Your biggest opponent would be the ASA. Being largely about control of their profession, the ASA and many of its membership would not want to see the AA disparaged in any way. The bias would be impossible to factor out of such a study.
And what would it prove.......nada.
Both CRNAs and AAs are likely exceptional providers or the rest of the system would not tolerate their existance. I mean, think about it.....if some group routinely is involved in the untimely and unexpected demise of large batch of patients....someone isn't going to raise hell and shut that profession down like NOW!!