Q:

Propensity Score Matching on demographic baseline

A client asks for a PSM on gender for their big dataset of >10000 cases.
About 20 variables are supposed to be included, most of them binomial.
They hypothesize, that a certain treatment has worse outcomes in women, because of unequally shared comorbidites. I already advocated them on using interaction terms instead, yet they demand PSM.
For these about 20 variables observations vary a lot with more often than not ~x*10^1 observations for single variables only. 
PSM not only seems to not work completely, but also loses about 90% of data and needs huge caliper widths.
Has anyone advice on this matter / can anyone criticize methodology etc.? Is it reasonable to match on gender, as it's independent and not a treatment decision? I am matching ATT, should I use another methodology (Inverse Probability Weighting or ATC)?
Any kind of comment, advise, opinion is appreciated even based on experience without references. 

A:

Although gender is theoretically not manipulable in this case, the analysis you're doing is consistent with that done in disparity research. Presumably, all the variables mediate the relationship between gender and the outcome; for example, maybe women are more likely to get certain kinds of cancer, and having cancer affects the outcome. Your client is interested in the direct effect of gender that does not pass through the gender-caused comorbidities.
By creating a matched sample, you eliminate the association between gender and those comorbidities so that in the matched sample, the simple difference in outcomes between the genders is the direct effect of gender on the outcome. With this in mind, there are a variety of strategies one can take.
PSM is a fine strategy, but others, including regression or weighting, work fine as well. I'm partial to entropy balancing, a form of weighting that yields exact balance on the covariates while preserving sample size. You can access it using the WeightIt package in R. 

