done is the strongest predictor of rated seriousness (more on this later).
Victims who were drunk at the time of their assault had somewhat different characteristics from the other victims (e.g. more men, less educated...) and that that assaults on drunk victims resulted in more serious injury than assaults on sober victims, so I thought it might be a good idea to match victims with just the 'drunk at time of assault' as a distinguishing factor ('treatment') so that I can compare (drunk) apples with (sober) apples. I have run propensity score matching using 14 theoretically-relevant variables to identify a matched sample of sober and drunk victims.
My problem is that, because important confounding factors like injury happened after the 'treatment allocation' (drunk at time of assault - intervention group; sober at time of assault - control group), I couldn't logically include those in my matching model. So, when I compare the groups, the biasing effect of injury on the outcome still remains.
As far as I can see, I'm faced with three options but I'm probably missing something:
Include the statistically relevant, but logically problematic, 'post-treatment' factors in the matching (they are logically problematic because they happened after the 'treatment' was delivered but are likely to affect the outcome).
Control for the propensity score and the post-treatment factors in a regression of the outcome on victim intoxication using just the matched sample.
Stop messing around with treatment evaluation on a cross-sectional data set and just stick with regression.
Thanks in advance