Actually, there were some studies done concerning prayer and healing for the sick. It was must mentioned within the last month of so on FR. I don’t recall when or where, however.
The mere presence of the study, however, does not answer how one "controls" for God's will.
Whether because He has some unknown purpose, or "do not put the Lord your God to the test", or any other mechanism including placebo effects and/or chain yanking, remains to be seen.
Cheers!