Maybe saying "none" was a mistake on my part. However, you have to keep in mind that:
1. There is a huge difference between an observational study, such as the ones you cite, and an experimental study. In observational studies, what can be said is,
at best, that in those particular cases, a slight statistical difference was noted. That's it.
2. There have been other studies, following similar guidelines, and which have been much more extensive (for longer periods of time and with more patients examined) which have showed no statistically significant benefit.
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http://tinyurl.com/y4n3x9
If prayer worked, we would expect
all studies to show significance.