That was also my first question. I looked at the original paper [1], the medication names they used to identify individuals on androgen deprivation therapy are listed in the 'eAppendix':

Leuprolide, goserelin, triptorelin, histrelin, Degarelix, flutamide, bicalutamide, nilutamide, Enzalutamide, Cyproterone acetate, Lupron, Zoladex, Trelstar, Vantas, Firmagon, Eulexin, Casodex, Nilandron, Xtandi, Nizoral, Androcur, Eligard, Cyprostat, Anandron, Flutamin, Cytomid, Cosudex, Calutide, Kalumid

So relax, finasteride does not seem to be on the list.

[1] http://jamanetwork.com/journals/jamaoncology/fullarticle/256... (probably paywalled)