Medical science is messy. Sometimes diseases just get better on their own, no matter what you do. Sometimes the act of treating people makes them feel (or report feeling) better, no matter what the treatment actually does.
These two case studies are anecdotal evidence. We will never be able to conclude from them alone that intercessory prayer helped. It may have been a coincidence. It may have been a mistake or a lie. It may have been some other confounding factor.
To address this, medical science uses randomised, double-blind placebo-controlled trials.
There have been many attempts at such trials of intercessory prayer, with varying results. Why would results vary? The results may have been a random coincidence (and larger samples are required). It may have been a mistake, poor design or a lie by biased researchers.
To address this, medical science uses systematic reviews. Experts in research and statistics do a careful search for all of the studies in the literature, and evaluate them on strict criteria to eliminate bias and understand how reliable a conclusion may be. One of the most prominent sources of high-quality systematic reviews in medicine is the Cochrane Library.
In 2009, Cochrane published a relevant systematic review: Intercessory prayer for the alleviation of ill health
This study included both proximal and non-proximal intercessory prayer:
We included any randomised trial comparing personal, focused, committed and organised intercessory prayer with those interceding holding some belief that they are praying to God or a god versus any other intervention. This prayer could be offered on behalf of anyone with health problems.
They found 10 relevant studies, with varying results.
They found that using the data as reported:
no significant difference in recovery from illness or death between those prayed for and those not prayed for.
- no significant differences to post‐operative or other complications, indeterminate and bad outcomes, or readmission to hospital.
Specific complications (cardiac arrest, major surgery before discharge, need for a monitoring catheter in the heart) were significantly more likely to occur among those in the group not receiving prayer.
- fewer post‐operative complications in those who had no knowledge of being prayed for, compared with those who knew.
However, they were leery of trusting these results, because of the low quality of the studies. They concluded:
it is only possible to state that intercessory prayer is neither significantly beneficial nor harmful for those who are sick. Further studies which are better designed and reported would be necessary to draw firmer conclusions.
They also recommend not following up with further studies, arguing that the resources used to further investigate could be better used in more promising areas.
In conclusion: based on the best research we have to date, intercessory prayer does not have any significant effect on the health of patients.