This is a subject quite close to my heart as a medical student.
Depression apparently depresses the immune system.
This is not to question the value of any healing. But seeking objective evidence can be tricky. Ideally, one would need to match a list of patients on medical criteria, and from each matched pair, randomly assign only one to be prayed for. This should be done without the knowledge of the physician or patient. At the end of the study, compare the medical records for the two groups and see if the healing rate is any different.