There have been any number of studies. It's basically a dead end.
Abstract
Religious traditions across the world display beliefs in healing through prayer. The healing powers of prayer have been examined in triple-blind, randomized controlled trials. We illustrate randomized controlled trials on prayer and healing, with one study in each of different categories of outcome. We provide a critical analysis of the scientific and philosophical dimensions of such research. Prayer has been reported to improve outcomes in human as well as nonhuman species, to have no effect on outcomes, to worsen outcomes and to have retrospective healing effects. For a multitude of reasons, research on the healing effects of prayer is riddled with assumptions, challenges and contradictions that make the subject a scientific and religious minefield. We believe that the research has led nowhere, and that future research, if any, will forever be constrained by the scientific limitations that we outline.
Prayer and healing: A medical and scientific perspective on randomized controlled trials - PMC (nih.gov)''Prayers offered by strangers had no effect on the recovery of people who were undergoing heart surgery, a large and long-awaited study has found.
And patients who knew they were being prayed for had a higher rate of post-operative complications like abnormal heart rhythms, perhaps because of the expectations the prayers created, the researchers suggested.
Because it is the most scientifically rigorous investigation of whether prayer can heal illness, the study, begun almost a decade ago and involving more than 1,800 patients, has for years been the subject of speculation.
In another of the study's findings, a significantly higher number of the patients who knew that they were being prayed for -- 59 percent -- suffered complications, compared with 51 percent of those who were uncertain. The authors left open the possibility that this was a chance finding. But they said that being aware of the strangers' prayers also may have caused some of the patients a kind of performance anxiety.
Long-Awaited Medical Study Questions the Power of Prayer - The New York Times (nytimes.com)And keep the placebo effect in mind, as well as confirmation bias, where those who do recover are attributed to God answering their prayers, while all the failures are put down to 'it was meant to be' or 'Gods will be done...''
